lepto-philic 2-hdm + singlet scalar portal induced ...lepto-philic 2-hdm + singlet scalar portal...

Lepto-philic 2-HDM + singlet scalar portal inducedfermionic dark matter

Sukanta Duttaa dagger Ashok Goyalb Manvinder Pal Singhab $

aSGTB Khalsa College University of Delhi Delhi IndiabDepartment of Physics amp Astrophysics University of Delhi Delhi India

E-mail daggerSukantaDuttagmailcom agoyal45yahoocom $

Corresponding Author manvinderpal666yahoocom

Abstract We explore the possibility that the discrepancy in the observed anomalousmagnetic moment of the muon ∆amicro and the predicted relic abundance of Dark Matter byPlanck data can be explained in a lepto-philic 2-HDM augmented by a real SM singletscalar of mass sim 10-80 GeV We constrain the model from the observed Higgs Decay widthat LHC LEP searches for low mass exotic scalars and anomalous magnetic moment of anelectron ∆ae This constrained light singlet scalar serves as a portal for the fermionic DarkMatter which contributes to the required relic density of the universe A large region ofmodel parameter space is found to be consistent with the present observations from theDirect and Indirect DM detection experiments

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Contents

1 Introduction 1

2 The Model 3

3 Electro-Weak Constraints 531 Anomalous Magnetic Moment of Muon 532 LEP and ∆ae Constraints 833 Constraints from Higgs decay-width 934 Lepton non-Universality and Precision Constraints 12

4 Dark matter Phenomenology 1341 Computation of the Relic Density 1342 Direct Detection 1643 Indirect detection 19

5 Summary 27

A Model Parameters 29

B Decay widths of the singlet scalar S0 29

C Thermally averaged scattering cross-sections 30

D Triple scalar coupling 31

1 Introduction

Investigations into the nature of dark matter (DM) particles and their interactions is animportant field of research in Astro-particle physics The Atlas and CMS collaborations atthe Large Hadron Collider (LHC) are searching for the signature of DM particles involvingmissing energy (6ET ) [1 2] accompanied by a single or two jet events Direct detectionexperiments measure the nuclear-recoil energy and its spectrum in DM-Nucleon elasticscattering [3 4] In addition there are Indirect detection experiment [5] searching for theDM annihilation into photons and neutrinos in cosmic rays These experiments have nowreached a level of sensitivity where a significant part of parameter space required for theobserved relic density if contributed by the dark matter composed of Weakly interactingmassive particles (WIMPs) that survive as thermal relics has been excluded The nullresults of these direct and indirect experiments have given rise to the consideration of ideaswhere the dark matter is restricted to couple exclusively to either Standard Model (SM)

ndash 1 ndash

leptons (lepto-philic) or only to top quarks (top-philic) In these scenarios the DM-Nucleonscattering occurs only at the loop level and the constraints from direct detection are weaker

Extended Higgs sector have been studied in literature [6ndash8] to explain discrepancy inanomalous magnetic moment of muon Recently a simplified Dark Higgs portal model ofthe order of few GeV that couples predominantly to leptons with the coupling constantsim mlvo where ml is the lepton mass and vo is the Higgs VEV has been considered in theliterature [9] This model induces large contribution to the anomalous magnetic moment ofmuon and can explain the existing discrepancy between the experimental observation aexp

micro =

11 659 2091(54)(33)times10minus10 [10] and theoretical prediction aSMmicro = 116 591 823(1)(34)(26)

times10minus11 [10 11] of the muon anomalous magnetic moment ∆amicro equiv aexpmicrominus minus a

SMmicrominus = 268(63) times

10minus11 [10] without compromising the experimental measurement of electron anomalousmagnetic moment aexp

e = (115965218091 plusmn 000000026) times 10minus6 [12] It has been shownin the literature [13] that with the inclusion of an additional singlet scalar below theelectro-weak scale to the lepto-philic 2-HDM makes the model UV complete This UVcomplete model with an extra singlet scalar sim lt 10 GeV successfully explains the existing3 σ discrepancy of muon anomalous magnetic moment and is consistent with the constraintson the model parameters from muon and meson decays [14ndash17] These results have beenanalysed for 001 GeV lt mS0 lt 10 GeV when compared with those for the singlet neutralvector Z prime searches at B factories such as BaBar [18] from electron beam dump experiments[19] and electroweak precision experiments [20] etc

In reference [21] the authors have explored the possibility of explaining the anomalousmagnetic moment of muon with an additional lepto-philic light scalar mediator assumingthe universal coupling of the scalar with all leptons constrained from the LEP [22] resonantproduction and the BaBar experiments [18] These constraints were found to exclude all ofthe scalar mediator mass range except between 10 MeV and 300 MeV

In the current paper we consider fermionic dark matter that couples predominately withSM leptons through the non-universal couplings with the scalar portal in the UV completelepto-philic 2-HDM model We relax the requirement of the very light scalar considered in[13] and investigate parameter space for a comparatively heavier scalar 10 GeV mS0 80GeV In section 2 we give a brief review of this simplified model using the full Lagrangianand couplings of the Singlet scalar S0 with all model particles In section 3 we calculatethe contribution from scalars (S0 H0 A0 Hplusmn) to the anomalous magnetic moment of themuon and discuss bounds on the model parameters from LEP-II ∆ae and upper boundon the observed total Higgs decay width Implications of the model contributions to thelepton couplings non-universality and the oblique corrections are briefly discussed along-with available constraints on them

In the present study we are motivated to explore the possibility of simultaneouslyexplaining the discrepancy in the observed anomalous magnetic moment of the muon on theone hand and the expected relic density contribution from DM on the other Accordinglyin section 4 we introduce the DM contributing to the relic density through dark matter -SM particles interactions induced by the additional scalar in the model and scan for theallowed parameter space which is consistent with direct and indirect experimental data aswell as with the observed value of the ∆amicro Section 5 is devoted to discussion and summary

ndash 2 ndash

of results

2 The Model

We consider a UV complete lepton specific 2-HDM with a singlet scalar portal interactingwith the fermionic DM In this model the two Higgs doublets Φ1 and Φ2 are so arrangedthat Φ1 couples exclusively to leptons while Φ2 couples exclusively to quarks The ratioof their VEVrsquos 〈Φ1〉〈Φ2〉 equiv v2 v1 = tanβ is assumed to be large In this model thescalars (other than that identified with the CP even h0 sim 125 GeV) couple to leptons andquarks with coupling enhanced and suppressed by tanβ respectively A mixing term in thepotential A12

[Φdagger1Φ2 + Φdagger2Φ1

]ϕ0 results in the physical scalar S0 coupling to leptons with

strength proportional to mlvo where

vo equivradicv2

1 + v22 = 246 GeV (21)

The full scalar potential is given by

V (Φ1Φ2 ϕ0) = V2minusHDM + Vϕ0 + Vportal (22)

where CP conserving V2minusHDM is given as

V2minusHDM (Φ1Φ2) = m211 Φdagger1Φ1 +m2

22 Φdagger2Φ2 minus(m2

12 Φdagger1Φ2 + hc)

+λ1

2

(Φdagger1Φ1

)2+λ2

2

(Φdagger2Φ2

)2

+λ3

(Φdagger1Φ1

)(Φdagger2Φ2

)+ λ4

(Φdagger1Φ2

)(Φdagger2Φ1

)+

λ5

2

(Φdagger1Φ2

)2+ hc

(23)

and Vϕ0 and Vportal is assumed to be

Vϕ0 = Bϕ0 +1

2m2

0(ϕ0)2 +Aϕ0

2(ϕ0)3 +

λϕ0

4(ϕ0)4 (24)

Vportal = A11

(Φdagger1Φ1

)ϕ0 +A12

(Φdagger1Φ2 + Φdagger2Φ1

)ϕ0 +A22

(Φdagger2Φ2

)ϕ0 (25)

where the scalar doublets

Φ1 =1radic2

( radic2ω+

1

ρ1 + vo cosβ + i z1

) Φ2 =

1radic2

( radic2ω+

2

ρ2 + vo sinβ + i z2

) (26)

are written in terms of the mass eigenstates G0 A0 Gplusmn and H∓ as(z1

z2

)=

(cosβ minus sinβ

sinβ cosβ

)(G0

A0

)

(ω1

ω2

)=

(cosβ minus sinβ

sinβ cosβ

)(Gplusmn

Hplusmn

)

(27)

Here G0 amp Gplusmn are Nambu-Goldstone Bosons absorbed by the Z0 and Wplusmn vector BosonsA0 is the pseudo-scalar and Hplusmn are the charged Higgs The three CP even neutral scalarmass eigen-states mix among themselves under small mixing angle approximations

sin δ13 sim δ13 minusv0A12

m2H0

and sin δ23 sim δ23 minusv0A12

m2h0

[1 + ξh

0

`

(1minus

m2h0

m2H0

)]cotβ (28)

ndash 3 ndash

ξφψξφV S0 h0 H0 A0 Hplusmn

` δ13cβ minussαcβ cαcβ minussβcβ minussβcβuq δ23sβ cαsβ sαsβ cβsβ cβsβdq δ23sβ cαsβ sαsβ minuscβsβ cβsβ

Z0Wplusmn δ13cβ + δ23sβ s(βminusα) c(βminusα) - -

Table 1 Values of ξφψ and ξφV for φ = S0 h0 H0 A0 and Hplusmn ψ = ` uq and dq V= Wplusmn and Z0

in the lepto-philic 2-HDM+S0 model These values coincide with couplings given in reference [13]in the alignment limit ie (β minus α) π2 In the table s and c stands for sin and cos respectively

to give three CP even neutral weak eigen-states as ρ1

ρ2

ϕ0

minus sinα cosα δ13

cosα sinα δ23

δ13 sinαminus δ23 cosα minusδ13 cosαminus δ23 sinα 1

h0

H0

S0

(29)

The mixing matrix given in equation (29) validates the orthogonality condition up to anorder O

(δ2

13 δ223 δ13δ23

) ξh0l is chosen to be sim 1 in the alignment ie (β minus α) π2

The spectrum of the model at the electro-weak scale is dominated by V2minusHDM TheVϕ0 and Vportal interactions are treated as perturbations After diagonalization of the scalarmass matrix the masses of the physical neutral scalars are given by

m2S0 m2

0 + 2δ13M213 + 2δ23M

223 (210)

m2h0 H0

1

2

[M2

11 +M222 ∓

radic(M2

11 minusM222

)2+ 4M4

12

](211)

where

M211 = m2

12 tanβ + λ1v20 cos2 β M2

12 = minusm212 + (λ3 + λ4 + λ5) v2

0 cosβ sinβ

M222 = m2

22 cotβ + λ2v20 sin2 β M2

13 = v0A12 sinβ M223 = v0A12 cosβ (212)

In the alignment limit one of the neutral CP even scalar h0 asymp 125 GeV is identified withthe SM Higgs

The coefficients m20 m2

11 m222 and λi for i = 1 middot middot middot 5 are explicitly defined in terms

of the physical scalar masses mixing angles α and β and the free parameter m212 and are

given in the Appendix A Terms associated with A11 are proportional to cotβ and thereforecan be neglected as they are highly suppressed in the large tanβ limit Terms proportionalto A22 are tightly constrained from the existing data at LHC on decay of a heavy exoticscalar to di-higgs channel and therefore they are dropped The coefficient B is fixed byredefinition of the field ϕ0 to avoid a non-zero VEV for itself

The Yukawa couplings arising due to Higgs Doublets Φ1 and Φ2 in type-X 2-HDM isgiven by

minus LY = LYeΦ1eR + QYdΦ2dR + QYuΦ2uR + hc (213)

me = cosβ times Yevoradic2 mu(d) = sinβ times

Yu(d)voradic2

(214)

ndash 4 ndash

We re-write the Yukawa interactions of the physical neutral states as

minusLY supsum

φequivS0h0H0

sumψ=` q

ξφψmψ

voφ ψψ (215)

The couplings ξφψ are given in the first three rows of table 1 It is important to mention herethat the Yukawa couplings are proportional to the fermion mass ie non-universal unlikethe consideration in reference [21]

The interaction of the neutral scalar mass eigenstates with the weak gauge Bosons aregiven by

L supsum

φequivS0h0H0

φ

vo

(2 ξφ

Wplusmn m2WplusmnW

+micro W

minusmicro + ξφZ0 m2

Z0 Z0microZ

0micro) (216)

The couplings ξφV are given in the last row of table 1 It is to be noted that formH0 gtgt mh0 the singlet scalar coupling with Z0 Boson can be fairly approximated as δ23 sinβ

The recent precision measurements at LHC constrains |κV | = 106+010minus010 [23 24] (where

κV is the scale factor for the SM Higgs Boson coupling) to the vector Bosons restrictsthe generic 2HDM Models and its extension like the one in discussion to comply with thealignment limit In this model the Higgs Vector Boson coupling to gauge Bosons is identicalto that of generic 2HDM model at tree level as the additional singlet scalar contributes toh0V V couplings only at the one loop level which is suppressed by δ2

23(16π2

)

The triple scalar couplings of the mass eigen states are given in the Appendix D someof which can be constrained from the observed Higgs decay width and exotic scalar Bosonsearches at LEP TeVatron and LHC

3 Electro-Weak Constraints

31 Anomalous Magnetic Moment of Muon

We begin our analysis by evaluating the parameter space allowed from 3 σ discrepancy aexpmicrominus minus

aSMmicrominus equiv ∆amicro = 268(63) times 10minus11 [10] In lepto-philic 2-HDM + singlet scalar portal model

all five additional scalars S0 H0 A0 Hplusmn couple to leptons with the coupling strengthsgiven in table 1 and thus give contributions to ∆amicro at the one-loop level and are expressedas

∆amicro = ∆amicro|S0 + ∆amicro|H0 + ∆amicro|A0 + ∆amicro|Hplusmn

=1

8π2

m2micro

v2o

tan2 β[δ2

13 IS0 + IH0 + IA0 + IHplusmn] (31)

Here Ii are the integrals given as

IS0 H0 =

int 1

0dz

(1 + z) (1minus z)2

(1minus z)2 + z rminus2S0 H0

IA0 = minusint 1

0dz

z3

rminus2A0 (1minus z) + z2

and

IHplusmn =

int 1

0dz

z(1minus z)(1minus z)minus rminus2

Hplusmn

with ri equivml

mifor i equiv S0 H0 A0 Hplusmn (32)

ndash 5 ndash

5x10-3

8x10-3

1x10-2

2x10-2

5x10-2

8x10-2

1x10-1

2x10-1

1 15 2 25 3 35 4 45 5

δ 23

δ13

mS0 = 10 GeV

mS0 = 20 GeV

mS0 = 30 GeV

mS0 = 40 GeV

mS0 = 50 GeV

mS0 = 60 GeV

mH0 = 400 GeV mA

0 = 200 GeV

(a)

5x10-3

8x10-3

1x10-2

2x10-2

5x10-2

8x10-2

1x10-1

2x10-1

1 15 2 25 3 35 4 45 5

δ 23

δ13

mS0 = 10 GeV

mS0 = 20 GeV

mS0 = 30 GeV

mS0 = 40 GeV

mS0 = 50 GeV

mS0 = 60 GeV

mH0 = 400 GeV mA

0 = 400 GeV

(b)

5x10-3

8x10-3

1x10-2

2x10-2

5x10-2

8x10-2

1x10-1

2x10-1

1 15 2 25 3 35 4 45 5

δ 23

δ13

mS0 = 10 GeV

mS0 = 20 GeV

mS0 = 30 GeV

mS0 = 40 GeV

mS0 = 50 GeV

mS0 = 60 GeV

mH0 = 400 GeV mA

0 = 600 GeV

(c)

1x10-2

2x10-2

5x10-2

1x10-1

2x10-1

5e-1

1 15 2 25 3 35 4 45 5

δ 23

δ13

mS0 = 10 GeV

mS0 = 20 GeV

mS0 = 30 GeV

mS0 = 40 GeV

mS0 = 50 GeV

mS0 = 60 GeV

mH0 = 600 GeV mA

0 = 400 GeV

(d)

Figure 1 Figures 1a 1b 1c and 1d show contours on the δ13 - δ23 plane satisfying ∆amicro =

268(63) times10minus11 corresponding to four different combinations of mH0 and mA0 respectively In eachpanel six contours are depicted corresponding to six choices of singlet masses 10 20 30 40 50 and60 GeV respectively

We observe that in the limit ri ltlt 1 the charged scalar integral IHplusmn is suppressed by2-3 orders of magnitude in comparison to the other integrals for the masses of the scalarsvarying between 150 GeV sim 16 TeV Since the present lower bound on the charged Higgsmass from its searches at LHC is 600 GeV [25] we can neglect its contribution to the ∆amicroin our calculations

It is also important to note that the one loop contribution from the pseudo-scalarintegral IA0 is opposite in sign to that of the other neutral scalars IH0 h0 S0 while atthe level of two loops the Barr-Zee diagrams [26] it gives positive contribution to ∆amicrowhich may be sizable for low pseudo-scalar mass mA0 because of large value of the couplingξA

0

l However for heavy A0 and H0 considered here we can safely neglect the two loopcontributions

In the alignment limit the mixing angle δ23 δ13m2

H0

m2h0

[2minus

m2h0

m2H0

]cotβ is fixed by con-

strains from ∆amicro and choice of δ13 and neutral CP-even scalar masses To understand themodel we study the correlation of the two mixing parameters δ13 and δ23 satisfying the

ndash 6 ndash

∆amicro for a given set of input masses of the physical scalars and show four correlation plotsin figures 1a 1b 1c and 1d for varying δ13 We find that δ23 remains small enough for allthe parameter space in order to fulfill the small angle approximation We have chosen sixsinglet scalar masses 10 20 30 40 50 and 60 GeV In each panel mH0 and mA0 are keptfixed at values namely (a) mH0 = 400 GeV mA0 = 200 GeV (b) mH0 = 400 GeV mA0

= 400 GeV (c) mH0 = 400 GeV mA0 = 600 GeV and (d) mH0 = 600 GeV mA0 = 400GeV We find that relatively larger values of δ13 are required with the increase in scalarmass mS0 Increase in the pseudo-scalar mass mA0 for fixed mH0 results in the lower valueof δ13 required to obtain the observed ∆amicro

On imposing the perturbativity constraints on the Yukawa coupling ξH0

τ equiv tanβ mτv0

involving the τplusmn and H0 we compute the upper bound on the model parameter tanβ 485 As a consequence we observe that the values of δ23 also gets restricted for eachvariation curve exhibited in figures 1a 1b 1c and 1d

3x101

5x101

7x101

1x102

2x102

3x102

4x102

5x102

6x102

5 10 20 30 40 50 60 70 80

tan

β

mS0 in GeV

δ13 = 01

δ13 = 02

δ13 = 03

δ13 = 04

δ13 = 05

Forbidden Region H0τ+τ-

coupling

mH0 = 400 GeV mA

0 = 200 GeV mHplusmn = 600 GeV

(a)

3x101

5x101

7x101

1x102

2x102

3x102

4x102

5x102

6x102

5 10 20 30 40 50 60 70 80

tan

β

mS0 in GeV

δ13 = 01

δ13 = 02

δ13 = 03

δ13 = 04

δ13 = 05


coupling

mH0 = mA


(b)

3x101

5x101

7x101

1x102

2x102

3x102

4x102

5x102

6x102

5 10 20 30 40 50 60 70 80

tan

β

mS0 in GeV

δ13 = 01

δ13 = 02

δ13 = 03

δ13 = 04

δ13 = 05


coupling

mH0 = 400 GeV mA


(c)

3x101

5x101

7x101

1x102

2x102

3x102

4x102

5x102

6x102

5 10 20 30 40 50 60 70 80

tan

β

mS0 in GeV

δ13 = 01

δ13 = 02

δ13 = 03

δ13 = 04

δ13 = 05


coupling

mH0 = 600 GeV mA


(d)

Figure 2 Figures 2a 2b 2c and 2d show contours on mS0 - tanβ plane satisfying ∆amicro =

268(63) times 10minus11 for fixed mHplusmn = 600 GeV and four different combinations of mH0 and mA0 asshown In each panel five contours along-with shaded one σ bands of ∆amicro are depicted correspondingto five choices of δ13 01 02 03 04 and 05 respectively The top horizontal band (shaded in red)in each panel shows the forbidden region on tanβ due to the perturbativity constraint on the upperlimit of H0τ+τminus coupling

ndash 7 ndash

The contours satisfying ∆amicro = 268(63) times 10minus11 on mS0 - tanβ plane for fixed chargedHiggs mass mHplusmn = 600 GeV are shown for four different combinations of heavy neutralHiggs mass and pseudo-scalar Higgs mass namely (a) mH0 = 400 GeV mA0 = 200 GeV(b) mH0 = 400 GeV mA0 = 400 GeV (c) mH0 = 400 GeV mA0 = 600 GeV and (d) mH0

= 600 GeV mA0 = 400 GeV respectively in figures 2a 2b 2c and 2d In each panel the fiveshaded regions correspond to five choices of mixing angle δ13 = 01 02 03 04 and 05respectively depict the 3 σ allowed regions for the discrepancy in ∆amicro around its centralvalue shown by the black lines The horizontal band appearing at the top in all these panelsshows the forbidden region on account of the perturbativity constraint on the upper limitof H0τ+τminus coupling as discussed above

As expected the allowed value of tanβ increases with the increasing singlet scalar massmS0 and decreasing mixing angle δ13 We find that a very narrow region of the singletscalar mass is allowed by ∆amicro corresponding to δ13 le 01

32 LEP and ∆ae Constraints

Searches for the light neutral Bosons were explored in the Higgs associated vector Bo-son production channels at LEP [27] We consider the s-channel bremsstrahlung processe+eminus rarr Z0γ0 + h0 rarr τ+τminusτ+τminus whose production cross-section can be expressed interms of the SM h0Z0 production cross-section and given as

σe+eminusrarrS0Z0rarrτ+τminusZ0 = σSMe+eminusrarrh0Z0 times

∣∣∣∣∣ξS0

Z0

ξh0

Z0

∣∣∣∣∣2

times BR(S0 rarr τ+τminus

)equiv σSM

e+eminusrarrh0Z0 times∣∣∣∣δ13cβ + δ23sβ

sin (β minus α)

∣∣∣∣2 times BR(S0 rarr τ+τminus

) (33)

Since the BR(S0 rarr τ+τminus

) 1 we can compute the exclusion limit on the upper bound

on∣∣∣ξS0

Z0

∣∣∣ equiv |δ13cβ + δ23sβ| from the LEP experimental data [27] which are shown in table2 for some chosen values of singlet scalar masses in the alignment limit

A light neutral Vector mediator Z prime0 has also been extensively searched at LEP [22]Vector mediator Z prime0 of mass le 209 GeV is ruled out for coupling to muons amp 001 [21]Assuming the same production cross-section corresponding to a light scalar mediator theconstraint on vector coupling can be translated to scalar coupling by multiplying a factorofradic

2 For the case of non-universal couplings where the scalar couples to the leptons withthe strength proportional to its mass as is the case in our model a further factor of

radicmmicrome

is multiplied We therefore find the upper limit on the Yukawa coupling for leptons to beξS

0

lmlv0

02From the constrained parameter space of the model explaining the muon ∆amicro we

find that the total contribution to anomalous magnetic moment of the electron comes outsim 10minus15 This is two order smaller in the magnitude than the error in the measurement ofae plusmn26 times 10minus13 [12] The present model is thus capable of accounting for the observedexperimental discrepancy in the ∆amicro without transgressing the allowed ∆ae

ndash 8 ndash

mS0(GeV) 12 15 20 25 30 35 40 45 50 55 60 65∣∣∣ξS0

Z0

∣∣∣ 285 316 398 530 751 1132 1028 457 260 199 169 093

Table 2 Upper limits on∣∣∣ξS0

Z0

∣∣∣ from bremsstrahlung process e+eminus rarr S0Z0 rarr τ+τminusτ+τminus LEPdata [27]

574

5 10 20 24 30 40

10-6

10-5

10-4

10-3

10-2

10-1

100

101485

100 G

eV

2

50 G

eV

2

30 G

eV

2

20 G

eV

2

10 G

eV

2

H0rarr

τ+τ- F

orb

idd

en

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

Forbidden

(a) mH0 = 400 GeV mA0 = 200 GeV

574

5 10 20 24 30 40

10-6

10-5

10-4

10-3

10-2

10-1

100

101485

100 G

eV

2

50 G

eV

2

30 G

eV

2

20 G

eV

2

10 GeV2

H0rarr

τ+τ- F

orb

idd

en

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

Forbidden

(b) mH0 = 400 GeV mA0 = 400 GeV

574

5 10 20 24 30 40

10-6

10-5

10-4

10-3

10-2

10-1

100

101485

100 G

eV

2

50 G

eV

2

30 G

eV

2

20 G

eV

2

10 GeV2

H0rarr

τ+τ- F

orb

idd

en

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

Forbidden

(c) mH0 = 400 GeV mA0 = 600 GeV

574

5 10 20 24 30 40

10-6

10-5

10-4

10-3

10-2

10-1

100

101485

100 G

eV

2

50 G

eV

2

30 G

eV

2

20 G

eV

2

10 GeV2

H0rarr

τ+τ- F

orb

idd

en

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

Forbidden

(d) mH0 = 600 GeV mA0 = 400 GeV

Figure 3 Figures 3a 3b 3c and 3d show Γh0rarrS0S0 variation with the mS0 for mHplusmn = 600 GeVδ13 = 02 and four different combinations of mH0 and mA0 respectively In each panel we shadefive regions corresponding to m2

12 = 10 20 30 50 100 GeV2 respectively All points on the solidcurves satisfy the discrepancy ∆amicro = 268(63) times 10minus11 and their corresponding values of tanβ areshown in the upper x-axis of all the panels We plot the contour corresponding to m2

12 = 0 GeV2

in black The top horizontal band is forbidden from the measurement of the total Higgs decay widthat LHC The red shaded region at the right in each panel is forbidden due to non-perturbativity ofH0τ+τminus coupling

33 Constraints from Higgs decay-width

Recently CMS analysed the partial decay widths of the off-shell Higgs Boson producedthrough gluon fusion decaying to W+Wminus Bosons [28] and then combined the analysis withthat for Z Z [29] vector Bosons to obtain 95 CL upper limit on the total observed

ndash 9 ndash

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2

30 GeV2

20 GeV2

10 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 400 GeV

mA0 = 200 GeV

(a)

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2

30 GeV2

20 GeV2

10 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 400 GeV

mA0 = 400 GeV

(b)

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2 30 GeV

2

20 GeV2

10 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 400 GeV

mA0 = 600 GeV

(c)

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2

30 GeV2

20 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 600 GeV

mA0 = 400 GeV

(d)



12 = 0 GeV2 inblack The top horizontal band is forbidden from the measurement of the total Higgs decay width atLHC

Higgs decay width of 24 times Γh0

SM [24 28] where Γh0

SM 41 MeV The authors have alsoinvestigated these decay channels for an off-shell Higgs Boson produced from the vectorBoson fusion channels and obtained the upper bound on the total observed Higgs decaywidth of 193 times Γh

0

SM [24 28] ATLAS also analysed the Higgs decay width assuming thatthere are no anomalous couplings of the Higgs boson to vector Bosons and obtained 95CL observed upper limit on the total width of 67times Γh

0

SM [30] However we have used theconservative upper limit on the total observed decay width of Higgs Boson of 24timesΓh

0

SM forrest of the analysis in our study

However in the present model the scalar identified with SM Higgs Boson h0 is inaddition likely to decay into two light singlet scalar portals h0 rarr S0 S0 for mS0 le mh0

2

ndash 10 ndash

5 10 20 30 40 50 60200

300

400

500

600

700

800

900

1000m

H0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 20 GeV

2

(a)

5 10 20 30 40 50 60200

300

400

500

600

700

800

900

1000

1100

mH

0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 30 GeV

2

(b)

5 10 20 30 40 50 60200

300

400

500

600

700

800

900

1000

1100

1200

mH

0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 50 GeV

2

(c)

5 10 20 30 40 50 60100

200

300

400

500

600

700

800

900

1000

mH

0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 100 GeV

2

(d)

Figure 5 Figures 5a 5b 5c and 5d show contours on the mS0 - mH0 plane satisfying the 95 CL upper limit on the total observed Higgs decay width Γh

0

obs le 24 times Γh0

SM for fixed mHplusmn =600 GeV δ13 = 04 and four different choices of m2

12 = 20 30 50 and 100 GeV2 All pointson the contours satisfy the discrepancy ∆amicro = 268(63) times 10minus11 Each panel has three contourscorresponding to mA0 = 200 400 and 600 GeV respectively

The partial decay width Γh0rarrS0S0 is given as

Γh0rarrS0S0 =C2h0S0S0

32πmh0

radic1minus

4m2S0

m2h0

(34)

The tri-scalar coupling Ch0S0S0 is given in equation D1As total Higgs decay width is known with a fair accuracy any contribution coming

from other than SM particles should fit into the combined theoretical and experimentaluncertainty Thus using the LHC data on the total observed Higgs decay-width we canput an upper limit on the tri-scalar coupling Ch0S0S0 This upper limit is then used toconstrain the parameter space of the model

Even restricting the parameter sets to satisfy the anomalous magnetic moment andLEP observations the model parameter m2

12 remains unconstrained However for a givenchoice of δ13 mH0 mA0 and mS0 an upper limit on |Ch0S0S0 | constrains m2

12 and thus fixesthe model for further validation at colliders

ndash 11 ndash

We study the partial decay-width Γh0rarrS0S0 wrt mS0 for five chosen values of thefree parameter m2

12 = 10 20 30 50 and 100 GeV2 We depict the variation of the partialdecay width Γh0rarrS0S0 corresponding to four different combinations of (mH0 mA0) in GeV(400 200) (400 400) (400 600) and (600 400) in figures 3a 3b 3c 3d respectively for δ13

= 02 and in figures 4a 4b 4c 4d respectively for δ13 = 04 The top horizontal bandin all the four panels in figures 3 and 4 corresponds to the forbidden region arising fromthe observed total Higgs decay width at LHC In figure 3 the parameter region for mS0

ge 24 GeV is forbidden by non-perturbativity of H0τ+τminus couplings We observe that theconstraints from the total Higgs decay width further shrinks the parameter space allowed by∆amicro between 10 GeV le mS0 le 62 GeV for δ13 = 04 corresponding to 100 GeV2 ge m2

12 ge10 GeV2

To have better insight of the bearings on the model from the observed total Higgs decaywidth we plot the contours on the mS0minusmH0 plane for mixing angle δ13 = 04 in figures 5a5b 5c and 5d satisfying the upper bound of the total observed Higgs decay width obtainedby CMS [28] We have considered four choices of m2

12 respectively In each panel threecurves depict the upper limits on the partial widths which are derived from the constraintson the total observed decay width from LHC corresponding to three chosen values mA0 =200 400 and 600 GeV respectively We note that with increasing m2

12 the allowed darkshaded region shrinks and remains confined towards a lighter mS0

34 Lepton non-Universality and Precision Constraints

Recently HFAG collaboration [31] provided stringent constraints on the departure of SMpredicted universal lepton-gauge couplings Non universality of the lepton-gauge couplingscan be parameterized as deviation from the ratio of the lepton-gauge couplings of any twodifferent generations from unity and is defined as δllprime equiv (glglprime)minus 1 For example the saiddeviation for τplusmn and microplusmn can be extracted from the measured respective pure leptonic decaymodes and is defined as

δτmicro equiv(gτminusgmicrominus

)minus 1 =

radicΓ (τminus rarr eminus νe ντ )radicΓ (microminus rarr eminus νe νmicro)

minus 1 (35)

The measured deviations of the three different ratios are found to be [31]

δlτmicro = 00011plusmn 00015 δlτe = 00029plusmn 00015 and δlmicroe = 00018plusmn 00014 (36)

out of which only two ratios are independent [8]The implication of these data on lepto-philic type X 2-HDM models have been studied

in great detail in reference [8] and are shown as contours in mHplusmn minus tanβ and mA0 minus tanβ

planes based on χ2 analysis of non-SM additional tree δtree and loop δloop contributions tothe lepton decay process in the leptonic mode [32] We find that the additional scalar inlepto-philic 2-HDM + singlet scalar model contribute to δτmicro δτe and δmicroe at the one looplevel which is δ2

13 suppressed However they make a negligibly small correction and renderthe δloop more negative

Further we constraint the model from the experimental bound on the S T and U [33]oblique parameters Constrains from these parameters for all variants of 2-HDM models

ndash 12 ndash

have been extensively studied in the literature [34] We compute the additional contributiondue to the singlet scalar at one loop for ∆S and ∆T in 2-HDM + singlet scalar model andfind that they are suppressed by the square of the mixing angle δ2

13 and are thereforeconsistent with the experimental observations as long as mHplusmn is degenerate either withmA0 or mH0 for large tanβ region to a range within sim 50 GeV [13]

4 Dark matter Phenomenology

We introduce a spin 12 fermionic dark matter particle χ which is taken to be a SM singletwith zero-hyper-charge and is odd under a discrete Z2 symmetry The DM χ interacts withthe SM particle through the scalar portal S0 The interaction Lagrangian LDM is given as

LDM = iχγmicropartmicroχminusmχχχ+ gχS0χχS0 (41)

We are now equipped to compute the relic density of the DM the scattering cross-sectionof such DM with the nucleon and its indirect detection annihilation cross-section

41 Computation of the Relic Density

In early universe when the temperature of the thermal bath was much greater than thecorresponding mass of the particle species the particles were in thermal equilibrium withthe background This equilibrium was maintained through interactions such as annihilationand scattering with other SM particles such that the interaction rate remained greater thanthe expansion rate of the universe As the Universe cooled massive particles such as our DMcandidate χ became non-relativistic and the interaction rate with other particles becamelower than the expansion rate of the universe hence decoupling the DM and giving us therelic abundance 0119 [35 36] we observe today Evolution of the number density of theDM nχ is governed by the Boltzmann equation

dnχdt

+ 3a

anχ = minus〈σ |~v|〉

(n2χ minus n2

χeq

)(42)

where aa =

radic8πρ

3MPl 〈σ |~v|〉 is thermally averaged cross-section and

n2χeq = g

(mχT2π

) 32

exp[minusmχT

]where g is the degrees of freedom and it is 2 for fermions

As for a massive thermal relics freeze-out occurs when the species is non-relativistic |~v| ltltc Therefore we expand 〈σ |~v|〉 as 〈σ |~v|〉 = a + b |~v|2 + O(|~v|4) The Boltzmann equationcan be solved to give the thermal relic density [37]

Ωχh2 107times 109xF

MPl

radicglowast(xF )(a+ 6b

xF)

(43)

where h is dimensionless Hubble parameter glowast(xF ) is total number of dynamic degrees offreedom near freeze-out temperature TF and xF =

mχTF

is given by

xF = ln

c (c+ 2)

radic45

8

gMPl mχ

(a+ 6 b

xF

)2π3radic

glowast (xF )radicxF

(44)

ndash 13 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 50 GeV

2

(f)

Figure 6 Figures 6a to 6f show contours on the mχ - gχS0 plane satisfying the relic density 0119[35 36] for fixed mHplusmn = 600 GeV δ13 = 02 and different choices of m2

12 and mA0 All points onthe contours satisfy the discrepancy ∆amicro = 268(63) times 10minus11 In the left and right panels we showallowed (shaded) regions for four and five combinations of mS0 mH0 respectively

where c is of the order 1 The thermal-averaged scattering cross-sections as a function ofDM mass mχ are given in the Appendix C

To compute relic density numerically we have used MadDM [38] and MadGraph [39]We have generated the input model file required by MadGraph using FeynRules [40] whichcalculates all the required couplings and Feynman rules by using the full Lagrangian

For a given charged Higgs mass of 600 GeV we depict the contours of constant relic

ndash 14 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

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2e-3

5e-3

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2e-2

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1e-1

2e-1

5e-1

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gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 50 GeV

2

(f)



density 0119 [35 36] in gχS0 (DM coupling) and mχ (DM mass) plane in figure 6corresponding to two choices of singlet scalar masses of 10 and 20 GeV for δ13 = 02 and infigure 7 corresponding to three choices of singlet scalar masses of 10 30 and 50 GeV for δ13

= 04 The six different panels in figures 6 and 7 correspond to the following six different

ndash 15 ndash

combinations of(mA0 m2

12

)(

200 GeV 30 GeV2)(200 GeV 50 GeV2

)(400 GeV 30 GeV2

)(

400 GeV 50 GeV2)(600 GeV 30 GeV2

)and

(600 GeV 50 GeV2

)

The un-shaded regions in gχS0 minusmχ plane in figures corresponding to over closing of theUniverse by DM relic density contribution The successive dips in the relic density contoursarise due to opening up of additional DM annihilation channel with the increasing DM massInitial dip is caused by s-channel propagator Dip observed around 02 TeV and 04 TeVare caused by opening of χχ rarr S0H0 and χχ rarr H0H0 (A0A0) channels The parametersets chosen for the calculation of the relic density are consistent with the observed value of∆amicro and measured total Higgs decay width

42 Direct Detection

Direct detection of DM measures the recoil generated by DM interaction with matter Forthe case of lepto-philic DM we have tree level DM-Electron interaction where DM canscatter with electron in-elastically leading to ionization of the atom to which it is bound orelastically where excitation of atom is succeeded by de-excitation releasing a photon TheDM-Nucleon scattering in this model occurs at the loop level and though suppressed byone or two powers of respective coupling strengths and the loop factor it vastly dominatesover the DM-Electron and DM-Atom scattering [41ndash43]

The scalar spin-independent DM-Nucleon scattering are induced through the effectiveDM-photon DM-quark and DM-gluon interactions which are mediated by the singlet scalarportal of the model Following reference [42] we approximate the DM-Nucleon scatteringcross-section through two photons by integrating out the contributions of heavier fermionsrunning in the loop The total cross-section Spin-Independent DM-Nucleon in this case isgiven as

σγγN =

(αemZ

π

)2[micro2N

π

(αemZ

πm2S0

)2](

π2

12

)2(microNv

mτ

)2

2

(gχS0ξS

0

l

mτ

v0

)2

(45)

where Z is the atomic number of the detector material microN is the reduced mass of theDM-Nucleon system and v is the DM velocity of the order of 10minus3

The effective DM-gluon interactions are induced through a quark triangle loop wherethe negligible contribution of light quarks u d and s to the loop integral can be droppedIn this approximation the effective Lagrangian for singlet scalar-gluon interactions can bederived by integrating out contributions from heavy quarks c b and t in the triangle loopand can be written as

LS0gg

eff = minusξS

0

q

12π

αsvo

sumq=cbt

Iq

GamicroνGmicroνaS0 (46)

where the loop integral Iq is given in Appendix B7 The DM-gluon effective Lagrangian isthe given as

Lχχggeff =αs(mS0)

12π

ξS0

q gχS0

vom2S0

sumq=cbt

Iq

χχGamicroνGmicroνa (47)

ndash 16 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV

XENON17 1T Forbidden Region

PANDA2X-II 2017

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 50 GeV

2

(f)

Figure 8 Figures 8a to 8f show the spin-independent DM-Nucleon cross-section variation with themχ for fixed mHplusmn = 600 GeV δ13 = 02 and different choices of m2

12 and mA0 All points on thecontours satisfy the relic density 0119 and also explain the discrepancy ∆amicro = 268(63) times10minus11 Inthe left and right panels we plot the variation curves (bold lines) and allowed (shaded) regions forfive combinations of mS0 and mH0 The upper limit from PANDA 2X-II 2017 [47] and XENON-1T[48 49] are also shown along with the forbidden region shaded in red

Using (47) the DM-gluon scattering cross-section can be computed and given as

σggN =

(2ξS

0

q gχS0mN

m2S027vo

)2∣∣∣∣∣∣sumq=cbt

Iq

∣∣∣∣∣∣2

2

π(mχ +mN )2m2Nm

2χ (48)

ndash 17 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

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10-49

10-48

10-47

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10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 50 GeV

2

(f)



To compare the cross-sections given in (45) and (48) we evaluate the ratio

σγγNσggN (αem)4 micro

2N

m2N

(ξS

0

τ

ξS0

q

)2(9

8

)2 v2

c2 10minus6 minus 10minus10 (49)

ndash 18 ndash

Thus even though the effective DM-quark coupling is suppressed by tan2 β wrt that ofDM-lepton coupling the scattering cross-sections induced via the singlet coupled to thequark-loop dominates over the σγγN due to suppression resulting from the fourth power ofthe electromagnetic coupling

We convolute the DM-quark and DM-gluon scattering cross-sections with the quarkform factor F qiN (q2) and gluon form factor F gN (q2) respectively to compute nuclearrecoil energy observed in the experiment However this form factor is extracted at lowq2 m2

N [44ndash46] The form factors are defined aslangN prime∣∣∣ αs12π

GamicroνGamicroν

∣∣∣Nrang = F gN (q2)uprimeNuN (410a)langN prime |mqi qiqi|N

rang= F qiN (q2)uprimeNuN (410b)

Since mN equivsum

uds 〈N |mq qq|N〉 minus 9αS8π 〈N |G

amicroνGamicroν |N〉 the gluon form factor can beexpressed as

F gN = 1minussumuds

FqiNS (q2)

mN= minus 1

mN

9αs8π〈N |GamicroνGamicroν |N〉 (411)

The F gN is found to be asymp 092 using the values for F qiNS (q2) as quoted in the literature[45] Thus at the low momentum transfer the quartic DM-gluon (χχgg) effective interactioninduced through relatively heavy quarks dominates over the quartic DM-quark (χχqq)

effective interactions for light quarks in the direct-detection experimentsUsing the expression 48 we have plotted the spin-independent DM-Nucleon scattering

cross-section as a function of the DM mass mχ Figures 8 and 9 corresponding to mixingangle δ13=02 and δ13=04 respectively The parameter sets used in the computation ofdirect detection cross-section are consistent with the observed relic density as given infigures 6 and 7 Different panels in figures 8 and 9 show combinations of mA0 and m2

12 Ineach panel different combinations of mS0 and mH0 are used as shown Current bounds onspin-independent interactions from experiments like PANDA 2X-II 2017 [47] and XENON-1T [48 49] are also shown It can be seen that most of the parameter space for mS0 lessthan 10 GeV is ruled out by the current bounds

43 Indirect detection

Observations of diffused gamma rays from the regions of our Galaxy such as Galactic Center(GC) and dwarf spheroidal galaxies (dsphs) where DM density appears to be high imposebounds on DM annihilation to SM particles Experiments like Fermi-LAT [50 51] andHESS [52] have investigated DM annihilation as a possible source of the incoming photon-flux These experiments provide us with an upper-limit to velocity-averaged scatteringcross-section for various channels which can attribute to the observed photon-flux

DM annihilations contribute to the photon-flux through Final State Radiation (FSR)and radiative decays [5 53] from leptonic channels in lepto-philic models FSR contributionsare important in understanding the photon-spectra from DM annihilations to charged finalstates and therefore are instrumental in calculation of the observed bounds by experiments

ndash 19 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

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ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV

Fermi-LATm122 = 30 GeV

2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

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vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

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vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

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ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

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ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

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10-37

10-35

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10-27

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ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)

Figure 10 Figures 10a to 10f show the velocity-averaged scattering cross-section lt σv gtτ+τminus

variation with the mχ for fixed mHplusmn = 600 GeV δ13 = 02 and different choices of m212 and

mA0 All points on the contours satisfy the relic density 0119 and also explain the discrepancy∆amicro = 268(63) times 10minus11 In the left and right panels we plot the variation curves (bold lines)and allowed (shaded) regions for four five combinations of mS0 and mH0 The upper limit onvelocity-averaged annihilation cross-section observed from Fermi-LAT [50] is shown

like Fermi-LAT [5 50 54 55] The radiation emitted by the charged relativistic final statefermions f in the annihilation process χ+χrarr f+f+γ are approximately collinear with the

ndash 20 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

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ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

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ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

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10-31

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10-27

10-25

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ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

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10-31

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10-27

10-25

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ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

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10-31

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10-27

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ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

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10-31

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ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)




charged fermions In this regime the differential cross-section for the real emission processcan be factorized into the a collinear factor and cross-section σ(χχ rarr ff) as discussed in

ndash 21 ndash

1 2 3 5 7 1 2 3 5 75

10-39

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ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

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10-27

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ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

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ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

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10-31

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ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

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ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)

Figure 12 Figures 12a to 12f show the velocity-averaged scattering cross-section lt σv gtW+Wminus


mA0 All points on the contours satisfy the relic density 0119 and also explain the discrepancy∆amicro = 268(63) times 10minus11 In the left and right panels we plot the variation curves (bold lines)and allowed (shaded) regions for five combinations of mS0 and mH0 The upper limit on velocity-averaged annihilation cross-section observed from Fermi-LAT [50] is shown

the reference [56]

dσ(χχrarr ffγ)dx asymp αemQ2

f

π Ff (x) log

(s(1minusx)m2f

)σ(χχrarr ff) (412)

ndash 22 ndash

1 2 3 5 7 1 2 3 5 75

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ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

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10-31

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ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

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10-31

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ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

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ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

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ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

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ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)




where Qf and mf are the electric charge and the mass of the f particle s is the center-of-mass energy and x = 2Eγ

radics For fermion final states the splitting function F is given

ndash 23 ndash

05 1 2 3 5 7 1 2 3 5 75

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vgt

in

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3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV

Fermi-LAT + HESS (Profumo 2017)m122 = 30 GeV

2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

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vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

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ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

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10-37

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10-33

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10-27

10-25

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ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

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10-33

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ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

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ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)

Figure 14 Figures 14a to 14f show the velocity-averaged scattering cross-section lt σv gtS0S0

variation with the mχ for fixed mHplusmn = 600 GeV δ13 = 02 and and different choices of m212 and

mA0 All points on the contours satisfy the relic density 0119 and also explain the discrepancy∆amicro = 268(63) times 10minus11 In the left and right panels we plot the variation curves (bold lines)and allowed (shaded) regions for five combinations of mS0 and mH0 The upper limit on velocity-averaged annihilation cross-section for the process χχ rarr S0S0 computed from 4τ final states fromFermi-LAT data[59] is shown

byFf (x) = 1+(1minusx)2

x(413)

ndash 24 ndash

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ltσ

vgt

in

cm

3 s

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mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

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vgt

in

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3 s

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mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

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ltσ

vgt

in

cm

3 s

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mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)



mA0 All points on the contours satisfy the relic density 0119 and also explain the discrepancy∆amicro = 268(63) times 10minus11 In the left and right panels we plot the variation curves (bold lines)and allowed (shaded) regions for five combinations of mS0 and mH0 The upper limit on velocity-averaged annihilation cross-section for the process χχ rarr S0S0 computed from 4τ final states fromFermi-LAT data [59] is shown

The suppression factor of p-wave suppressed thermal averaged cross-sectionlangσ(χχrarr ff) v

rang

ndash 25 ndash

is mitigated in the thermal averaged cross-section of the real emission processlangσ(χχrarr ffγ) v

rangby the virtue of collinear factor given in equation (412)

In the present model the fermionic DM can annihilate to SM particles via sminuschannnelthrough the scalar portal as well as to a pair of singlet scalars through tminuschannel diagramsRecently authors of the reference [57 58] explored the discovery potential of the pair pro-duction of such lepto-philic scalars which pre-dominantly decay into pairs of charged leptonsat Cherenkov Telescope Array (CTA) Given the spectrum of pair produced SM particlesthrough single scalar mediator and into two pairs of charged leptons through scalar pairproduction we should be able to simulate the expected DM fluxes which will enable usto get the upper limits on the annihilation cross section for a given mediator mass in themodel

We calculate the velocity averaged cross-sections analytically for the annihilation pro-cesses χ χrarr ff χ χrarr Z0Z0 χ χrarrW+Wminus χ χrarr γγ and χ χrarr HiHj and are given inequations (C1) (C2) (C3) (C5) and (C6) respectively where Hi equiv h0 H0 S0 and A0

are the scalars of the model In addition the velocity averaged annihilation cross-sectionfor χ χrarr S0S0 through the t and u channel diagrams are given in (C7) We observe thatthe velocity averaged scattering cross-sections for all these processes are p-wave suppressedand are therefore sensitive to the choice of velocity distribution of the DM in the galaxy

The annihilation channels to fermions are proportional to the Yukawa coupling of thefermions with S0 We present the analysis for the most dominant sminus channel annihilationprocess χ χrarr τ+τminus which is enhanced due to its coupling strength being proportional tomτ tanβ and plot the variation of the velocity averaged scattering cross-section 〈σv〉 (χχrarrτ+τminus) as a function of the DM mass in figures 10 and 11 for mixing angle δ13 = 02 and 04respectively The coupling gχS0 for a given DM mass and all other parameters are chosento satisfy the observed relic density and electro-weak constraints as shown in the figures 6and 7 Annihilation of DM pairs to gauge Bosons are proportional to the square of theirmasses and therefore it is the second dominant process followed by the annihilation to τplusmnpairs Similarly we show the variation of the velocity averaged scattering cross-section〈σv〉 (χχ rarr W+Wminus) as a function of the DM mass in figures 12 and 13 for δ13 = 02and 04 respectively The DM pair annihilation to photons is loop suppressed and is notdiscussed further The s channel mediated DM pair annihilation to pair of scalars in thetheory involve the triple scalar couplings which are experimentally constrained and aretherefore suppressed

As mentioned above the t-channel pair production of singlet scalars dominates over theother channels The S0 pair production through its decay to dominant τ pairs will modifythe γ ray spectrum that one would have expected from the two body decay processes Weplot the velocity averaged scattering cross-section 〈σv〉 (χχ rarr S0S0) as a function of theDM mass which satisfies the relic density constraint in figures 14 and 15 for δ13 = 02 and04 respectively with all the other parameters fixed from the observed relic density andelectro-weak constraints The experimental upper limit on velocity-averaged annihilationcross-section for the process χχ rarr S0S0 for the varying DM mass are derived from theupper limits on the events contributed to 4τ final states at Fermi-LAT [59] and shown infigures 14 and 15

ndash 26 ndash

We find that the annihilation cross-sections for all these processes are three or moreorders of magnitude smaller than the current upper-bounds from Fermi-Lat data [50 59]

5 Summary

In this article we have made an attempt to address the observed discrepancy in anomalousmagnetic moment of muon by considering a lepto-philic type X 2-HDM and a singlet scalarportal for fermionic DM We have presented the model in such a manner where most of itrsquosscalar sector parameters can be constrained in terms of the lower bound on the physicalneutral and charged scalarrsquos masses derived from the direct and indirect searches at LEPand LHC

The model is analysed in the alignment limit where one of its scalar is identified withthe Higgs Boson of SM and the Yukawa couplings of fermions with the singlet scalar arefound to be proportional to mass of the fermions ie non-universal It is then validatedwith low energy constraints We have illustrated the constraints from anomalous magneticmoment in figures 1 and 2 and fixed the parameters tanβ and δ23 for a given δ13 We haveconsidered two choices 02 and 04 respectively for the mixing angle δ13 Contrary to theresults obtained in reference [21] for the singlet scalar with mass lying between 10 - 300 MeVwith universal couplings to leptons this study establishes the acceptability of the model toexplain the discrepancy ∆amicro for singlet scalar mass lying between 10 GeV le mS0 le 80 GeVwith couplings to leptons being non-universal The requirement of the Yukawa couplingH0 τ+τminus to remain perturbative further imposes an upper limit tanβ le 485 which in turnprovides the upper bound on the allowed mass range of singlet scalars to be sim 80 GeV

Exclusion limits on the couplings of SM gauge Bosons with the singlet scalars areobtained from the process e+eminus rarr Z0S0 at LEP-II experiment and have been displayed intable 2 for some chosen singlet scalar masses

Validation of the model is further subjected to the observed total Higgs decay widthat LHC [24 28] It is shown that the parameter m2

12 which has no bearing on the ∆amicrocan now be constrained from the from upper bound on the triple scalar coupling involvedin the decay of SM like Higgs to a pair of singlet scalars h0 rarr S0S0 The observed totaldecay width of SM like Higgs h0 restricts this additional channel and put a upper limit onthe partial decay width which has been shown in figures 3 for δ13 = 02 and in figures 4and 5 δ13 = 04 respectively We have found that in the probed region of interest for singletscalar mass m2

12 greater than 100 GeV2 and less than 0 GeV2 are forbiddenWe have addressed reasons for which there can be a deviation from SM predicted

universality in lepton-gauge Boson couplings The precision constraints are also discussedfor our model and found that corrections are suppressed due to the smallness of mixingangle

We augment our analysis by including a fermionic DM candidate χ and compute therelic density which are depicted in figures 6 amp 7 for δ13 = 02 and 04 respectively Theparameter sets chosen corresponding to points lying on contours satisfying relic density of0119 also fulfill the ∆amicro discrepancy and are consistent with the total Higgs decay widthobserved at LHC and LEP data

ndash 27 ndash

The scalar portal induced DM interactions are now probed in the Direct-detectionexperiment by the DM-nucleon scattering propelled through the gluons The variation ofspin-independent scattering cross-sections with the DM mass are shown in figures 8 and 9for δ13 = 02 and 04 respectively It can be seen that most of the parameter space for mS0

lighter than 10 GeV is excluded by current Direct-detection constraints from PANDA 2X-IIand XENON-1T experiments

The velocity averaged cross-sections for dominant DM pair annihilation channels likeτ+τminus W+Wminus S0S0 and γγ are analytically derived analysed and compared with theavailable space borne indirect-detection experiments The velocity averaged cross-sectionsvariation wrt DM mass are shown for δ13 = 02 and 04 in figures 10 and 11 respectivelyfor χχ rarr τ+τminus in figures 12 and 13 respectively for χχ rarr W+Wminus in figures 14 and 15respectively for χχrarr S0S0 We find that the contribution to the gamma ray spectrum fromthe most dominant annihilation channel to τplusmn pairs is at least three orders of magnitudelower than the current reach for the DM mass varying between 5 GeV - 8 TeV

In conclusion the lepton-specific type X 2-HDM model with a singlet scalar portalfor fermionic dark matter is capable of explaining both the observed discrepancy in theanomalous magnetic moment of the muon and the observed relic density This model withthe shrunk parameter space after being constrained by low energy experiments LEP Dataobserved total decay width of Higgs at LHC and constrained by dark matter detectionexperiments can now be tested at the ongoing and upcoming collider searches

Acknowledgments

Authors acknowledge the fruitful discussions with Mamta SD and MPS acknowledge thepartial financial support from the CSIR grant No 03(1340)15EMR-II MPS acknowledgesthe CSIR JRF fellowship for the partial financial support SD and MPS thank IUCAAPune for providing the hospitality and facilities where this work was initiated

ndash 28 ndash

Appendix

A Model Parameters

The parameters used in the Lagrangian for lepto-philic 2-HDM and dark matter portalsinglet scalar given in equation 23 are expressed in terms of the physical scalar massesmixing angles α and β and the model parameter m2

12

m211 = minus1

2

[m2H0 cos2 α+m2

h0 sin2 α+

sinα cosα(m2H0 minusm2

h0)minus 2m2

12

tanβ

](A1)

m222 = minus1

2

[m2h0 cos2 α+m2

H0 sin2 α+


h0)minus 2m2

12

cotβ

](A2)

λ1 =1

v2o cos2 β

[m2H0 cos2 α+m2

h0 sin2 αminusm212 tanβ

](A3)

λ2 =1

v2o sin2 β

[m2h0 cos2 α+m2

H0 sin2 αminusm212 cotβ

](A4)

λ3 =2

v2o sin (2β)

[sinα cosα

(m2H0 minusm2

h0)minusm2

12 + m2H+ sin (2β)

](A5)

λ4 =1

v2o sin (2β)

[2m2

12 +(m2A0 minus 2m2

H+

)sin (2β)

](A6)

λ5 =1

v2o sin (2β)

[2m2

12 minusm2A0 sin (2β)

](A7)

B Decay widths of the singlet scalar S0

The tree level partial decay widths of the scalar mediator are computed and are given by

Γ(S0 rarr f f) =Nc

8π

(ξSfmf

vo

)2

mS0

(1minus

4m2f

m2S0

)32

θ (mS0 minus 2mf) (B1)

where Nc = 1 for leptons and 3 for quarks

Γ(S0 rarrW+Wminus) =(ξS

0

V )2

16π v2o

m3S0

(1minus

4m2W

m2S0

)12[

12

(mW

mS0

)4

minus 4

(mW

mS0

)2

+ 1

]timesθ (mS0 minus 2mW ) (B2)

Γ(S0 rarr Z0 Z0) =1

2Γ(S0 rarrW+Wminus) with mW rarr mZ (B3)

Γ(S0 rarr χ χ) =g2χS0

8πmS0

(1minus

4m2χ

m2S0

)32

θ (mS0 minus 2mχ) (B4)

The one loop induced partial decay width of the scalar to gluons in this model arisesmainly from relatively heavy quarks and is given by

Γ(S0 rarr gg) =

(mtξ

S0

q

vo

)2α2s

72π3

m3S0

m2t

∣∣∣∣∣∣sumq=cbt

Iq

∣∣∣∣∣∣2

(B5)

ndash 29 ndash

For the case of photons it is given by

Γ(S0 rarr γγ) =m3S0

16πv20

(αemπ

)2∣∣∣∣∣sumq

ξS0

q Q2qIq +

suml

ξS0

l Q2qIq minus ξS

0

WplusmnIWplusmn + CSH+Hminusvo

2m2Hplusmn

IHplusmn

∣∣∣∣∣2

(B6)The integrals are given as

Iq = 3[2λq + λq(4λq minus 1)f(λq)] Il = 2λq + λq(4λq minus 1)f(λq)

IW = 3λW (1minus 2λW )f(λW )minus λW minus1

2 IHplusmn = minusλHplusmn [1 + 2λHplusmnf(Hplusmn)] (B7)

The integrals are defined in terms of dimensionless parameter λi = m2i m

2S0 and its function

f(λ) as

f(λ) = minus2

(sinminus1 1

2radicλ

)2

for λ gt1

4

=1

2

(lnη+

ηminus

)2

minus π2

2minus iπ η

+

ηminus for λ lt

1

4(B8)

with ηplusmn = 12 plusmn

radic14 minus λ

C Thermally averaged scattering cross-sections

We compute the thermal averaged annihilation cross-section of the fermionic DM via thesinglet scalar portal S0 to the SM final states These processes contributes to the relicdensity of the universe and are directly used in computing the annihilation cross-section forindirect detection of the DMlang

σ(χχrarr ff) vrang

=

(mfξ

S0

f

vo

)2

g2χS0

1

4π

(1minus

m2l

m2χ

) 32 m2

χ

(4m2χ minusm2

φ)2

(3

xf

)θ (mχ minusmf )

(C1)langσ(χχrarr Z0Z0

)vrang

=

(ξS

0

V

vo

)2g2χS0

8π

radic1minus

m2Z

m2χ

(16m4χ + 12m4

Z minus 16m2χm

2Z)

(4m2χ minusm2

S0)2

(3

xf

)times θ (mχ minusmZ0) (C2)lang

σ(χχrarrW+Wminus

)vrang

=

(ξS

0

V

vo

)2g2χS0

16π

radic1minus

m2W

m2χ

(16m4χ + 12m4

W minus 16m2χm

2W )

(4m2χ minusm2

S0)2

(3

xf

)times θ (mχ minusmWplusmn) (C3)

〈σ(χχrarr gg) v〉 =

(ξS

0

q αs gχS0

3π32vo

)2m4χ

(4m2χ minusm2

S0)2 +m2S0Γ

(3

2xf

) ∣∣∣∣∣∣sumq=cbt

Iq

∣∣∣∣∣∣2

(C4)

〈σ (χχrarr γγ) v〉 =g2χS0α

2em

2π3v2o

m4χ

∣∣∣∣sumq ξS0

q Q2qIq +

suml ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn

∣∣∣∣2(4mχ minusm2

S0)2 +m2S0Γ2

times(

3

xf

)(C5)

ndash 30 ndash

langσ(χχrarr H iHj) v

rang= c0

sumHiHjequivH0 A0 Hplusmn

C2S0HiHj

g2χS0

16πλ

12

(1m2Hi

4m2χ

m2Hj

4m2χ

)

times 1

(4m2χ minusm2

φ)2

(3

xf

)(C6)

where CS0HiHj are the tri-linear scalar couplings given in the Appendix D c0 = 12 for i=j

and c0 = 1 for i 6=j λ(X a b) = X2 + a2 + b2 minus 2abminus 2aX minus 2bXIn addition to s-channel processes considered above we also have contributions to the

relic density from t-channel process χχrarr S0S0 given bylangσ(χχrarr S0S0

)vrang

=3g4χS0

64πm2χ

(3

xf

)θ (mχ minusmS0) (C7)

D Triple scalar coupling

Here we extract the triple scalar coupling from the 2-HDM + singlet scalar Lagrangian inthe alignment limit Some of these scalars can be directly constrained from the ongoing

experiments at the Colliders We define dimensionless ratios r0 =m2H0

m2h0

and s0 =m2

12

m2h0 All

triple scalar couplings are defined in terms of r0 s0 and tanβ

Ch0S0S0 =δ213m

2h0

vo

(minus4δ213r

20

tanβ+

2δ213r0tanβ

minus 8r30tan4 β

+8r20s0tan3 β

+4r20

tan4 βminus 8r0s0

tan3 βminus 8r0s0

tanβ

+2r0

tan4 βminus 2r0

tan2 β+

2s0tan3 β

+ 2s0 tanβ +4δ213s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1

)(D1)

CS0h0h0 =δ13m

2h0

vo

(minus4δ213r

20

tan2 β+

2δ213r0tan2 β

minus 2δ213r0 minus6r0

tan3 βminus 4r0

tanβ

)(D2)

CS0H0H0 =δ13m

2h0

vo

(minus8δ213r

30

tan2 β+

12δ213r20

tan2 βminus 4δ213r0

tan2 βminus 6r20

tan5 βminus 4r20

tan3 β+

2r20tanβ

+6r0s0tan4 β

+4r0s0tan2 β

minus2r0s0 +3r0

tan5 β+

r0tan3 β

minus 3r0 tanβ minus 7r0tanβ

minus 3s0tan4 β

+ 3s0 tan2 β minus 3s0tan2 β

+ 3s0

)(D3)

CS0S0H0 =δ213m

2h0

vo

(minus8δ213r

30

tan2 β+

8δ213r20


tan2 β+

12r30tan5 β

+4r30

tan3 βminus 12r20s0

tan4 βminus 4r20s0

tan2 βminus 12r20

tan5 β

+8r20

tanβ+

12r0s0tan4 β

+8r0s0tan2 β

minus 4r0s0 +3r0

tan5 βminus r0

tan3 βminus 3r0 tanβ minus 11r0

tanβ

minus 3s0tan4 β


+ 3s0

)(D4)

CS0H0h0 =δ13m

2h0

vo

(minus4δ213r

30

tan3 β+

4δ213r20

tan3 βminus 4δ213r

20

tanβminus δ213r0

tan3 β+

3δ213r0tanβ

+4r20

tan4 β+

4r20tan2 β

minus 4r0s0tan3 β

minus4r0s0tanβ

minus 3r0tan2 β

minus r0 +2s0

tan3 β+ 2s0 tanβ +

4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1

)(D5)

ndash 31 ndash

CS0H+Hminus =δ13m

2h0

vo

(minus 2r20

tan5 β+

2r20tanβ

+2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0 +r0

tan5 βminus r0

tan3 βminus r0 tanβ

minus 5r0tanβ

minus s0tan4 β

+ s0 tan2 β minus s0tan2 β

+ s0 minus4m2

Hplusmnr0

tan3 βm2h0

minus4m2

Hplusmnr0

tanβm2h0

)(D6)

CS0A0A0 =δ13m

2h0

vo

(minus

4m2A0r0

tan3 βm2h0

minus4m2

A0r0tanβm2

h0

minus 2r20tan5 β

+2r20

tanβ+

2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0

+r0

tan5 βminus r0

tan3 βminus r0 tanβ minus 5r0

tanβminus s0

tan4 β+ s0 tan2 β minus s0

tan2 β+ s0

)(D7)

CS0S0S0 =δ313m

2h0

vo

(minus 24r40

tan5 β+

24r30s0tan4 β

+36r30

tan5 βminus 12r30



tan2 βminus 18r20

tan5 β+

12r20tan3 β

+18r20tanβ

+18r0s0tan4 β

+12r0s0tan2 β

minus 6r0s0 +3r0

tan5 βminus 3r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D8)

Ch0H+Hminus =m2h0

vo

(2δ213r0tanβ

+2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1minus

2m2Hplusmn

tan4 βm2h0

minus4m2

Hplusmn

tan2 βm2h0

minus2m2

Hplusmn

m2h0

) (D9)

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[40] A Alloul N D Christensen C Degrande C Duhr and B Fuks Comput Phys Commun185 2250 (2014) doi101016jcpc201404012 [arXiv13101921 [hep-ph]]

[41] J Kopp L Michaels and J Smirnov JCAP 1404 022 (2014)doi1010881475-7516201404022 [arXiv14016457 [hep-ph]]

[42] J Kopp V Niro T Schwetz and J Zupan Phys Rev D 80 083502 (2009)doi101103PhysRevD80083502 [arXiv09073159 [hep-ph]]

[43] F DrsquoEramo B J Kavanagh and P Panci Phys Lett B 771 339 (2017)doi101016jphysletb201705063 [arXiv170200016 [hep-ph]]

[44] F Bishara J Brod B Grinstein and J Zupan arXiv170802678 [hep-ph]

[45] M Cirelli E Del Nobile and P Panci JCAP 1310 019 (2013)doi1010881475-7516201310019 [arXiv13075955 [hep-ph]]

[46] S Dutta A Goyal and L K Saini JHEP 1802 023 (2018) doi101007JHEP02(2018)023[arXiv170900720 [hep-ph]]

[47] X Cui et al [PandaX-II Collaboration] Phys Rev Lett 119 no 18 181302 (2017)doi101103PhysRevLett119181302 [arXiv170806917 [astro-phCO]]

[48] E Aprile et al [XENON Collaboration] JCAP 1604 no 04 027 (2016)doi1010881475-7516201604027 [arXiv151207501 [physicsins-det]]

[49] E Aprile et al [XENON Collaboration] Eur Phys J C 77 no 12 881 (2017)doi101140epjcs10052-017-5326-3 [arXiv170807051 [astro-phIM]]

[50] M Ackermann et al [Fermi-LAT Collaboration] Phys Rev Lett 115 no 23 231301 (2015)doi101103PhysRevLett115231301 [arXiv150302641 [astro-phHE]]

[51] M Ajello et al [Fermi-LAT Collaboration] Astrophys J 819 no 1 44 (2016)doi1038470004-637X819144 [arXiv151102938 [astro-phHE]]

[52] E Moulin [HESS Collaboration] In Karlsruhe 2007 SUSY 2007 854-857[arXiv07102493 [astro-ph]]

ndash 34 ndash

[53] M N Mazziotta Int J Mod Phys A 29 1430030 (2014) doi101142S0217751X14300300[arXiv14042538 [astro-phHE]]

[54] R Essig N Sehgal and L E Strigari Phys Rev D 80 023506 (2009)doi101103PhysRevD80023506 [arXiv09024750 [hep-ph]]

[55] T Bringmann L Bergstrom and J Edsjo JHEP 0801 049 (2008)doi1010881126-6708200801049 [arXiv07103169 [hep-ph]]

[56] A Birkedal K T Matchev M Perelstein and A Spray hep-ph0507194

[57] C Siqueira arXiv190111055 [hep-ph]

[58] F S Queiroz and C Siqueira arXiv190110494 [hep-ph]

[59] S Profumo F S Queiroz J Silk and C Siqueira JCAP 1803 no 03 010 (2018)doi1010881475-7516201803010 [arXiv171103133 [hep-ph]]

ndash 35 ndash

1 Introduction

2 The Model



32 LEP and ae Constraints





42 Direct Detection


5 Summary

A Model Parameters




Contents

1 Introduction 1

2 The Model 3

3 Electro-Weak Constraints 531 Anomalous Magnetic Moment of Muon 532 LEP and ∆ae Constraints 833 Constraints from Higgs decay-width 934 Lepton non-Universality and Precision Constraints 12

4 Dark matter Phenomenology 1341 Computation of the Relic Density 1342 Direct Detection 1643 Indirect detection 19

5 Summary 27

A Model Parameters 29

B Decay widths of the singlet scalar S0 29

C Thermally averaged scattering cross-sections 30

D Triple scalar coupling 31

1 Introduction

Investigations into the nature of dark matter (DM) particles and their interactions is animportant field of research in Astro-particle physics The Atlas and CMS collaborations atthe Large Hadron Collider (LHC) are searching for the signature of DM particles involvingmissing energy (6ET ) [1 2] accompanied by a single or two jet events Direct detectionexperiments measure the nuclear-recoil energy and its spectrum in DM-Nucleon elasticscattering [3 4] In addition there are Indirect detection experiment [5] searching for theDM annihilation into photons and neutrinos in cosmic rays These experiments have nowreached a level of sensitivity where a significant part of parameter space required for theobserved relic density if contributed by the dark matter composed of Weakly interactingmassive particles (WIMPs) that survive as thermal relics has been excluded The nullresults of these direct and indirect experiments have given rise to the consideration of ideaswhere the dark matter is restricted to couple exclusively to either Standard Model (SM)

ndash 1 ndash



micro =









ndash 2 ndash

of results

2 The Model





vo equivradicv2

1 + v22 = 246 GeV (21)







+λ1

2

(Φdagger1Φ1

)2+λ2

2

(Φdagger2Φ2

)2

+λ3

(Φdagger1Φ1

)(Φdagger2Φ2

)+ λ4

(Φdagger1Φ2

)(Φdagger2Φ1

)+

λ5

2

(Φdagger1Φ2

)2+ hc

(23)


Vϕ0 = Bϕ0 +1

2m2

0(ϕ0)2 +Aϕ0

2(ϕ0)3 +

λϕ0

4(ϕ0)4 (24)

Vportal = A11

(Φdagger1Φ1

)ϕ0 +A12


)ϕ0 +A22

(Φdagger2Φ2

)ϕ0 (25)


Φ1 =1radic2

( radic2ω+

1


) Φ2 =

1radic2

( radic2ω+

2


) (26)


z2

)=

(cosβ minus sinβ

sinβ cosβ

)(G0

A0

)

(ω1

ω2

)=

(cosβ minus sinβ

sinβ cosβ

)(Gplusmn

Hplusmn

)

(27)



m2H0


m2h0

[1 + ξh

0

`

(1minus

m2h0

m2H0

)]cotβ (28)

ndash 3 ndash







ρ2

ϕ0


cosα sinα δ23


h0

H0

S0

(29)


(δ2

13 δ223 δ13δ23



m2S0 m2

0 + 2δ13M213 + 2δ23M

223 (210)

m2h0 H0

1

2

[M2

11 +M222 ∓

radic(M2

11 minusM222

)2+ 4M4

12

](211)

where

M211 = m2


12 = minusm212 + (λ3 + λ4 + λ5) v2

0 cosβ sinβ

M222 = m2


13 = v0A12 sinβ M223 = v0A12 cosβ (212)









Yu(d)voradic2

(214)

ndash 4 ndash


minusLY supsum

φequivS0h0H0

sumψ=` q

ξφψmψ

voφ ψψ (215)



L supsum

φequivS0h0H0

φ

vo

(2 ξφ

Wplusmn m2WplusmnW

+micro W


Z0 Z0microZ

0micro) (216)




23(16π2

)








=1

8π2

m2micro

v2o

tan2 β[δ2



IS0 H0 =

int 1

0dz

(1 + z) (1minus z)2


IA0 = minusint 1

0dz

z3


and

IHplusmn =

int 1

0dz


Hplusmn

with ri equivml


ndash 5 ndash

5x10-3

8x10-3

1x10-2

2x10-2

5x10-2

8x10-2

1x10-1

2x10-1

1 15 2 25 3 35 4 45 5

δ 23

δ13

mS0 = 10 GeV

mS0 = 20 GeV

mS0 = 30 GeV

mS0 = 40 GeV

mS0 = 50 GeV

mS0 = 60 GeV

mH0 = 400 GeV mA

0 = 200 GeV

(a)

5x10-3

8x10-3

1x10-2

2x10-2

5x10-2

8x10-2

1x10-1

2x10-1

1 15 2 25 3 35 4 45 5

δ 23

δ13

mS0 = 10 GeV

mS0 = 20 GeV

mS0 = 30 GeV

mS0 = 40 GeV

mS0 = 50 GeV

mS0 = 60 GeV

mH0 = 400 GeV mA

0 = 400 GeV

(b)

5x10-3

8x10-3

1x10-2

2x10-2

5x10-2

8x10-2

1x10-1

2x10-1

1 15 2 25 3 35 4 45 5

δ 23

δ13

mS0 = 10 GeV

mS0 = 20 GeV

mS0 = 30 GeV

mS0 = 40 GeV

mS0 = 50 GeV

mS0 = 60 GeV

mH0 = 400 GeV mA

0 = 600 GeV

(c)

1x10-2

2x10-2

5x10-2

1x10-1

2x10-1

5e-1

1 15 2 25 3 35 4 45 5

δ 23

δ13

mS0 = 10 GeV

mS0 = 20 GeV

mS0 = 30 GeV

mS0 = 40 GeV

mS0 = 50 GeV

mS0 = 60 GeV

mH0 = 600 GeV mA

0 = 400 GeV

(d)





0



H0

m2h0

[2minus

m2h0

m2H0



ndash 6 ndash






3x101

5x101

7x101

1x102

2x102

3x102

4x102

5x102

6x102

5 10 20 30 40 50 60 70 80

tan

β

mS0 in GeV

δ13 = 01

δ13 = 02

δ13 = 03

δ13 = 04

δ13 = 05


coupling

mH0 = 400 GeV mA


(a)

3x101

5x101

7x101

1x102

2x102

3x102

4x102

5x102

6x102

5 10 20 30 40 50 60 70 80

tan

β

mS0 in GeV

δ13 = 01

δ13 = 02

δ13 = 03

δ13 = 04

δ13 = 05


coupling

mH0 = mA


(b)

3x101

5x101

7x101

1x102

2x102

3x102

4x102

5x102

6x102

5 10 20 30 40 50 60 70 80

tan

β

mS0 in GeV

δ13 = 01

δ13 = 02

δ13 = 03

δ13 = 04

δ13 = 05


coupling

mH0 = 400 GeV mA


(c)

3x101

5x101

7x101

1x102

2x102

3x102

4x102

5x102

6x102

5 10 20 30 40 50 60 70 80

tan

β

mS0 in GeV

δ13 = 01

δ13 = 02

δ13 = 03

δ13 = 04

δ13 = 05


coupling

mH0 = 600 GeV mA


(d)



ndash 7 ndash







∣∣∣∣∣ξS0

Z0

ξh0

Z0

∣∣∣∣∣2


)equiv σSM


sin (β minus α)


) (33)



on∣∣∣ξS0

Z0




radicmmicrome


0

lmlv0



ndash 8 ndash

mS0(GeV) 12 15 20 25 30 35 40 45 50 55 60 65∣∣∣ξS0

Z0

∣∣∣ 285 316 398 530 751 1132 1028 457 260 199 169 093


Z0


574

5 10 20 24 30 40

10-6

10-5

10-4

10-3

10-2

10-1

100

101485

100 G

eV

2

50 G

eV

2

30 G

eV

2

20 G

eV

2

10 G

eV

2

H0rarr

τ+τ- F

orb

idd

en

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

Forbidden

(a) mH0 = 400 GeV mA0 = 200 GeV

574

5 10 20 24 30 40

10-6

10-5

10-4

10-3

10-2

10-1

100

101485

100 G

eV

2

50 G

eV

2

30 G

eV

2

20 G

eV

2

10 GeV2

H0rarr

τ+τ- F

orb

idd

en

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

Forbidden

(b) mH0 = 400 GeV mA0 = 400 GeV

574

5 10 20 24 30 40

10-6

10-5

10-4

10-3

10-2

10-1

100

101485

100 G

eV

2

50 G

eV

2

30 G

eV

2

20 G

eV

2

10 GeV2

H0rarr

τ+τ- F

orb

idd

en

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

Forbidden

(c) mH0 = 400 GeV mA0 = 600 GeV

574

5 10 20 24 30 40

10-6

10-5

10-4

10-3

10-2

10-1

100

101485

100 G

eV

2

50 G

eV

2

30 G

eV

2

20 G

eV

2

10 GeV2

H0rarr

τ+τ- F

orb

idd

en

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

Forbidden

(d) mH0 = 600 GeV mA0 = 400 GeV



12 = 0 GeV2




ndash 9 ndash

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2

30 GeV2

20 GeV2

10 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 400 GeV

mA0 = 200 GeV

(a)

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2

30 GeV2

20 GeV2

10 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 400 GeV

mA0 = 400 GeV

(b)

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2 30 GeV

2

20 GeV2

10 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 400 GeV

mA0 = 600 GeV

(c)

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2

30 GeV2

20 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 600 GeV

mA0 = 400 GeV

(d)







0


0


0



2

ndash 10 ndash

5 10 20 30 40 50 60200

300

400

500

600

700

800

900

1000m

H0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 20 GeV

2

(a)

5 10 20 30 40 50 60200

300

400

500

600

700

800

900

1000

1100

mH

0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 30 GeV

2

(b)

5 10 20 30 40 50 60200

300

400

500

600

700

800

900

1000

1100

1200

mH

0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 50 GeV

2

(c)

5 10 20 30 40 50 60100

200

300

400

500

600

700

800

900

1000

mH

0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 100 GeV

2

(d)


0






32πmh0

radic1minus

4m2S0

m2h0

(34)






ndash 11 ndash





12 ge10 GeV2







)minus 1 =


minus 1 (35)








ndash 12 ndash









dnχdt

+ 3a


(n2χ minus n2

χeq

)(42)

where aa =

radic8πρ


n2χeq = g

(mχT2π

) 32

exp[minusmχT




MPl


xF)

(43)


mχTF

is given by

xF = ln

c (c+ 2)

radic45

8

gMPl mχ

(a+ 6 b

xF

)2π3radic


(44)

ndash 13 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 50 GeV

2

(f)






ndash 14 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 50 GeV

2

(f)





ndash 15 ndash


12

)(

200 GeV 30 GeV2)(200 GeV 50 GeV2

)(400 GeV 30 GeV2

)(

400 GeV 50 GeV2)(600 GeV 30 GeV2

)and

(600 GeV 50 GeV2

)


42 Direct Detection



σγγN =

(αemZ

π

)2[micro2N

π

(αemZ

πm2S0

)2](

π2

12

)2(microNv

mτ

)2

2

(gχS0ξS

0

l

mτ

v0

)2

(45)



LS0gg

eff = minusξS

0

q

12π

αsvo

sumq=cbt

Iq




12π

ξS0

q gχS0

vom2S0

sumq=cbt

Iq


ndash 16 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 50 GeV

2

(f)




σggN =

(2ξS

0

q gχS0mN

m2S027vo


Iq

∣∣∣∣∣∣2

2

π(mχ +mN )2m2Nm

2χ (48)

ndash 17 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 50 GeV

2

(f)





2N

m2N

(ξS

0

τ

ξS0

q

)2(9

8

)2 v2


ndash 18 ndash




GamicroνGamicroν



Since mN equivsum



F gN = 1minussumuds

FqiNS (q2)

mN= minus 1

mN









ndash 19 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





ndash 20 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





ndash 21 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)




the reference [56]


f

π Ff (x) log

(s(1minusx)m2f


ndash 22 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)






ndash 23 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





x(413)

ndash 24 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





rang

ndash 25 ndash








ndash 26 ndash


5 Summary









ndash 27 ndash





Acknowledgments


ndash 28 ndash

Appendix

A Model Parameters


12

m211 = minus1

2

[m2H0 cos2 α+m2

h0 sin2 α+


h0)minus 2m2

12

tanβ

](A1)

m222 = minus1

2

[m2h0 cos2 α+m2

H0 sin2 α+


h0)minus 2m2

12

cotβ

](A2)

λ1 =1

v2o cos2 β

[m2H0 cos2 α+m2


](A3)

λ2 =1

v2o sin2 β

[m2h0 cos2 α+m2


](A4)

λ3 =2

v2o sin (2β)

[sinα cosα

(m2H0 minusm2

h0)minusm2

12 + m2H+ sin (2β)

](A5)

λ4 =1

v2o sin (2β)

[2m2

12 +(m2A0 minus 2m2

H+

)sin (2β)

](A6)

λ5 =1

v2o sin (2β)

[2m2


](A7)



Γ(S0 rarr f f) =Nc

8π

(ξSfmf

vo

)2

mS0

(1minus

4m2f

m2S0

)32




0

V )2

16π v2o

m3S0

(1minus

4m2W

m2S0

)12[

12

(mW

mS0

)4

minus 4

(mW

mS0

)2

+ 1





8πmS0

(1minus

4m2χ

m2S0

)32



Γ(S0 rarr gg) =

(mtξ

S0

q

vo

)2α2s

72π3

m3S0

m2t


Iq

∣∣∣∣∣∣2

(B5)

ndash 29 ndash



16πv20

(αemπ

)2∣∣∣∣∣sumq

ξS0

q Q2qIq +

suml

ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn

∣∣∣∣∣2







f(λ) as

f(λ) = minus2

(sinminus1 1

2radicλ

)2

for λ gt1

4

=1

2

(lnη+

ηminus

)2

minus π2

2minus iπ η

+

ηminus for λ lt

1

4(B8)


radic14 minus λ




=

(mfξ

S0

f

vo

)2

g2χS0

1

4π

(1minus

m2l

m2χ

) 32 m2

χ

(4m2χ minusm2

φ)2

(3

xf

)θ (mχ minusmf )


)vrang

=

(ξS

0

V

vo

)2g2χS0

8π

radic1minus

m2Z

m2χ

(16m4χ + 12m4

Z minus 16m2χm

2Z)

(4m2χ minusm2

S0)2

(3

xf


σ(χχrarrW+Wminus

)vrang

=

(ξS

0

V

vo

)2g2χS0

16π

radic1minus

m2W

m2χ

(16m4χ + 12m4

W minus 16m2χm

2W )

(4m2χ minusm2

S0)2

(3

xf



(ξS

0

q αs gχS0

3π32vo

)2m4χ

(4m2χ minusm2

S0)2 +m2S0Γ

(3

2xf


Iq

∣∣∣∣∣∣2

(C4)


2em

2π3v2o

m4χ


q Q2qIq +

suml ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn


S0)2 +m2S0Γ2

times(

3

xf

)(C5)

ndash 30 ndash


rang= c0


C2S0HiHj

g2χS0

16πλ

12

(1m2Hi

4m2χ

m2Hj

4m2χ

)

times 1

(4m2χ minusm2

φ)2

(3

xf

)(C6)




)vrang

=3g4χS0

64πm2χ

(3

xf





m2h0

and s0 =m2

12

m2h0 All


Ch0S0S0 =δ213m

2h0

vo

(minus4δ213r

20

tanβ+

2δ213r0tanβ

minus 8r30tan4 β

+8r20s0tan3 β

+4r20

tan4 βminus 8r0s0

tan3 βminus 8r0s0

tanβ

+2r0

tan4 βminus 2r0

tan2 β+

2s0tan3 β


minus 1

tan4 βminus 2

tan2 βminus 1

)(D1)

CS0h0h0 =δ13m

2h0

vo

(minus4δ213r

20

tan2 β+

2δ213r0tan2 β


tan3 βminus 4r0

tanβ

)(D2)

CS0H0H0 =δ13m

2h0

vo

(minus8δ213r

30

tan2 β+

12δ213r20


tan2 βminus 6r20

tan5 βminus 4r20

tan3 β+

2r20tanβ

+6r0s0tan4 β

+4r0s0tan2 β

minus2r0s0 +3r0

tan5 β+

r0tan3 β


minus 3s0tan4 β


+ 3s0

)(D3)

CS0S0H0 =δ213m

2h0

vo

(minus8δ213r

30

tan2 β+

8δ213r20


tan2 β+

12r30tan5 β

+4r30


tan4 βminus 4r20s0

tan2 βminus 12r20

tan5 β

+8r20

tanβ+

12r0s0tan4 β

+8r0s0tan2 β

minus 4r0s0 +3r0

tan5 βminus r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D4)

CS0H0h0 =δ13m

2h0

vo

(minus4δ213r

30

tan3 β+

4δ213r20


20

tanβminus δ213r0

tan3 β+

3δ213r0tanβ

+4r20

tan4 β+

4r20tan2 β

minus 4r0s0tan3 β

minus4r0s0tanβ

minus 3r0tan2 β

minus r0 +2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1

)(D5)

ndash 31 ndash

CS0H+Hminus =δ13m

2h0

vo

(minus 2r20

tan5 β+

2r20tanβ

+2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0 +r0

tan5 βminus r0


minus 5r0tanβ

minus s0tan4 β


+ s0 minus4m2

Hplusmnr0

tan3 βm2h0

minus4m2

Hplusmnr0

tanβm2h0

)(D6)

CS0A0A0 =δ13m

2h0

vo

(minus

4m2A0r0

tan3 βm2h0

minus4m2

A0r0tanβm2

h0

minus 2r20tan5 β

+2r20

tanβ+

2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0

+r0

tan5 βminus r0


tanβminus s0


tan2 β+ s0

)(D7)

CS0S0S0 =δ313m

2h0

vo

(minus 24r40

tan5 β+

24r30s0tan4 β

+36r30

tan5 βminus 12r30



tan2 βminus 18r20

tan5 β+

12r20tan3 β

+18r20tanβ

+18r0s0tan4 β

+12r0s0tan2 β

minus 6r0s0 +3r0

tan5 βminus 3r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D8)

Ch0H+Hminus =m2h0

vo

(2δ213r0tanβ

+2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1minus

2m2Hplusmn

tan4 βm2h0

minus4m2

Hplusmn

tan2 βm2h0

minus2m2

Hplusmn

m2h0

) (D9)

References










ndash 32 ndash























ndash 33 ndash






















ndash 34 ndash








ndash 35 ndash

1 Introduction

2 The Model








42 Direct Detection


5 Summary

A Model Parameters






micro =









ndash 2 ndash

of results

2 The Model





vo equivradicv2

1 + v22 = 246 GeV (21)







+λ1

2

(Φdagger1Φ1

)2+λ2

2

(Φdagger2Φ2

)2

+λ3

(Φdagger1Φ1

)(Φdagger2Φ2

)+ λ4

(Φdagger1Φ2

)(Φdagger2Φ1

)+

λ5

2

(Φdagger1Φ2

)2+ hc

(23)


Vϕ0 = Bϕ0 +1

2m2

0(ϕ0)2 +Aϕ0

2(ϕ0)3 +

λϕ0

4(ϕ0)4 (24)

Vportal = A11

(Φdagger1Φ1

)ϕ0 +A12


)ϕ0 +A22

(Φdagger2Φ2

)ϕ0 (25)


Φ1 =1radic2

( radic2ω+

1


) Φ2 =

1radic2

( radic2ω+

2


) (26)


z2

)=

(cosβ minus sinβ

sinβ cosβ

)(G0

A0

)

(ω1

ω2

)=

(cosβ minus sinβ

sinβ cosβ

)(Gplusmn

Hplusmn

)

(27)



m2H0


m2h0

[1 + ξh

0

`

(1minus

m2h0

m2H0

)]cotβ (28)

ndash 3 ndash







ρ2

ϕ0


cosα sinα δ23


h0

H0

S0

(29)


(δ2

13 δ223 δ13δ23



m2S0 m2

0 + 2δ13M213 + 2δ23M

223 (210)

m2h0 H0

1

2

[M2

11 +M222 ∓

radic(M2

11 minusM222

)2+ 4M4

12

](211)

where

M211 = m2


12 = minusm212 + (λ3 + λ4 + λ5) v2

0 cosβ sinβ

M222 = m2


13 = v0A12 sinβ M223 = v0A12 cosβ (212)









Yu(d)voradic2

(214)

ndash 4 ndash


minusLY supsum

φequivS0h0H0

sumψ=` q

ξφψmψ

voφ ψψ (215)



L supsum

φequivS0h0H0

φ

vo

(2 ξφ

Wplusmn m2WplusmnW

+micro W


Z0 Z0microZ

0micro) (216)




23(16π2

)








=1

8π2

m2micro

v2o

tan2 β[δ2



IS0 H0 =

int 1

0dz

(1 + z) (1minus z)2


IA0 = minusint 1

0dz

z3


and

IHplusmn =

int 1

0dz


Hplusmn

with ri equivml


ndash 5 ndash

5x10-3

8x10-3

1x10-2

2x10-2

5x10-2

8x10-2

1x10-1

2x10-1

1 15 2 25 3 35 4 45 5

δ 23

δ13

mS0 = 10 GeV

mS0 = 20 GeV

mS0 = 30 GeV

mS0 = 40 GeV

mS0 = 50 GeV

mS0 = 60 GeV

mH0 = 400 GeV mA

0 = 200 GeV

(a)

5x10-3

8x10-3

1x10-2

2x10-2

5x10-2

8x10-2

1x10-1

2x10-1

1 15 2 25 3 35 4 45 5

δ 23

δ13

mS0 = 10 GeV

mS0 = 20 GeV

mS0 = 30 GeV

mS0 = 40 GeV

mS0 = 50 GeV

mS0 = 60 GeV

mH0 = 400 GeV mA

0 = 400 GeV

(b)

5x10-3

8x10-3

1x10-2

2x10-2

5x10-2

8x10-2

1x10-1

2x10-1

1 15 2 25 3 35 4 45 5

δ 23

δ13

mS0 = 10 GeV

mS0 = 20 GeV

mS0 = 30 GeV

mS0 = 40 GeV

mS0 = 50 GeV

mS0 = 60 GeV

mH0 = 400 GeV mA

0 = 600 GeV

(c)

1x10-2

2x10-2

5x10-2

1x10-1

2x10-1

5e-1

1 15 2 25 3 35 4 45 5

δ 23

δ13

mS0 = 10 GeV

mS0 = 20 GeV

mS0 = 30 GeV

mS0 = 40 GeV

mS0 = 50 GeV

mS0 = 60 GeV

mH0 = 600 GeV mA

0 = 400 GeV

(d)





0



H0

m2h0

[2minus

m2h0

m2H0



ndash 6 ndash






3x101

5x101

7x101

1x102

2x102

3x102

4x102

5x102

6x102

5 10 20 30 40 50 60 70 80

tan

β

mS0 in GeV

δ13 = 01

δ13 = 02

δ13 = 03

δ13 = 04

δ13 = 05


coupling

mH0 = 400 GeV mA


(a)

3x101

5x101

7x101

1x102

2x102

3x102

4x102

5x102

6x102

5 10 20 30 40 50 60 70 80

tan

β

mS0 in GeV

δ13 = 01

δ13 = 02

δ13 = 03

δ13 = 04

δ13 = 05


coupling

mH0 = mA


(b)

3x101

5x101

7x101

1x102

2x102

3x102

4x102

5x102

6x102

5 10 20 30 40 50 60 70 80

tan

β

mS0 in GeV

δ13 = 01

δ13 = 02

δ13 = 03

δ13 = 04

δ13 = 05


coupling

mH0 = 400 GeV mA


(c)

3x101

5x101

7x101

1x102

2x102

3x102

4x102

5x102

6x102

5 10 20 30 40 50 60 70 80

tan

β

mS0 in GeV

δ13 = 01

δ13 = 02

δ13 = 03

δ13 = 04

δ13 = 05


coupling

mH0 = 600 GeV mA


(d)



ndash 7 ndash







∣∣∣∣∣ξS0

Z0

ξh0

Z0

∣∣∣∣∣2


)equiv σSM


sin (β minus α)


) (33)



on∣∣∣ξS0

Z0




radicmmicrome


0

lmlv0



ndash 8 ndash

mS0(GeV) 12 15 20 25 30 35 40 45 50 55 60 65∣∣∣ξS0

Z0

∣∣∣ 285 316 398 530 751 1132 1028 457 260 199 169 093


Z0


574

5 10 20 24 30 40

10-6

10-5

10-4

10-3

10-2

10-1

100

101485

100 G

eV

2

50 G

eV

2

30 G

eV

2

20 G

eV

2

10 G

eV

2

H0rarr

τ+τ- F

orb

idd

en

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

Forbidden

(a) mH0 = 400 GeV mA0 = 200 GeV

574

5 10 20 24 30 40

10-6

10-5

10-4

10-3

10-2

10-1

100

101485

100 G

eV

2

50 G

eV

2

30 G

eV

2

20 G

eV

2

10 GeV2

H0rarr

τ+τ- F

orb

idd

en

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

Forbidden

(b) mH0 = 400 GeV mA0 = 400 GeV

574

5 10 20 24 30 40

10-6

10-5

10-4

10-3

10-2

10-1

100

101485

100 G

eV

2

50 G

eV

2

30 G

eV

2

20 G

eV

2

10 GeV2

H0rarr

τ+τ- F

orb

idd

en

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

Forbidden

(c) mH0 = 400 GeV mA0 = 600 GeV

574

5 10 20 24 30 40

10-6

10-5

10-4

10-3

10-2

10-1

100

101485

100 G

eV

2

50 G

eV

2

30 G

eV

2

20 G

eV

2

10 GeV2

H0rarr

τ+τ- F

orb

idd

en

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

Forbidden

(d) mH0 = 600 GeV mA0 = 400 GeV



12 = 0 GeV2




ndash 9 ndash

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2

30 GeV2

20 GeV2

10 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 400 GeV

mA0 = 200 GeV

(a)

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2

30 GeV2

20 GeV2

10 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 400 GeV

mA0 = 400 GeV

(b)

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2 30 GeV

2

20 GeV2

10 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 400 GeV

mA0 = 600 GeV

(c)

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2

30 GeV2

20 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 600 GeV

mA0 = 400 GeV

(d)







0


0


0



2

ndash 10 ndash

5 10 20 30 40 50 60200

300

400

500

600

700

800

900

1000m

H0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 20 GeV

2

(a)

5 10 20 30 40 50 60200

300

400

500

600

700

800

900

1000

1100

mH

0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 30 GeV

2

(b)

5 10 20 30 40 50 60200

300

400

500

600

700

800

900

1000

1100

1200

mH

0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 50 GeV

2

(c)

5 10 20 30 40 50 60100

200

300

400

500

600

700

800

900

1000

mH

0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 100 GeV

2

(d)


0






32πmh0

radic1minus

4m2S0

m2h0

(34)






ndash 11 ndash





12 ge10 GeV2







)minus 1 =


minus 1 (35)








ndash 12 ndash









dnχdt

+ 3a


(n2χ minus n2

χeq

)(42)

where aa =

radic8πρ


n2χeq = g

(mχT2π

) 32

exp[minusmχT




MPl


xF)

(43)


mχTF

is given by

xF = ln

c (c+ 2)

radic45

8

gMPl mχ

(a+ 6 b

xF

)2π3radic


(44)

ndash 13 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 50 GeV

2

(f)






ndash 14 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 50 GeV

2

(f)





ndash 15 ndash


12

)(

200 GeV 30 GeV2)(200 GeV 50 GeV2

)(400 GeV 30 GeV2

)(

400 GeV 50 GeV2)(600 GeV 30 GeV2

)and

(600 GeV 50 GeV2

)


42 Direct Detection



σγγN =

(αemZ

π

)2[micro2N

π

(αemZ

πm2S0

)2](

π2

12

)2(microNv

mτ

)2

2

(gχS0ξS

0

l

mτ

v0

)2

(45)



LS0gg

eff = minusξS

0

q

12π

αsvo

sumq=cbt

Iq




12π

ξS0

q gχS0

vom2S0

sumq=cbt

Iq


ndash 16 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 50 GeV

2

(f)




σggN =

(2ξS

0

q gχS0mN

m2S027vo


Iq

∣∣∣∣∣∣2

2

π(mχ +mN )2m2Nm

2χ (48)

ndash 17 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 50 GeV

2

(f)





2N

m2N

(ξS

0

τ

ξS0

q

)2(9

8

)2 v2


ndash 18 ndash




GamicroνGamicroν



Since mN equivsum



F gN = 1minussumuds

FqiNS (q2)

mN= minus 1

mN









ndash 19 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





ndash 20 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





ndash 21 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)




the reference [56]


f

π Ff (x) log

(s(1minusx)m2f


ndash 22 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)






ndash 23 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





x(413)

ndash 24 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





rang

ndash 25 ndash








ndash 26 ndash


5 Summary









ndash 27 ndash





Acknowledgments


ndash 28 ndash

Appendix

A Model Parameters


12

m211 = minus1

2

[m2H0 cos2 α+m2

h0 sin2 α+


h0)minus 2m2

12

tanβ

](A1)

m222 = minus1

2

[m2h0 cos2 α+m2

H0 sin2 α+


h0)minus 2m2

12

cotβ

](A2)

λ1 =1

v2o cos2 β

[m2H0 cos2 α+m2


](A3)

λ2 =1

v2o sin2 β

[m2h0 cos2 α+m2


](A4)

λ3 =2

v2o sin (2β)

[sinα cosα

(m2H0 minusm2

h0)minusm2

12 + m2H+ sin (2β)

](A5)

λ4 =1

v2o sin (2β)

[2m2

12 +(m2A0 minus 2m2

H+

)sin (2β)

](A6)

λ5 =1

v2o sin (2β)

[2m2


](A7)



Γ(S0 rarr f f) =Nc

8π

(ξSfmf

vo

)2

mS0

(1minus

4m2f

m2S0

)32




0

V )2

16π v2o

m3S0

(1minus

4m2W

m2S0

)12[

12

(mW

mS0

)4

minus 4

(mW

mS0

)2

+ 1





8πmS0

(1minus

4m2χ

m2S0

)32



Γ(S0 rarr gg) =

(mtξ

S0

q

vo

)2α2s

72π3

m3S0

m2t


Iq

∣∣∣∣∣∣2

(B5)

ndash 29 ndash



16πv20

(αemπ

)2∣∣∣∣∣sumq

ξS0

q Q2qIq +

suml

ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn

∣∣∣∣∣2







f(λ) as

f(λ) = minus2

(sinminus1 1

2radicλ

)2

for λ gt1

4

=1

2

(lnη+

ηminus

)2

minus π2

2minus iπ η

+

ηminus for λ lt

1

4(B8)


radic14 minus λ




=

(mfξ

S0

f

vo

)2

g2χS0

1

4π

(1minus

m2l

m2χ

) 32 m2

χ

(4m2χ minusm2

φ)2

(3

xf

)θ (mχ minusmf )


)vrang

=

(ξS

0

V

vo

)2g2χS0

8π

radic1minus

m2Z

m2χ

(16m4χ + 12m4

Z minus 16m2χm

2Z)

(4m2χ minusm2

S0)2

(3

xf


σ(χχrarrW+Wminus

)vrang

=

(ξS

0

V

vo

)2g2χS0

16π

radic1minus

m2W

m2χ

(16m4χ + 12m4

W minus 16m2χm

2W )

(4m2χ minusm2

S0)2

(3

xf



(ξS

0

q αs gχS0

3π32vo

)2m4χ

(4m2χ minusm2

S0)2 +m2S0Γ

(3

2xf


Iq

∣∣∣∣∣∣2

(C4)


2em

2π3v2o

m4χ


q Q2qIq +

suml ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn


S0)2 +m2S0Γ2

times(

3

xf

)(C5)

ndash 30 ndash


rang= c0


C2S0HiHj

g2χS0

16πλ

12

(1m2Hi

4m2χ

m2Hj

4m2χ

)

times 1

(4m2χ minusm2

φ)2

(3

xf

)(C6)




)vrang

=3g4χS0

64πm2χ

(3

xf





m2h0

and s0 =m2

12

m2h0 All


Ch0S0S0 =δ213m

2h0

vo

(minus4δ213r

20

tanβ+

2δ213r0tanβ

minus 8r30tan4 β

+8r20s0tan3 β

+4r20

tan4 βminus 8r0s0

tan3 βminus 8r0s0

tanβ

+2r0

tan4 βminus 2r0

tan2 β+

2s0tan3 β


minus 1

tan4 βminus 2

tan2 βminus 1

)(D1)

CS0h0h0 =δ13m

2h0

vo

(minus4δ213r

20

tan2 β+

2δ213r0tan2 β


tan3 βminus 4r0

tanβ

)(D2)

CS0H0H0 =δ13m

2h0

vo

(minus8δ213r

30

tan2 β+

12δ213r20


tan2 βminus 6r20

tan5 βminus 4r20

tan3 β+

2r20tanβ

+6r0s0tan4 β

+4r0s0tan2 β

minus2r0s0 +3r0

tan5 β+

r0tan3 β


minus 3s0tan4 β


+ 3s0

)(D3)

CS0S0H0 =δ213m

2h0

vo

(minus8δ213r

30

tan2 β+

8δ213r20


tan2 β+

12r30tan5 β

+4r30


tan4 βminus 4r20s0

tan2 βminus 12r20

tan5 β

+8r20

tanβ+

12r0s0tan4 β

+8r0s0tan2 β

minus 4r0s0 +3r0

tan5 βminus r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D4)

CS0H0h0 =δ13m

2h0

vo

(minus4δ213r

30

tan3 β+

4δ213r20


20

tanβminus δ213r0

tan3 β+

3δ213r0tanβ

+4r20

tan4 β+

4r20tan2 β

minus 4r0s0tan3 β

minus4r0s0tanβ

minus 3r0tan2 β

minus r0 +2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1

)(D5)

ndash 31 ndash

CS0H+Hminus =δ13m

2h0

vo

(minus 2r20

tan5 β+

2r20tanβ

+2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0 +r0

tan5 βminus r0


minus 5r0tanβ

minus s0tan4 β


+ s0 minus4m2

Hplusmnr0

tan3 βm2h0

minus4m2

Hplusmnr0

tanβm2h0

)(D6)

CS0A0A0 =δ13m

2h0

vo

(minus

4m2A0r0

tan3 βm2h0

minus4m2

A0r0tanβm2

h0

minus 2r20tan5 β

+2r20

tanβ+

2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0

+r0

tan5 βminus r0


tanβminus s0


tan2 β+ s0

)(D7)

CS0S0S0 =δ313m

2h0

vo

(minus 24r40

tan5 β+

24r30s0tan4 β

+36r30

tan5 βminus 12r30



tan2 βminus 18r20

tan5 β+

12r20tan3 β

+18r20tanβ

+18r0s0tan4 β

+12r0s0tan2 β

minus 6r0s0 +3r0

tan5 βminus 3r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D8)

Ch0H+Hminus =m2h0

vo

(2δ213r0tanβ

+2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1minus

2m2Hplusmn

tan4 βm2h0

minus4m2

Hplusmn

tan2 βm2h0

minus2m2

Hplusmn

m2h0

) (D9)

References










ndash 32 ndash























ndash 33 ndash






















ndash 34 ndash








ndash 35 ndash

1 Introduction

2 The Model








42 Direct Detection


5 Summary

A Model Parameters




of results

2 The Model





vo equivradicv2

1 + v22 = 246 GeV (21)







+λ1

2

(Φdagger1Φ1

)2+λ2

2

(Φdagger2Φ2

)2

+λ3

(Φdagger1Φ1

)(Φdagger2Φ2

)+ λ4

(Φdagger1Φ2

)(Φdagger2Φ1

)+

λ5

2

(Φdagger1Φ2

)2+ hc

(23)


Vϕ0 = Bϕ0 +1

2m2

0(ϕ0)2 +Aϕ0

2(ϕ0)3 +

λϕ0

4(ϕ0)4 (24)

Vportal = A11

(Φdagger1Φ1

)ϕ0 +A12


)ϕ0 +A22

(Φdagger2Φ2

)ϕ0 (25)


Φ1 =1radic2

( radic2ω+

1


) Φ2 =

1radic2

( radic2ω+

2


) (26)


z2

)=

(cosβ minus sinβ

sinβ cosβ

)(G0

A0

)

(ω1

ω2

)=

(cosβ minus sinβ

sinβ cosβ

)(Gplusmn

Hplusmn

)

(27)



m2H0


m2h0

[1 + ξh

0

`

(1minus

m2h0

m2H0

)]cotβ (28)

ndash 3 ndash







ρ2

ϕ0


cosα sinα δ23


h0

H0

S0

(29)


(δ2

13 δ223 δ13δ23



m2S0 m2

0 + 2δ13M213 + 2δ23M

223 (210)

m2h0 H0

1

2

[M2

11 +M222 ∓

radic(M2

11 minusM222

)2+ 4M4

12

](211)

where

M211 = m2


12 = minusm212 + (λ3 + λ4 + λ5) v2

0 cosβ sinβ

M222 = m2


13 = v0A12 sinβ M223 = v0A12 cosβ (212)









Yu(d)voradic2

(214)

ndash 4 ndash


minusLY supsum

φequivS0h0H0

sumψ=` q

ξφψmψ

voφ ψψ (215)



L supsum

φequivS0h0H0

φ

vo

(2 ξφ

Wplusmn m2WplusmnW

+micro W


Z0 Z0microZ

0micro) (216)




23(16π2

)








=1

8π2

m2micro

v2o

tan2 β[δ2



IS0 H0 =

int 1

0dz

(1 + z) (1minus z)2


IA0 = minusint 1

0dz

z3


and

IHplusmn =

int 1

0dz


Hplusmn

with ri equivml


ndash 5 ndash

5x10-3

8x10-3

1x10-2

2x10-2

5x10-2

8x10-2

1x10-1

2x10-1

1 15 2 25 3 35 4 45 5

δ 23

δ13

mS0 = 10 GeV

mS0 = 20 GeV

mS0 = 30 GeV

mS0 = 40 GeV

mS0 = 50 GeV

mS0 = 60 GeV

mH0 = 400 GeV mA

0 = 200 GeV

(a)

5x10-3

8x10-3

1x10-2

2x10-2

5x10-2

8x10-2

1x10-1

2x10-1

1 15 2 25 3 35 4 45 5

δ 23

δ13

mS0 = 10 GeV

mS0 = 20 GeV

mS0 = 30 GeV

mS0 = 40 GeV

mS0 = 50 GeV

mS0 = 60 GeV

mH0 = 400 GeV mA

0 = 400 GeV

(b)

5x10-3

8x10-3

1x10-2

2x10-2

5x10-2

8x10-2

1x10-1

2x10-1

1 15 2 25 3 35 4 45 5

δ 23

δ13

mS0 = 10 GeV

mS0 = 20 GeV

mS0 = 30 GeV

mS0 = 40 GeV

mS0 = 50 GeV

mS0 = 60 GeV

mH0 = 400 GeV mA

0 = 600 GeV

(c)

1x10-2

2x10-2

5x10-2

1x10-1

2x10-1

5e-1

1 15 2 25 3 35 4 45 5

δ 23

δ13

mS0 = 10 GeV

mS0 = 20 GeV

mS0 = 30 GeV

mS0 = 40 GeV

mS0 = 50 GeV

mS0 = 60 GeV

mH0 = 600 GeV mA

0 = 400 GeV

(d)





0



H0

m2h0

[2minus

m2h0

m2H0



ndash 6 ndash






3x101

5x101

7x101

1x102

2x102

3x102

4x102

5x102

6x102

5 10 20 30 40 50 60 70 80

tan

β

mS0 in GeV

δ13 = 01

δ13 = 02

δ13 = 03

δ13 = 04

δ13 = 05


coupling

mH0 = 400 GeV mA


(a)

3x101

5x101

7x101

1x102

2x102

3x102

4x102

5x102

6x102

5 10 20 30 40 50 60 70 80

tan

β

mS0 in GeV

δ13 = 01

δ13 = 02

δ13 = 03

δ13 = 04

δ13 = 05


coupling

mH0 = mA


(b)

3x101

5x101

7x101

1x102

2x102

3x102

4x102

5x102

6x102

5 10 20 30 40 50 60 70 80

tan

β

mS0 in GeV

δ13 = 01

δ13 = 02

δ13 = 03

δ13 = 04

δ13 = 05


coupling

mH0 = 400 GeV mA


(c)

3x101

5x101

7x101

1x102

2x102

3x102

4x102

5x102

6x102

5 10 20 30 40 50 60 70 80

tan

β

mS0 in GeV

δ13 = 01

δ13 = 02

δ13 = 03

δ13 = 04

δ13 = 05


coupling

mH0 = 600 GeV mA


(d)



ndash 7 ndash







∣∣∣∣∣ξS0

Z0

ξh0

Z0

∣∣∣∣∣2


)equiv σSM


sin (β minus α)


) (33)



on∣∣∣ξS0

Z0




radicmmicrome


0

lmlv0



ndash 8 ndash

mS0(GeV) 12 15 20 25 30 35 40 45 50 55 60 65∣∣∣ξS0

Z0

∣∣∣ 285 316 398 530 751 1132 1028 457 260 199 169 093


Z0


574

5 10 20 24 30 40

10-6

10-5

10-4

10-3

10-2

10-1

100

101485

100 G

eV

2

50 G

eV

2

30 G

eV

2

20 G

eV

2

10 G

eV

2

H0rarr

τ+τ- F

orb

idd

en

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

Forbidden

(a) mH0 = 400 GeV mA0 = 200 GeV

574

5 10 20 24 30 40

10-6

10-5

10-4

10-3

10-2

10-1

100

101485

100 G

eV

2

50 G

eV

2

30 G

eV

2

20 G

eV

2

10 GeV2

H0rarr

τ+τ- F

orb

idd

en

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

Forbidden

(b) mH0 = 400 GeV mA0 = 400 GeV

574

5 10 20 24 30 40

10-6

10-5

10-4

10-3

10-2

10-1

100

101485

100 G

eV

2

50 G

eV

2

30 G

eV

2

20 G

eV

2

10 GeV2

H0rarr

τ+τ- F

orb

idd

en

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

Forbidden

(c) mH0 = 400 GeV mA0 = 600 GeV

574

5 10 20 24 30 40

10-6

10-5

10-4

10-3

10-2

10-1

100

101485

100 G

eV

2

50 G

eV

2

30 G

eV

2

20 G

eV

2

10 GeV2

H0rarr

τ+τ- F

orb

idd

en

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

Forbidden

(d) mH0 = 600 GeV mA0 = 400 GeV



12 = 0 GeV2




ndash 9 ndash

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2

30 GeV2

20 GeV2

10 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 400 GeV

mA0 = 200 GeV

(a)

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2

30 GeV2

20 GeV2

10 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 400 GeV

mA0 = 400 GeV

(b)

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2 30 GeV

2

20 GeV2

10 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 400 GeV

mA0 = 600 GeV

(c)

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2

30 GeV2

20 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 600 GeV

mA0 = 400 GeV

(d)







0


0


0



2

ndash 10 ndash

5 10 20 30 40 50 60200

300

400

500

600

700

800

900

1000m

H0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 20 GeV

2

(a)

5 10 20 30 40 50 60200

300

400

500

600

700

800

900

1000

1100

mH

0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 30 GeV

2

(b)

5 10 20 30 40 50 60200

300

400

500

600

700

800

900

1000

1100

1200

mH

0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 50 GeV

2

(c)

5 10 20 30 40 50 60100

200

300

400

500

600

700

800

900

1000

mH

0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 100 GeV

2

(d)


0






32πmh0

radic1minus

4m2S0

m2h0

(34)






ndash 11 ndash





12 ge10 GeV2







)minus 1 =


minus 1 (35)








ndash 12 ndash









dnχdt

+ 3a


(n2χ minus n2

χeq

)(42)

where aa =

radic8πρ


n2χeq = g

(mχT2π

) 32

exp[minusmχT




MPl


xF)

(43)


mχTF

is given by

xF = ln

c (c+ 2)

radic45

8

gMPl mχ

(a+ 6 b

xF

)2π3radic


(44)

ndash 13 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 50 GeV

2

(f)






ndash 14 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 50 GeV

2

(f)





ndash 15 ndash


12

)(

200 GeV 30 GeV2)(200 GeV 50 GeV2

)(400 GeV 30 GeV2

)(

400 GeV 50 GeV2)(600 GeV 30 GeV2

)and

(600 GeV 50 GeV2

)


42 Direct Detection



σγγN =

(αemZ

π

)2[micro2N

π

(αemZ

πm2S0

)2](

π2

12

)2(microNv

mτ

)2

2

(gχS0ξS

0

l

mτ

v0

)2

(45)



LS0gg

eff = minusξS

0

q

12π

αsvo

sumq=cbt

Iq




12π

ξS0

q gχS0

vom2S0

sumq=cbt

Iq


ndash 16 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 50 GeV

2

(f)




σggN =

(2ξS

0

q gχS0mN

m2S027vo


Iq

∣∣∣∣∣∣2

2

π(mχ +mN )2m2Nm

2χ (48)

ndash 17 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 50 GeV

2

(f)





2N

m2N

(ξS

0

τ

ξS0

q

)2(9

8

)2 v2


ndash 18 ndash




GamicroνGamicroν



Since mN equivsum



F gN = 1minussumuds

FqiNS (q2)

mN= minus 1

mN









ndash 19 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





ndash 20 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





ndash 21 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)




the reference [56]


f

π Ff (x) log

(s(1minusx)m2f


ndash 22 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)






ndash 23 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





x(413)

ndash 24 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





rang

ndash 25 ndash








ndash 26 ndash


5 Summary









ndash 27 ndash





Acknowledgments


ndash 28 ndash

Appendix

A Model Parameters


12

m211 = minus1

2

[m2H0 cos2 α+m2

h0 sin2 α+


h0)minus 2m2

12

tanβ

](A1)

m222 = minus1

2

[m2h0 cos2 α+m2

H0 sin2 α+


h0)minus 2m2

12

cotβ

](A2)

λ1 =1

v2o cos2 β

[m2H0 cos2 α+m2


](A3)

λ2 =1

v2o sin2 β

[m2h0 cos2 α+m2


](A4)

λ3 =2

v2o sin (2β)

[sinα cosα

(m2H0 minusm2

h0)minusm2

12 + m2H+ sin (2β)

](A5)

λ4 =1

v2o sin (2β)

[2m2

12 +(m2A0 minus 2m2

H+

)sin (2β)

](A6)

λ5 =1

v2o sin (2β)

[2m2


](A7)



Γ(S0 rarr f f) =Nc

8π

(ξSfmf

vo

)2

mS0

(1minus

4m2f

m2S0

)32




0

V )2

16π v2o

m3S0

(1minus

4m2W

m2S0

)12[

12

(mW

mS0

)4

minus 4

(mW

mS0

)2

+ 1





8πmS0

(1minus

4m2χ

m2S0

)32



Γ(S0 rarr gg) =

(mtξ

S0

q

vo

)2α2s

72π3

m3S0

m2t


Iq

∣∣∣∣∣∣2

(B5)

ndash 29 ndash



16πv20

(αemπ

)2∣∣∣∣∣sumq

ξS0

q Q2qIq +

suml

ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn

∣∣∣∣∣2







f(λ) as

f(λ) = minus2

(sinminus1 1

2radicλ

)2

for λ gt1

4

=1

2

(lnη+

ηminus

)2

minus π2

2minus iπ η

+

ηminus for λ lt

1

4(B8)


radic14 minus λ




=

(mfξ

S0

f

vo

)2

g2χS0

1

4π

(1minus

m2l

m2χ

) 32 m2

χ

(4m2χ minusm2

φ)2

(3

xf

)θ (mχ minusmf )


)vrang

=

(ξS

0

V

vo

)2g2χS0

8π

radic1minus

m2Z

m2χ

(16m4χ + 12m4

Z minus 16m2χm

2Z)

(4m2χ minusm2

S0)2

(3

xf


σ(χχrarrW+Wminus

)vrang

=

(ξS

0

V

vo

)2g2χS0

16π

radic1minus

m2W

m2χ

(16m4χ + 12m4

W minus 16m2χm

2W )

(4m2χ minusm2

S0)2

(3

xf



(ξS

0

q αs gχS0

3π32vo

)2m4χ

(4m2χ minusm2

S0)2 +m2S0Γ

(3

2xf


Iq

∣∣∣∣∣∣2

(C4)


2em

2π3v2o

m4χ


q Q2qIq +

suml ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn


S0)2 +m2S0Γ2

times(

3

xf

)(C5)

ndash 30 ndash


rang= c0


C2S0HiHj

g2χS0

16πλ

12

(1m2Hi

4m2χ

m2Hj

4m2χ

)

times 1

(4m2χ minusm2

φ)2

(3

xf

)(C6)




)vrang

=3g4χS0

64πm2χ

(3

xf





m2h0

and s0 =m2

12

m2h0 All


Ch0S0S0 =δ213m

2h0

vo

(minus4δ213r

20

tanβ+

2δ213r0tanβ

minus 8r30tan4 β

+8r20s0tan3 β

+4r20

tan4 βminus 8r0s0

tan3 βminus 8r0s0

tanβ

+2r0

tan4 βminus 2r0

tan2 β+

2s0tan3 β


minus 1

tan4 βminus 2

tan2 βminus 1

)(D1)

CS0h0h0 =δ13m

2h0

vo

(minus4δ213r

20

tan2 β+

2δ213r0tan2 β


tan3 βminus 4r0

tanβ

)(D2)

CS0H0H0 =δ13m

2h0

vo

(minus8δ213r

30

tan2 β+

12δ213r20


tan2 βminus 6r20

tan5 βminus 4r20

tan3 β+

2r20tanβ

+6r0s0tan4 β

+4r0s0tan2 β

minus2r0s0 +3r0

tan5 β+

r0tan3 β


minus 3s0tan4 β


+ 3s0

)(D3)

CS0S0H0 =δ213m

2h0

vo

(minus8δ213r

30

tan2 β+

8δ213r20


tan2 β+

12r30tan5 β

+4r30


tan4 βminus 4r20s0

tan2 βminus 12r20

tan5 β

+8r20

tanβ+

12r0s0tan4 β

+8r0s0tan2 β

minus 4r0s0 +3r0

tan5 βminus r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D4)

CS0H0h0 =δ13m

2h0

vo

(minus4δ213r

30

tan3 β+

4δ213r20


20

tanβminus δ213r0

tan3 β+

3δ213r0tanβ

+4r20

tan4 β+

4r20tan2 β

minus 4r0s0tan3 β

minus4r0s0tanβ

minus 3r0tan2 β

minus r0 +2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1

)(D5)

ndash 31 ndash

CS0H+Hminus =δ13m

2h0

vo

(minus 2r20

tan5 β+

2r20tanβ

+2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0 +r0

tan5 βminus r0


minus 5r0tanβ

minus s0tan4 β


+ s0 minus4m2

Hplusmnr0

tan3 βm2h0

minus4m2

Hplusmnr0

tanβm2h0

)(D6)

CS0A0A0 =δ13m

2h0

vo

(minus

4m2A0r0

tan3 βm2h0

minus4m2

A0r0tanβm2

h0

minus 2r20tan5 β

+2r20

tanβ+

2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0

+r0

tan5 βminus r0


tanβminus s0


tan2 β+ s0

)(D7)

CS0S0S0 =δ313m

2h0

vo

(minus 24r40

tan5 β+

24r30s0tan4 β

+36r30

tan5 βminus 12r30



tan2 βminus 18r20

tan5 β+

12r20tan3 β

+18r20tanβ

+18r0s0tan4 β

+12r0s0tan2 β

minus 6r0s0 +3r0

tan5 βminus 3r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D8)

Ch0H+Hminus =m2h0

vo

(2δ213r0tanβ

+2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1minus

2m2Hplusmn

tan4 βm2h0

minus4m2

Hplusmn

tan2 βm2h0

minus2m2

Hplusmn

m2h0

) (D9)

References










ndash 32 ndash























ndash 33 ndash






















ndash 34 ndash








ndash 35 ndash

1 Introduction

2 The Model








42 Direct Detection


5 Summary

A Model Parameters










ρ2

ϕ0


cosα sinα δ23


h0

H0

S0

(29)


(δ2

13 δ223 δ13δ23



m2S0 m2

0 + 2δ13M213 + 2δ23M

223 (210)

m2h0 H0

1

2

[M2

11 +M222 ∓

radic(M2

11 minusM222

)2+ 4M4

12

](211)

where

M211 = m2


12 = minusm212 + (λ3 + λ4 + λ5) v2

0 cosβ sinβ

M222 = m2


13 = v0A12 sinβ M223 = v0A12 cosβ (212)









Yu(d)voradic2

(214)

ndash 4 ndash


minusLY supsum

φequivS0h0H0

sumψ=` q

ξφψmψ

voφ ψψ (215)



L supsum

φequivS0h0H0

φ

vo

(2 ξφ

Wplusmn m2WplusmnW

+micro W


Z0 Z0microZ

0micro) (216)




23(16π2

)








=1

8π2

m2micro

v2o

tan2 β[δ2



IS0 H0 =

int 1

0dz

(1 + z) (1minus z)2


IA0 = minusint 1

0dz

z3


and

IHplusmn =

int 1

0dz


Hplusmn

with ri equivml


ndash 5 ndash

5x10-3

8x10-3

1x10-2

2x10-2

5x10-2

8x10-2

1x10-1

2x10-1

1 15 2 25 3 35 4 45 5

δ 23

δ13

mS0 = 10 GeV

mS0 = 20 GeV

mS0 = 30 GeV

mS0 = 40 GeV

mS0 = 50 GeV

mS0 = 60 GeV

mH0 = 400 GeV mA

0 = 200 GeV

(a)

5x10-3

8x10-3

1x10-2

2x10-2

5x10-2

8x10-2

1x10-1

2x10-1

1 15 2 25 3 35 4 45 5

δ 23

δ13

mS0 = 10 GeV

mS0 = 20 GeV

mS0 = 30 GeV

mS0 = 40 GeV

mS0 = 50 GeV

mS0 = 60 GeV

mH0 = 400 GeV mA

0 = 400 GeV

(b)

5x10-3

8x10-3

1x10-2

2x10-2

5x10-2

8x10-2

1x10-1

2x10-1

1 15 2 25 3 35 4 45 5

δ 23

δ13

mS0 = 10 GeV

mS0 = 20 GeV

mS0 = 30 GeV

mS0 = 40 GeV

mS0 = 50 GeV

mS0 = 60 GeV

mH0 = 400 GeV mA

0 = 600 GeV

(c)

1x10-2

2x10-2

5x10-2

1x10-1

2x10-1

5e-1

1 15 2 25 3 35 4 45 5

δ 23

δ13

mS0 = 10 GeV

mS0 = 20 GeV

mS0 = 30 GeV

mS0 = 40 GeV

mS0 = 50 GeV

mS0 = 60 GeV

mH0 = 600 GeV mA

0 = 400 GeV

(d)





0



H0

m2h0

[2minus

m2h0

m2H0



ndash 6 ndash






3x101

5x101

7x101

1x102

2x102

3x102

4x102

5x102

6x102

5 10 20 30 40 50 60 70 80

tan

β

mS0 in GeV

δ13 = 01

δ13 = 02

δ13 = 03

δ13 = 04

δ13 = 05


coupling

mH0 = 400 GeV mA


(a)

3x101

5x101

7x101

1x102

2x102

3x102

4x102

5x102

6x102

5 10 20 30 40 50 60 70 80

tan

β

mS0 in GeV

δ13 = 01

δ13 = 02

δ13 = 03

δ13 = 04

δ13 = 05


coupling

mH0 = mA


(b)

3x101

5x101

7x101

1x102

2x102

3x102

4x102

5x102

6x102

5 10 20 30 40 50 60 70 80

tan

β

mS0 in GeV

δ13 = 01

δ13 = 02

δ13 = 03

δ13 = 04

δ13 = 05


coupling

mH0 = 400 GeV mA


(c)

3x101

5x101

7x101

1x102

2x102

3x102

4x102

5x102

6x102

5 10 20 30 40 50 60 70 80

tan

β

mS0 in GeV

δ13 = 01

δ13 = 02

δ13 = 03

δ13 = 04

δ13 = 05


coupling

mH0 = 600 GeV mA


(d)



ndash 7 ndash







∣∣∣∣∣ξS0

Z0

ξh0

Z0

∣∣∣∣∣2


)equiv σSM


sin (β minus α)


) (33)



on∣∣∣ξS0

Z0




radicmmicrome


0

lmlv0



ndash 8 ndash

mS0(GeV) 12 15 20 25 30 35 40 45 50 55 60 65∣∣∣ξS0

Z0

∣∣∣ 285 316 398 530 751 1132 1028 457 260 199 169 093


Z0


574

5 10 20 24 30 40

10-6

10-5

10-4

10-3

10-2

10-1

100

101485

100 G

eV

2

50 G

eV

2

30 G

eV

2

20 G

eV

2

10 G

eV

2

H0rarr

τ+τ- F

orb

idd

en

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

Forbidden

(a) mH0 = 400 GeV mA0 = 200 GeV

574

5 10 20 24 30 40

10-6

10-5

10-4

10-3

10-2

10-1

100

101485

100 G

eV

2

50 G

eV

2

30 G

eV

2

20 G

eV

2

10 GeV2

H0rarr

τ+τ- F

orb

idd

en

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

Forbidden

(b) mH0 = 400 GeV mA0 = 400 GeV

574

5 10 20 24 30 40

10-6

10-5

10-4

10-3

10-2

10-1

100

101485

100 G

eV

2

50 G

eV

2

30 G

eV

2

20 G

eV

2

10 GeV2

H0rarr

τ+τ- F

orb

idd

en

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

Forbidden

(c) mH0 = 400 GeV mA0 = 600 GeV

574

5 10 20 24 30 40

10-6

10-5

10-4

10-3

10-2

10-1

100

101485

100 G

eV

2

50 G

eV

2

30 G

eV

2

20 G

eV

2

10 GeV2

H0rarr

τ+τ- F

orb

idd

en

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

Forbidden

(d) mH0 = 600 GeV mA0 = 400 GeV



12 = 0 GeV2




ndash 9 ndash

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2

30 GeV2

20 GeV2

10 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 400 GeV

mA0 = 200 GeV

(a)

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2

30 GeV2

20 GeV2

10 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 400 GeV

mA0 = 400 GeV

(b)

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2 30 GeV

2

20 GeV2

10 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 400 GeV

mA0 = 600 GeV

(c)

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2

30 GeV2

20 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 600 GeV

mA0 = 400 GeV

(d)







0


0


0



2

ndash 10 ndash

5 10 20 30 40 50 60200

300

400

500

600

700

800

900

1000m

H0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 20 GeV

2

(a)

5 10 20 30 40 50 60200

300

400

500

600

700

800

900

1000

1100

mH

0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 30 GeV

2

(b)

5 10 20 30 40 50 60200

300

400

500

600

700

800

900

1000

1100

1200

mH

0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 50 GeV

2

(c)

5 10 20 30 40 50 60100

200

300

400

500

600

700

800

900

1000

mH

0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 100 GeV

2

(d)


0






32πmh0

radic1minus

4m2S0

m2h0

(34)






ndash 11 ndash





12 ge10 GeV2







)minus 1 =


minus 1 (35)








ndash 12 ndash









dnχdt

+ 3a


(n2χ minus n2

χeq

)(42)

where aa =

radic8πρ


n2χeq = g

(mχT2π

) 32

exp[minusmχT




MPl


xF)

(43)


mχTF

is given by

xF = ln

c (c+ 2)

radic45

8

gMPl mχ

(a+ 6 b

xF

)2π3radic


(44)

ndash 13 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 50 GeV

2

(f)






ndash 14 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 50 GeV

2

(f)





ndash 15 ndash


12

)(

200 GeV 30 GeV2)(200 GeV 50 GeV2

)(400 GeV 30 GeV2

)(

400 GeV 50 GeV2)(600 GeV 30 GeV2

)and

(600 GeV 50 GeV2

)


42 Direct Detection



σγγN =

(αemZ

π

)2[micro2N

π

(αemZ

πm2S0

)2](

π2

12

)2(microNv

mτ

)2

2

(gχS0ξS

0

l

mτ

v0

)2

(45)



LS0gg

eff = minusξS

0

q

12π

αsvo

sumq=cbt

Iq




12π

ξS0

q gχS0

vom2S0

sumq=cbt

Iq


ndash 16 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 50 GeV

2

(f)




σggN =

(2ξS

0

q gχS0mN

m2S027vo


Iq

∣∣∣∣∣∣2

2

π(mχ +mN )2m2Nm

2χ (48)

ndash 17 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 50 GeV

2

(f)





2N

m2N

(ξS

0

τ

ξS0

q

)2(9

8

)2 v2


ndash 18 ndash




GamicroνGamicroν



Since mN equivsum



F gN = 1minussumuds

FqiNS (q2)

mN= minus 1

mN









ndash 19 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





ndash 20 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





ndash 21 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)




the reference [56]


f

π Ff (x) log

(s(1minusx)m2f


ndash 22 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)






ndash 23 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





x(413)

ndash 24 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





rang

ndash 25 ndash








ndash 26 ndash


5 Summary









ndash 27 ndash





Acknowledgments


ndash 28 ndash

Appendix

A Model Parameters


12

m211 = minus1

2

[m2H0 cos2 α+m2

h0 sin2 α+


h0)minus 2m2

12

tanβ

](A1)

m222 = minus1

2

[m2h0 cos2 α+m2

H0 sin2 α+


h0)minus 2m2

12

cotβ

](A2)

λ1 =1

v2o cos2 β

[m2H0 cos2 α+m2


](A3)

λ2 =1

v2o sin2 β

[m2h0 cos2 α+m2


](A4)

λ3 =2

v2o sin (2β)

[sinα cosα

(m2H0 minusm2

h0)minusm2

12 + m2H+ sin (2β)

](A5)

λ4 =1

v2o sin (2β)

[2m2

12 +(m2A0 minus 2m2

H+

)sin (2β)

](A6)

λ5 =1

v2o sin (2β)

[2m2


](A7)



Γ(S0 rarr f f) =Nc

8π

(ξSfmf

vo

)2

mS0

(1minus

4m2f

m2S0

)32




0

V )2

16π v2o

m3S0

(1minus

4m2W

m2S0

)12[

12

(mW

mS0

)4

minus 4

(mW

mS0

)2

+ 1





8πmS0

(1minus

4m2χ

m2S0

)32



Γ(S0 rarr gg) =

(mtξ

S0

q

vo

)2α2s

72π3

m3S0

m2t


Iq

∣∣∣∣∣∣2

(B5)

ndash 29 ndash



16πv20

(αemπ

)2∣∣∣∣∣sumq

ξS0

q Q2qIq +

suml

ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn

∣∣∣∣∣2







f(λ) as

f(λ) = minus2

(sinminus1 1

2radicλ

)2

for λ gt1

4

=1

2

(lnη+

ηminus

)2

minus π2

2minus iπ η

+

ηminus for λ lt

1

4(B8)


radic14 minus λ




=

(mfξ

S0

f

vo

)2

g2χS0

1

4π

(1minus

m2l

m2χ

) 32 m2

χ

(4m2χ minusm2

φ)2

(3

xf

)θ (mχ minusmf )


)vrang

=

(ξS

0

V

vo

)2g2χS0

8π

radic1minus

m2Z

m2χ

(16m4χ + 12m4

Z minus 16m2χm

2Z)

(4m2χ minusm2

S0)2

(3

xf


σ(χχrarrW+Wminus

)vrang

=

(ξS

0

V

vo

)2g2χS0

16π

radic1minus

m2W

m2χ

(16m4χ + 12m4

W minus 16m2χm

2W )

(4m2χ minusm2

S0)2

(3

xf



(ξS

0

q αs gχS0

3π32vo

)2m4χ

(4m2χ minusm2

S0)2 +m2S0Γ

(3

2xf


Iq

∣∣∣∣∣∣2

(C4)


2em

2π3v2o

m4χ


q Q2qIq +

suml ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn


S0)2 +m2S0Γ2

times(

3

xf

)(C5)

ndash 30 ndash


rang= c0


C2S0HiHj

g2χS0

16πλ

12

(1m2Hi

4m2χ

m2Hj

4m2χ

)

times 1

(4m2χ minusm2

φ)2

(3

xf

)(C6)




)vrang

=3g4χS0

64πm2χ

(3

xf





m2h0

and s0 =m2

12

m2h0 All


Ch0S0S0 =δ213m

2h0

vo

(minus4δ213r

20

tanβ+

2δ213r0tanβ

minus 8r30tan4 β

+8r20s0tan3 β

+4r20

tan4 βminus 8r0s0

tan3 βminus 8r0s0

tanβ

+2r0

tan4 βminus 2r0

tan2 β+

2s0tan3 β


minus 1

tan4 βminus 2

tan2 βminus 1

)(D1)

CS0h0h0 =δ13m

2h0

vo

(minus4δ213r

20

tan2 β+

2δ213r0tan2 β


tan3 βminus 4r0

tanβ

)(D2)

CS0H0H0 =δ13m

2h0

vo

(minus8δ213r

30

tan2 β+

12δ213r20


tan2 βminus 6r20

tan5 βminus 4r20

tan3 β+

2r20tanβ

+6r0s0tan4 β

+4r0s0tan2 β

minus2r0s0 +3r0

tan5 β+

r0tan3 β


minus 3s0tan4 β


+ 3s0

)(D3)

CS0S0H0 =δ213m

2h0

vo

(minus8δ213r

30

tan2 β+

8δ213r20


tan2 β+

12r30tan5 β

+4r30


tan4 βminus 4r20s0

tan2 βminus 12r20

tan5 β

+8r20

tanβ+

12r0s0tan4 β

+8r0s0tan2 β

minus 4r0s0 +3r0

tan5 βminus r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D4)

CS0H0h0 =δ13m

2h0

vo

(minus4δ213r

30

tan3 β+

4δ213r20


20

tanβminus δ213r0

tan3 β+

3δ213r0tanβ

+4r20

tan4 β+

4r20tan2 β

minus 4r0s0tan3 β

minus4r0s0tanβ

minus 3r0tan2 β

minus r0 +2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1

)(D5)

ndash 31 ndash

CS0H+Hminus =δ13m

2h0

vo

(minus 2r20

tan5 β+

2r20tanβ

+2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0 +r0

tan5 βminus r0


minus 5r0tanβ

minus s0tan4 β


+ s0 minus4m2

Hplusmnr0

tan3 βm2h0

minus4m2

Hplusmnr0

tanβm2h0

)(D6)

CS0A0A0 =δ13m

2h0

vo

(minus

4m2A0r0

tan3 βm2h0

minus4m2

A0r0tanβm2

h0

minus 2r20tan5 β

+2r20

tanβ+

2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0

+r0

tan5 βminus r0


tanβminus s0


tan2 β+ s0

)(D7)

CS0S0S0 =δ313m

2h0

vo

(minus 24r40

tan5 β+

24r30s0tan4 β

+36r30

tan5 βminus 12r30



tan2 βminus 18r20

tan5 β+

12r20tan3 β

+18r20tanβ

+18r0s0tan4 β

+12r0s0tan2 β

minus 6r0s0 +3r0

tan5 βminus 3r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D8)

Ch0H+Hminus =m2h0

vo

(2δ213r0tanβ

+2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1minus

2m2Hplusmn

tan4 βm2h0

minus4m2

Hplusmn

tan2 βm2h0

minus2m2

Hplusmn

m2h0

) (D9)

References










ndash 32 ndash























ndash 33 ndash






















ndash 34 ndash








ndash 35 ndash

1 Introduction

2 The Model








42 Direct Detection


5 Summary

A Model Parameters





minusLY supsum

φequivS0h0H0

sumψ=` q

ξφψmψ

voφ ψψ (215)



L supsum

φequivS0h0H0

φ

vo

(2 ξφ

Wplusmn m2WplusmnW

+micro W


Z0 Z0microZ

0micro) (216)




23(16π2

)








=1

8π2

m2micro

v2o

tan2 β[δ2



IS0 H0 =

int 1

0dz

(1 + z) (1minus z)2


IA0 = minusint 1

0dz

z3


and

IHplusmn =

int 1

0dz


Hplusmn

with ri equivml


ndash 5 ndash

5x10-3

8x10-3

1x10-2

2x10-2

5x10-2

8x10-2

1x10-1

2x10-1

1 15 2 25 3 35 4 45 5

δ 23

δ13

mS0 = 10 GeV

mS0 = 20 GeV

mS0 = 30 GeV

mS0 = 40 GeV

mS0 = 50 GeV

mS0 = 60 GeV

mH0 = 400 GeV mA

0 = 200 GeV

(a)

5x10-3

8x10-3

1x10-2

2x10-2

5x10-2

8x10-2

1x10-1

2x10-1

1 15 2 25 3 35 4 45 5

δ 23

δ13

mS0 = 10 GeV

mS0 = 20 GeV

mS0 = 30 GeV

mS0 = 40 GeV

mS0 = 50 GeV

mS0 = 60 GeV

mH0 = 400 GeV mA

0 = 400 GeV

(b)

5x10-3

8x10-3

1x10-2

2x10-2

5x10-2

8x10-2

1x10-1

2x10-1

1 15 2 25 3 35 4 45 5

δ 23

δ13

mS0 = 10 GeV

mS0 = 20 GeV

mS0 = 30 GeV

mS0 = 40 GeV

mS0 = 50 GeV

mS0 = 60 GeV

mH0 = 400 GeV mA

0 = 600 GeV

(c)

1x10-2

2x10-2

5x10-2

1x10-1

2x10-1

5e-1

1 15 2 25 3 35 4 45 5

δ 23

δ13

mS0 = 10 GeV

mS0 = 20 GeV

mS0 = 30 GeV

mS0 = 40 GeV

mS0 = 50 GeV

mS0 = 60 GeV

mH0 = 600 GeV mA

0 = 400 GeV

(d)





0



H0

m2h0

[2minus

m2h0

m2H0



ndash 6 ndash






3x101

5x101

7x101

1x102

2x102

3x102

4x102

5x102

6x102

5 10 20 30 40 50 60 70 80

tan

β

mS0 in GeV

δ13 = 01

δ13 = 02

δ13 = 03

δ13 = 04

δ13 = 05


coupling

mH0 = 400 GeV mA


(a)

3x101

5x101

7x101

1x102

2x102

3x102

4x102

5x102

6x102

5 10 20 30 40 50 60 70 80

tan

β

mS0 in GeV

δ13 = 01

δ13 = 02

δ13 = 03

δ13 = 04

δ13 = 05


coupling

mH0 = mA


(b)

3x101

5x101

7x101

1x102

2x102

3x102

4x102

5x102

6x102

5 10 20 30 40 50 60 70 80

tan

β

mS0 in GeV

δ13 = 01

δ13 = 02

δ13 = 03

δ13 = 04

δ13 = 05


coupling

mH0 = 400 GeV mA


(c)

3x101

5x101

7x101

1x102

2x102

3x102

4x102

5x102

6x102

5 10 20 30 40 50 60 70 80

tan

β

mS0 in GeV

δ13 = 01

δ13 = 02

δ13 = 03

δ13 = 04

δ13 = 05


coupling

mH0 = 600 GeV mA


(d)



ndash 7 ndash







∣∣∣∣∣ξS0

Z0

ξh0

Z0

∣∣∣∣∣2


)equiv σSM


sin (β minus α)


) (33)



on∣∣∣ξS0

Z0




radicmmicrome


0

lmlv0



ndash 8 ndash

mS0(GeV) 12 15 20 25 30 35 40 45 50 55 60 65∣∣∣ξS0

Z0

∣∣∣ 285 316 398 530 751 1132 1028 457 260 199 169 093


Z0


574

5 10 20 24 30 40

10-6

10-5

10-4

10-3

10-2

10-1

100

101485

100 G

eV

2

50 G

eV

2

30 G

eV

2

20 G

eV

2

10 G

eV

2

H0rarr

τ+τ- F

orb

idd

en

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

Forbidden

(a) mH0 = 400 GeV mA0 = 200 GeV

574

5 10 20 24 30 40

10-6

10-5

10-4

10-3

10-2

10-1

100

101485

100 G

eV

2

50 G

eV

2

30 G

eV

2

20 G

eV

2

10 GeV2

H0rarr

τ+τ- F

orb

idd

en

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

Forbidden

(b) mH0 = 400 GeV mA0 = 400 GeV

574

5 10 20 24 30 40

10-6

10-5

10-4

10-3

10-2

10-1

100

101485

100 G

eV

2

50 G

eV

2

30 G

eV

2

20 G

eV

2

10 GeV2

H0rarr

τ+τ- F

orb

idd

en

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

Forbidden

(c) mH0 = 400 GeV mA0 = 600 GeV

574

5 10 20 24 30 40

10-6

10-5

10-4

10-3

10-2

10-1

100

101485

100 G

eV

2

50 G

eV

2

30 G

eV

2

20 G

eV

2

10 GeV2

H0rarr

τ+τ- F

orb

idd

en

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

Forbidden

(d) mH0 = 600 GeV mA0 = 400 GeV



12 = 0 GeV2




ndash 9 ndash

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2

30 GeV2

20 GeV2

10 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 400 GeV

mA0 = 200 GeV

(a)

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2

30 GeV2

20 GeV2

10 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 400 GeV

mA0 = 400 GeV

(b)

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2 30 GeV

2

20 GeV2

10 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 400 GeV

mA0 = 600 GeV

(c)

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2

30 GeV2

20 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 600 GeV

mA0 = 400 GeV

(d)







0


0


0



2

ndash 10 ndash

5 10 20 30 40 50 60200

300

400

500

600

700

800

900

1000m

H0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 20 GeV

2

(a)

5 10 20 30 40 50 60200

300

400

500

600

700

800

900

1000

1100

mH

0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 30 GeV

2

(b)

5 10 20 30 40 50 60200

300

400

500

600

700

800

900

1000

1100

1200

mH

0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 50 GeV

2

(c)

5 10 20 30 40 50 60100

200

300

400

500

600

700

800

900

1000

mH

0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 100 GeV

2

(d)


0






32πmh0

radic1minus

4m2S0

m2h0

(34)






ndash 11 ndash





12 ge10 GeV2







)minus 1 =


minus 1 (35)








ndash 12 ndash









dnχdt

+ 3a


(n2χ minus n2

χeq

)(42)

where aa =

radic8πρ


n2χeq = g

(mχT2π

) 32

exp[minusmχT




MPl


xF)

(43)


mχTF

is given by

xF = ln

c (c+ 2)

radic45

8

gMPl mχ

(a+ 6 b

xF

)2π3radic


(44)

ndash 13 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 50 GeV

2

(f)






ndash 14 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 50 GeV

2

(f)





ndash 15 ndash


12

)(

200 GeV 30 GeV2)(200 GeV 50 GeV2

)(400 GeV 30 GeV2

)(

400 GeV 50 GeV2)(600 GeV 30 GeV2

)and

(600 GeV 50 GeV2

)


42 Direct Detection



σγγN =

(αemZ

π

)2[micro2N

π

(αemZ

πm2S0

)2](

π2

12

)2(microNv

mτ

)2

2

(gχS0ξS

0

l

mτ

v0

)2

(45)



LS0gg

eff = minusξS

0

q

12π

αsvo

sumq=cbt

Iq




12π

ξS0

q gχS0

vom2S0

sumq=cbt

Iq


ndash 16 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 50 GeV

2

(f)




σggN =

(2ξS

0

q gχS0mN

m2S027vo


Iq

∣∣∣∣∣∣2

2

π(mχ +mN )2m2Nm

2χ (48)

ndash 17 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 50 GeV

2

(f)





2N

m2N

(ξS

0

τ

ξS0

q

)2(9

8

)2 v2


ndash 18 ndash




GamicroνGamicroν



Since mN equivsum



F gN = 1minussumuds

FqiNS (q2)

mN= minus 1

mN









ndash 19 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





ndash 20 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





ndash 21 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)




the reference [56]


f

π Ff (x) log

(s(1minusx)m2f


ndash 22 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)






ndash 23 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





x(413)

ndash 24 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





rang

ndash 25 ndash








ndash 26 ndash


5 Summary









ndash 27 ndash





Acknowledgments


ndash 28 ndash

Appendix

A Model Parameters


12

m211 = minus1

2

[m2H0 cos2 α+m2

h0 sin2 α+


h0)minus 2m2

12

tanβ

](A1)

m222 = minus1

2

[m2h0 cos2 α+m2

H0 sin2 α+


h0)minus 2m2

12

cotβ

](A2)

λ1 =1

v2o cos2 β

[m2H0 cos2 α+m2


](A3)

λ2 =1

v2o sin2 β

[m2h0 cos2 α+m2


](A4)

λ3 =2

v2o sin (2β)

[sinα cosα

(m2H0 minusm2

h0)minusm2

12 + m2H+ sin (2β)

](A5)

λ4 =1

v2o sin (2β)

[2m2

12 +(m2A0 minus 2m2

H+

)sin (2β)

](A6)

λ5 =1

v2o sin (2β)

[2m2


](A7)



Γ(S0 rarr f f) =Nc

8π

(ξSfmf

vo

)2

mS0

(1minus

4m2f

m2S0

)32




0

V )2

16π v2o

m3S0

(1minus

4m2W

m2S0

)12[

12

(mW

mS0

)4

minus 4

(mW

mS0

)2

+ 1





8πmS0

(1minus

4m2χ

m2S0

)32



Γ(S0 rarr gg) =

(mtξ

S0

q

vo

)2α2s

72π3

m3S0

m2t


Iq

∣∣∣∣∣∣2

(B5)

ndash 29 ndash



16πv20

(αemπ

)2∣∣∣∣∣sumq

ξS0

q Q2qIq +

suml

ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn

∣∣∣∣∣2







f(λ) as

f(λ) = minus2

(sinminus1 1

2radicλ

)2

for λ gt1

4

=1

2

(lnη+

ηminus

)2

minus π2

2minus iπ η

+

ηminus for λ lt

1

4(B8)


radic14 minus λ




=

(mfξ

S0

f

vo

)2

g2χS0

1

4π

(1minus

m2l

m2χ

) 32 m2

χ

(4m2χ minusm2

φ)2

(3

xf

)θ (mχ minusmf )


)vrang

=

(ξS

0

V

vo

)2g2χS0

8π

radic1minus

m2Z

m2χ

(16m4χ + 12m4

Z minus 16m2χm

2Z)

(4m2χ minusm2

S0)2

(3

xf


σ(χχrarrW+Wminus

)vrang

=

(ξS

0

V

vo

)2g2χS0

16π

radic1minus

m2W

m2χ

(16m4χ + 12m4

W minus 16m2χm

2W )

(4m2χ minusm2

S0)2

(3

xf



(ξS

0

q αs gχS0

3π32vo

)2m4χ

(4m2χ minusm2

S0)2 +m2S0Γ

(3

2xf


Iq

∣∣∣∣∣∣2

(C4)


2em

2π3v2o

m4χ


q Q2qIq +

suml ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn


S0)2 +m2S0Γ2

times(

3

xf

)(C5)

ndash 30 ndash


rang= c0


C2S0HiHj

g2χS0

16πλ

12

(1m2Hi

4m2χ

m2Hj

4m2χ

)

times 1

(4m2χ minusm2

φ)2

(3

xf

)(C6)




)vrang

=3g4χS0

64πm2χ

(3

xf





m2h0

and s0 =m2

12

m2h0 All


Ch0S0S0 =δ213m

2h0

vo

(minus4δ213r

20

tanβ+

2δ213r0tanβ

minus 8r30tan4 β

+8r20s0tan3 β

+4r20

tan4 βminus 8r0s0

tan3 βminus 8r0s0

tanβ

+2r0

tan4 βminus 2r0

tan2 β+

2s0tan3 β


minus 1

tan4 βminus 2

tan2 βminus 1

)(D1)

CS0h0h0 =δ13m

2h0

vo

(minus4δ213r

20

tan2 β+

2δ213r0tan2 β


tan3 βminus 4r0

tanβ

)(D2)

CS0H0H0 =δ13m

2h0

vo

(minus8δ213r

30

tan2 β+

12δ213r20


tan2 βminus 6r20

tan5 βminus 4r20

tan3 β+

2r20tanβ

+6r0s0tan4 β

+4r0s0tan2 β

minus2r0s0 +3r0

tan5 β+

r0tan3 β


minus 3s0tan4 β


+ 3s0

)(D3)

CS0S0H0 =δ213m

2h0

vo

(minus8δ213r

30

tan2 β+

8δ213r20


tan2 β+

12r30tan5 β

+4r30


tan4 βminus 4r20s0

tan2 βminus 12r20

tan5 β

+8r20

tanβ+

12r0s0tan4 β

+8r0s0tan2 β

minus 4r0s0 +3r0

tan5 βminus r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D4)

CS0H0h0 =δ13m

2h0

vo

(minus4δ213r

30

tan3 β+

4δ213r20


20

tanβminus δ213r0

tan3 β+

3δ213r0tanβ

+4r20

tan4 β+

4r20tan2 β

minus 4r0s0tan3 β

minus4r0s0tanβ

minus 3r0tan2 β

minus r0 +2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1

)(D5)

ndash 31 ndash

CS0H+Hminus =δ13m

2h0

vo

(minus 2r20

tan5 β+

2r20tanβ

+2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0 +r0

tan5 βminus r0


minus 5r0tanβ

minus s0tan4 β


+ s0 minus4m2

Hplusmnr0

tan3 βm2h0

minus4m2

Hplusmnr0

tanβm2h0

)(D6)

CS0A0A0 =δ13m

2h0

vo

(minus

4m2A0r0

tan3 βm2h0

minus4m2

A0r0tanβm2

h0

minus 2r20tan5 β

+2r20

tanβ+

2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0

+r0

tan5 βminus r0


tanβminus s0


tan2 β+ s0

)(D7)

CS0S0S0 =δ313m

2h0

vo

(minus 24r40

tan5 β+

24r30s0tan4 β

+36r30

tan5 βminus 12r30



tan2 βminus 18r20

tan5 β+

12r20tan3 β

+18r20tanβ

+18r0s0tan4 β

+12r0s0tan2 β

minus 6r0s0 +3r0

tan5 βminus 3r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D8)

Ch0H+Hminus =m2h0

vo

(2δ213r0tanβ

+2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1minus

2m2Hplusmn

tan4 βm2h0

minus4m2

Hplusmn

tan2 βm2h0

minus2m2

Hplusmn

m2h0

) (D9)

References










ndash 32 ndash























ndash 33 ndash






















ndash 34 ndash








ndash 35 ndash

1 Introduction

2 The Model








42 Direct Detection


5 Summary

A Model Parameters




5x10-3

8x10-3

1x10-2

2x10-2

5x10-2

8x10-2

1x10-1

2x10-1

1 15 2 25 3 35 4 45 5

δ 23

δ13

mS0 = 10 GeV

mS0 = 20 GeV

mS0 = 30 GeV

mS0 = 40 GeV

mS0 = 50 GeV

mS0 = 60 GeV

mH0 = 400 GeV mA

0 = 200 GeV

(a)

5x10-3

8x10-3

1x10-2

2x10-2

5x10-2

8x10-2

1x10-1

2x10-1

1 15 2 25 3 35 4 45 5

δ 23

δ13

mS0 = 10 GeV

mS0 = 20 GeV

mS0 = 30 GeV

mS0 = 40 GeV

mS0 = 50 GeV

mS0 = 60 GeV

mH0 = 400 GeV mA

0 = 400 GeV

(b)

5x10-3

8x10-3

1x10-2

2x10-2

5x10-2

8x10-2

1x10-1

2x10-1

1 15 2 25 3 35 4 45 5

δ 23

δ13

mS0 = 10 GeV

mS0 = 20 GeV

mS0 = 30 GeV

mS0 = 40 GeV

mS0 = 50 GeV

mS0 = 60 GeV

mH0 = 400 GeV mA

0 = 600 GeV

(c)

1x10-2

2x10-2

5x10-2

1x10-1

2x10-1

5e-1

1 15 2 25 3 35 4 45 5

δ 23

δ13

mS0 = 10 GeV

mS0 = 20 GeV

mS0 = 30 GeV

mS0 = 40 GeV

mS0 = 50 GeV

mS0 = 60 GeV

mH0 = 600 GeV mA

0 = 400 GeV

(d)





0



H0

m2h0

[2minus

m2h0

m2H0



ndash 6 ndash






3x101

5x101

7x101

1x102

2x102

3x102

4x102

5x102

6x102

5 10 20 30 40 50 60 70 80

tan

β

mS0 in GeV

δ13 = 01

δ13 = 02

δ13 = 03

δ13 = 04

δ13 = 05


coupling

mH0 = 400 GeV mA


(a)

3x101

5x101

7x101

1x102

2x102

3x102

4x102

5x102

6x102

5 10 20 30 40 50 60 70 80

tan

β

mS0 in GeV

δ13 = 01

δ13 = 02

δ13 = 03

δ13 = 04

δ13 = 05


coupling

mH0 = mA


(b)

3x101

5x101

7x101

1x102

2x102

3x102

4x102

5x102

6x102

5 10 20 30 40 50 60 70 80

tan

β

mS0 in GeV

δ13 = 01

δ13 = 02

δ13 = 03

δ13 = 04

δ13 = 05


coupling

mH0 = 400 GeV mA


(c)

3x101

5x101

7x101

1x102

2x102

3x102

4x102

5x102

6x102

5 10 20 30 40 50 60 70 80

tan

β

mS0 in GeV

δ13 = 01

δ13 = 02

δ13 = 03

δ13 = 04

δ13 = 05


coupling

mH0 = 600 GeV mA


(d)



ndash 7 ndash







∣∣∣∣∣ξS0

Z0

ξh0

Z0

∣∣∣∣∣2


)equiv σSM


sin (β minus α)


) (33)



on∣∣∣ξS0

Z0




radicmmicrome


0

lmlv0



ndash 8 ndash

mS0(GeV) 12 15 20 25 30 35 40 45 50 55 60 65∣∣∣ξS0

Z0

∣∣∣ 285 316 398 530 751 1132 1028 457 260 199 169 093


Z0


574

5 10 20 24 30 40

10-6

10-5

10-4

10-3

10-2

10-1

100

101485

100 G

eV

2

50 G

eV

2

30 G

eV

2

20 G

eV

2

10 G

eV

2

H0rarr

τ+τ- F

orb

idd

en

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

Forbidden

(a) mH0 = 400 GeV mA0 = 200 GeV

574

5 10 20 24 30 40

10-6

10-5

10-4

10-3

10-2

10-1

100

101485

100 G

eV

2

50 G

eV

2

30 G

eV

2

20 G

eV

2

10 GeV2

H0rarr

τ+τ- F

orb

idd

en

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

Forbidden

(b) mH0 = 400 GeV mA0 = 400 GeV

574

5 10 20 24 30 40

10-6

10-5

10-4

10-3

10-2

10-1

100

101485

100 G

eV

2

50 G

eV

2

30 G

eV

2

20 G

eV

2

10 GeV2

H0rarr

τ+τ- F

orb

idd

en

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

Forbidden

(c) mH0 = 400 GeV mA0 = 600 GeV

574

5 10 20 24 30 40

10-6

10-5

10-4

10-3

10-2

10-1

100

101485

100 G

eV

2

50 G

eV

2

30 G

eV

2

20 G

eV

2

10 GeV2

H0rarr

τ+τ- F

orb

idd

en

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

Forbidden

(d) mH0 = 600 GeV mA0 = 400 GeV



12 = 0 GeV2




ndash 9 ndash

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2

30 GeV2

20 GeV2

10 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 400 GeV

mA0 = 200 GeV

(a)

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2

30 GeV2

20 GeV2

10 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 400 GeV

mA0 = 400 GeV

(b)

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2 30 GeV

2

20 GeV2

10 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 400 GeV

mA0 = 600 GeV

(c)

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2

30 GeV2

20 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 600 GeV

mA0 = 400 GeV

(d)







0


0


0



2

ndash 10 ndash

5 10 20 30 40 50 60200

300

400

500

600

700

800

900

1000m

H0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 20 GeV

2

(a)

5 10 20 30 40 50 60200

300

400

500

600

700

800

900

1000

1100

mH

0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 30 GeV

2

(b)

5 10 20 30 40 50 60200

300

400

500

600

700

800

900

1000

1100

1200

mH

0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 50 GeV

2

(c)

5 10 20 30 40 50 60100

200

300

400

500

600

700

800

900

1000

mH

0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 100 GeV

2

(d)


0






32πmh0

radic1minus

4m2S0

m2h0

(34)






ndash 11 ndash





12 ge10 GeV2







)minus 1 =


minus 1 (35)








ndash 12 ndash









dnχdt

+ 3a


(n2χ minus n2

χeq

)(42)

where aa =

radic8πρ


n2χeq = g

(mχT2π

) 32

exp[minusmχT




MPl


xF)

(43)


mχTF

is given by

xF = ln

c (c+ 2)

radic45

8

gMPl mχ

(a+ 6 b

xF

)2π3radic


(44)

ndash 13 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 50 GeV

2

(f)






ndash 14 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 50 GeV

2

(f)





ndash 15 ndash


12

)(

200 GeV 30 GeV2)(200 GeV 50 GeV2

)(400 GeV 30 GeV2

)(

400 GeV 50 GeV2)(600 GeV 30 GeV2

)and

(600 GeV 50 GeV2

)


42 Direct Detection



σγγN =

(αemZ

π

)2[micro2N

π

(αemZ

πm2S0

)2](

π2

12

)2(microNv

mτ

)2

2

(gχS0ξS

0

l

mτ

v0

)2

(45)



LS0gg

eff = minusξS

0

q

12π

αsvo

sumq=cbt

Iq




12π

ξS0

q gχS0

vom2S0

sumq=cbt

Iq


ndash 16 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 50 GeV

2

(f)




σggN =

(2ξS

0

q gχS0mN

m2S027vo


Iq

∣∣∣∣∣∣2

2

π(mχ +mN )2m2Nm

2χ (48)

ndash 17 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 50 GeV

2

(f)





2N

m2N

(ξS

0

τ

ξS0

q

)2(9

8

)2 v2


ndash 18 ndash




GamicroνGamicroν



Since mN equivsum



F gN = 1minussumuds

FqiNS (q2)

mN= minus 1

mN









ndash 19 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





ndash 20 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





ndash 21 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)




the reference [56]


f

π Ff (x) log

(s(1minusx)m2f


ndash 22 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)






ndash 23 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





x(413)

ndash 24 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





rang

ndash 25 ndash








ndash 26 ndash


5 Summary









ndash 27 ndash





Acknowledgments


ndash 28 ndash

Appendix

A Model Parameters


12

m211 = minus1

2

[m2H0 cos2 α+m2

h0 sin2 α+


h0)minus 2m2

12

tanβ

](A1)

m222 = minus1

2

[m2h0 cos2 α+m2

H0 sin2 α+


h0)minus 2m2

12

cotβ

](A2)

λ1 =1

v2o cos2 β

[m2H0 cos2 α+m2


](A3)

λ2 =1

v2o sin2 β

[m2h0 cos2 α+m2


](A4)

λ3 =2

v2o sin (2β)

[sinα cosα

(m2H0 minusm2

h0)minusm2

12 + m2H+ sin (2β)

](A5)

λ4 =1

v2o sin (2β)

[2m2

12 +(m2A0 minus 2m2

H+

)sin (2β)

](A6)

λ5 =1

v2o sin (2β)

[2m2


](A7)



Γ(S0 rarr f f) =Nc

8π

(ξSfmf

vo

)2

mS0

(1minus

4m2f

m2S0

)32




0

V )2

16π v2o

m3S0

(1minus

4m2W

m2S0

)12[

12

(mW

mS0

)4

minus 4

(mW

mS0

)2

+ 1





8πmS0

(1minus

4m2χ

m2S0

)32



Γ(S0 rarr gg) =

(mtξ

S0

q

vo

)2α2s

72π3

m3S0

m2t


Iq

∣∣∣∣∣∣2

(B5)

ndash 29 ndash



16πv20

(αemπ

)2∣∣∣∣∣sumq

ξS0

q Q2qIq +

suml

ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn

∣∣∣∣∣2







f(λ) as

f(λ) = minus2

(sinminus1 1

2radicλ

)2

for λ gt1

4

=1

2

(lnη+

ηminus

)2

minus π2

2minus iπ η

+

ηminus for λ lt

1

4(B8)


radic14 minus λ




=

(mfξ

S0

f

vo

)2

g2χS0

1

4π

(1minus

m2l

m2χ

) 32 m2

χ

(4m2χ minusm2

φ)2

(3

xf

)θ (mχ minusmf )


)vrang

=

(ξS

0

V

vo

)2g2χS0

8π

radic1minus

m2Z

m2χ

(16m4χ + 12m4

Z minus 16m2χm

2Z)

(4m2χ minusm2

S0)2

(3

xf


σ(χχrarrW+Wminus

)vrang

=

(ξS

0

V

vo

)2g2χS0

16π

radic1minus

m2W

m2χ

(16m4χ + 12m4

W minus 16m2χm

2W )

(4m2χ minusm2

S0)2

(3

xf



(ξS

0

q αs gχS0

3π32vo

)2m4χ

(4m2χ minusm2

S0)2 +m2S0Γ

(3

2xf


Iq

∣∣∣∣∣∣2

(C4)


2em

2π3v2o

m4χ


q Q2qIq +

suml ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn


S0)2 +m2S0Γ2

times(

3

xf

)(C5)

ndash 30 ndash


rang= c0


C2S0HiHj

g2χS0

16πλ

12

(1m2Hi

4m2χ

m2Hj

4m2χ

)

times 1

(4m2χ minusm2

φ)2

(3

xf

)(C6)




)vrang

=3g4χS0

64πm2χ

(3

xf





m2h0

and s0 =m2

12

m2h0 All


Ch0S0S0 =δ213m

2h0

vo

(minus4δ213r

20

tanβ+

2δ213r0tanβ

minus 8r30tan4 β

+8r20s0tan3 β

+4r20

tan4 βminus 8r0s0

tan3 βminus 8r0s0

tanβ

+2r0

tan4 βminus 2r0

tan2 β+

2s0tan3 β


minus 1

tan4 βminus 2

tan2 βminus 1

)(D1)

CS0h0h0 =δ13m

2h0

vo

(minus4δ213r

20

tan2 β+

2δ213r0tan2 β


tan3 βminus 4r0

tanβ

)(D2)

CS0H0H0 =δ13m

2h0

vo

(minus8δ213r

30

tan2 β+

12δ213r20


tan2 βminus 6r20

tan5 βminus 4r20

tan3 β+

2r20tanβ

+6r0s0tan4 β

+4r0s0tan2 β

minus2r0s0 +3r0

tan5 β+

r0tan3 β


minus 3s0tan4 β


+ 3s0

)(D3)

CS0S0H0 =δ213m

2h0

vo

(minus8δ213r

30

tan2 β+

8δ213r20


tan2 β+

12r30tan5 β

+4r30


tan4 βminus 4r20s0

tan2 βminus 12r20

tan5 β

+8r20

tanβ+

12r0s0tan4 β

+8r0s0tan2 β

minus 4r0s0 +3r0

tan5 βminus r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D4)

CS0H0h0 =δ13m

2h0

vo

(minus4δ213r

30

tan3 β+

4δ213r20


20

tanβminus δ213r0

tan3 β+

3δ213r0tanβ

+4r20

tan4 β+

4r20tan2 β

minus 4r0s0tan3 β

minus4r0s0tanβ

minus 3r0tan2 β

minus r0 +2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1

)(D5)

ndash 31 ndash

CS0H+Hminus =δ13m

2h0

vo

(minus 2r20

tan5 β+

2r20tanβ

+2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0 +r0

tan5 βminus r0


minus 5r0tanβ

minus s0tan4 β


+ s0 minus4m2

Hplusmnr0

tan3 βm2h0

minus4m2

Hplusmnr0

tanβm2h0

)(D6)

CS0A0A0 =δ13m

2h0

vo

(minus

4m2A0r0

tan3 βm2h0

minus4m2

A0r0tanβm2

h0

minus 2r20tan5 β

+2r20

tanβ+

2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0

+r0

tan5 βminus r0


tanβminus s0


tan2 β+ s0

)(D7)

CS0S0S0 =δ313m

2h0

vo

(minus 24r40

tan5 β+

24r30s0tan4 β

+36r30

tan5 βminus 12r30



tan2 βminus 18r20

tan5 β+

12r20tan3 β

+18r20tanβ

+18r0s0tan4 β

+12r0s0tan2 β

minus 6r0s0 +3r0

tan5 βminus 3r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D8)

Ch0H+Hminus =m2h0

vo

(2δ213r0tanβ

+2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1minus

2m2Hplusmn

tan4 βm2h0

minus4m2

Hplusmn

tan2 βm2h0

minus2m2

Hplusmn

m2h0

) (D9)

References










ndash 32 ndash























ndash 33 ndash






















ndash 34 ndash








ndash 35 ndash

1 Introduction

2 The Model








42 Direct Detection


5 Summary

A Model Parameters









3x101

5x101

7x101

1x102

2x102

3x102

4x102

5x102

6x102

5 10 20 30 40 50 60 70 80

tan

β

mS0 in GeV

δ13 = 01

δ13 = 02

δ13 = 03

δ13 = 04

δ13 = 05


coupling

mH0 = 400 GeV mA


(a)

3x101

5x101

7x101

1x102

2x102

3x102

4x102

5x102

6x102

5 10 20 30 40 50 60 70 80

tan

β

mS0 in GeV

δ13 = 01

δ13 = 02

δ13 = 03

δ13 = 04

δ13 = 05


coupling

mH0 = mA


(b)

3x101

5x101

7x101

1x102

2x102

3x102

4x102

5x102

6x102

5 10 20 30 40 50 60 70 80

tan

β

mS0 in GeV

δ13 = 01

δ13 = 02

δ13 = 03

δ13 = 04

δ13 = 05


coupling

mH0 = 400 GeV mA


(c)

3x101

5x101

7x101

1x102

2x102

3x102

4x102

5x102

6x102

5 10 20 30 40 50 60 70 80

tan

β

mS0 in GeV

δ13 = 01

δ13 = 02

δ13 = 03

δ13 = 04

δ13 = 05


coupling

mH0 = 600 GeV mA


(d)



ndash 7 ndash







∣∣∣∣∣ξS0

Z0

ξh0

Z0

∣∣∣∣∣2


)equiv σSM


sin (β minus α)


) (33)



on∣∣∣ξS0

Z0




radicmmicrome


0

lmlv0



ndash 8 ndash

mS0(GeV) 12 15 20 25 30 35 40 45 50 55 60 65∣∣∣ξS0

Z0

∣∣∣ 285 316 398 530 751 1132 1028 457 260 199 169 093


Z0


574

5 10 20 24 30 40

10-6

10-5

10-4

10-3

10-2

10-1

100

101485

100 G

eV

2

50 G

eV

2

30 G

eV

2

20 G

eV

2

10 G

eV

2

H0rarr

τ+τ- F

orb

idd

en

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

Forbidden

(a) mH0 = 400 GeV mA0 = 200 GeV

574

5 10 20 24 30 40

10-6

10-5

10-4

10-3

10-2

10-1

100

101485

100 G

eV

2

50 G

eV

2

30 G

eV

2

20 G

eV

2

10 GeV2

H0rarr

τ+τ- F

orb

idd

en

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

Forbidden

(b) mH0 = 400 GeV mA0 = 400 GeV

574

5 10 20 24 30 40

10-6

10-5

10-4

10-3

10-2

10-1

100

101485

100 G

eV

2

50 G

eV

2

30 G

eV

2

20 G

eV

2

10 GeV2

H0rarr

τ+τ- F

orb

idd

en

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

Forbidden

(c) mH0 = 400 GeV mA0 = 600 GeV

574

5 10 20 24 30 40

10-6

10-5

10-4

10-3

10-2

10-1

100

101485

100 G

eV

2

50 G

eV

2

30 G

eV

2

20 G

eV

2

10 GeV2

H0rarr

τ+τ- F

orb

idd

en

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

Forbidden

(d) mH0 = 600 GeV mA0 = 400 GeV



12 = 0 GeV2




ndash 9 ndash

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2

30 GeV2

20 GeV2

10 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 400 GeV

mA0 = 200 GeV

(a)

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2

30 GeV2

20 GeV2

10 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 400 GeV

mA0 = 400 GeV

(b)

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2 30 GeV

2

20 GeV2

10 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 400 GeV

mA0 = 600 GeV

(c)

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2

30 GeV2

20 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 600 GeV

mA0 = 400 GeV

(d)







0


0


0



2

ndash 10 ndash

5 10 20 30 40 50 60200

300

400

500

600

700

800

900

1000m

H0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 20 GeV

2

(a)

5 10 20 30 40 50 60200

300

400

500

600

700

800

900

1000

1100

mH

0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 30 GeV

2

(b)

5 10 20 30 40 50 60200

300

400

500

600

700

800

900

1000

1100

1200

mH

0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 50 GeV

2

(c)

5 10 20 30 40 50 60100

200

300

400

500

600

700

800

900

1000

mH

0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 100 GeV

2

(d)


0






32πmh0

radic1minus

4m2S0

m2h0

(34)






ndash 11 ndash





12 ge10 GeV2







)minus 1 =


minus 1 (35)








ndash 12 ndash









dnχdt

+ 3a


(n2χ minus n2

χeq

)(42)

where aa =

radic8πρ


n2χeq = g

(mχT2π

) 32

exp[minusmχT




MPl


xF)

(43)


mχTF

is given by

xF = ln

c (c+ 2)

radic45

8

gMPl mχ

(a+ 6 b

xF

)2π3radic


(44)

ndash 13 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 50 GeV

2

(f)






ndash 14 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 50 GeV

2

(f)





ndash 15 ndash


12

)(

200 GeV 30 GeV2)(200 GeV 50 GeV2

)(400 GeV 30 GeV2

)(

400 GeV 50 GeV2)(600 GeV 30 GeV2

)and

(600 GeV 50 GeV2

)


42 Direct Detection



σγγN =

(αemZ

π

)2[micro2N

π

(αemZ

πm2S0

)2](

π2

12

)2(microNv

mτ

)2

2

(gχS0ξS

0

l

mτ

v0

)2

(45)



LS0gg

eff = minusξS

0

q

12π

αsvo

sumq=cbt

Iq




12π

ξS0

q gχS0

vom2S0

sumq=cbt

Iq


ndash 16 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 50 GeV

2

(f)




σggN =

(2ξS

0

q gχS0mN

m2S027vo


Iq

∣∣∣∣∣∣2

2

π(mχ +mN )2m2Nm

2χ (48)

ndash 17 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 50 GeV

2

(f)





2N

m2N

(ξS

0

τ

ξS0

q

)2(9

8

)2 v2


ndash 18 ndash




GamicroνGamicroν



Since mN equivsum



F gN = 1minussumuds

FqiNS (q2)

mN= minus 1

mN









ndash 19 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





ndash 20 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





ndash 21 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)




the reference [56]


f

π Ff (x) log

(s(1minusx)m2f


ndash 22 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)






ndash 23 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





x(413)

ndash 24 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





rang

ndash 25 ndash








ndash 26 ndash


5 Summary









ndash 27 ndash





Acknowledgments


ndash 28 ndash

Appendix

A Model Parameters


12

m211 = minus1

2

[m2H0 cos2 α+m2

h0 sin2 α+


h0)minus 2m2

12

tanβ

](A1)

m222 = minus1

2

[m2h0 cos2 α+m2

H0 sin2 α+


h0)minus 2m2

12

cotβ

](A2)

λ1 =1

v2o cos2 β

[m2H0 cos2 α+m2


](A3)

λ2 =1

v2o sin2 β

[m2h0 cos2 α+m2


](A4)

λ3 =2

v2o sin (2β)

[sinα cosα

(m2H0 minusm2

h0)minusm2

12 + m2H+ sin (2β)

](A5)

λ4 =1

v2o sin (2β)

[2m2

12 +(m2A0 minus 2m2

H+

)sin (2β)

](A6)

λ5 =1

v2o sin (2β)

[2m2


](A7)



Γ(S0 rarr f f) =Nc

8π

(ξSfmf

vo

)2

mS0

(1minus

4m2f

m2S0

)32




0

V )2

16π v2o

m3S0

(1minus

4m2W

m2S0

)12[

12

(mW

mS0

)4

minus 4

(mW

mS0

)2

+ 1





8πmS0

(1minus

4m2χ

m2S0

)32



Γ(S0 rarr gg) =

(mtξ

S0

q

vo

)2α2s

72π3

m3S0

m2t


Iq

∣∣∣∣∣∣2

(B5)

ndash 29 ndash



16πv20

(αemπ

)2∣∣∣∣∣sumq

ξS0

q Q2qIq +

suml

ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn

∣∣∣∣∣2







f(λ) as

f(λ) = minus2

(sinminus1 1

2radicλ

)2

for λ gt1

4

=1

2

(lnη+

ηminus

)2

minus π2

2minus iπ η

+

ηminus for λ lt

1

4(B8)


radic14 minus λ




=

(mfξ

S0

f

vo

)2

g2χS0

1

4π

(1minus

m2l

m2χ

) 32 m2

χ

(4m2χ minusm2

φ)2

(3

xf

)θ (mχ minusmf )


)vrang

=

(ξS

0

V

vo

)2g2χS0

8π

radic1minus

m2Z

m2χ

(16m4χ + 12m4

Z minus 16m2χm

2Z)

(4m2χ minusm2

S0)2

(3

xf


σ(χχrarrW+Wminus

)vrang

=

(ξS

0

V

vo

)2g2χS0

16π

radic1minus

m2W

m2χ

(16m4χ + 12m4

W minus 16m2χm

2W )

(4m2χ minusm2

S0)2

(3

xf



(ξS

0

q αs gχS0

3π32vo

)2m4χ

(4m2χ minusm2

S0)2 +m2S0Γ

(3

2xf


Iq

∣∣∣∣∣∣2

(C4)


2em

2π3v2o

m4χ


q Q2qIq +

suml ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn


S0)2 +m2S0Γ2

times(

3

xf

)(C5)

ndash 30 ndash


rang= c0


C2S0HiHj

g2χS0

16πλ

12

(1m2Hi

4m2χ

m2Hj

4m2χ

)

times 1

(4m2χ minusm2

φ)2

(3

xf

)(C6)




)vrang

=3g4χS0

64πm2χ

(3

xf





m2h0

and s0 =m2

12

m2h0 All


Ch0S0S0 =δ213m

2h0

vo

(minus4δ213r

20

tanβ+

2δ213r0tanβ

minus 8r30tan4 β

+8r20s0tan3 β

+4r20

tan4 βminus 8r0s0

tan3 βminus 8r0s0

tanβ

+2r0

tan4 βminus 2r0

tan2 β+

2s0tan3 β


minus 1

tan4 βminus 2

tan2 βminus 1

)(D1)

CS0h0h0 =δ13m

2h0

vo

(minus4δ213r

20

tan2 β+

2δ213r0tan2 β


tan3 βminus 4r0

tanβ

)(D2)

CS0H0H0 =δ13m

2h0

vo

(minus8δ213r

30

tan2 β+

12δ213r20


tan2 βminus 6r20

tan5 βminus 4r20

tan3 β+

2r20tanβ

+6r0s0tan4 β

+4r0s0tan2 β

minus2r0s0 +3r0

tan5 β+

r0tan3 β


minus 3s0tan4 β


+ 3s0

)(D3)

CS0S0H0 =δ213m

2h0

vo

(minus8δ213r

30

tan2 β+

8δ213r20


tan2 β+

12r30tan5 β

+4r30


tan4 βminus 4r20s0

tan2 βminus 12r20

tan5 β

+8r20

tanβ+

12r0s0tan4 β

+8r0s0tan2 β

minus 4r0s0 +3r0

tan5 βminus r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D4)

CS0H0h0 =δ13m

2h0

vo

(minus4δ213r

30

tan3 β+

4δ213r20


20

tanβminus δ213r0

tan3 β+

3δ213r0tanβ

+4r20

tan4 β+

4r20tan2 β

minus 4r0s0tan3 β

minus4r0s0tanβ

minus 3r0tan2 β

minus r0 +2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1

)(D5)

ndash 31 ndash

CS0H+Hminus =δ13m

2h0

vo

(minus 2r20

tan5 β+

2r20tanβ

+2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0 +r0

tan5 βminus r0


minus 5r0tanβ

minus s0tan4 β


+ s0 minus4m2

Hplusmnr0

tan3 βm2h0

minus4m2

Hplusmnr0

tanβm2h0

)(D6)

CS0A0A0 =δ13m

2h0

vo

(minus

4m2A0r0

tan3 βm2h0

minus4m2

A0r0tanβm2

h0

minus 2r20tan5 β

+2r20

tanβ+

2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0

+r0

tan5 βminus r0


tanβminus s0


tan2 β+ s0

)(D7)

CS0S0S0 =δ313m

2h0

vo

(minus 24r40

tan5 β+

24r30s0tan4 β

+36r30

tan5 βminus 12r30



tan2 βminus 18r20

tan5 β+

12r20tan3 β

+18r20tanβ

+18r0s0tan4 β

+12r0s0tan2 β

minus 6r0s0 +3r0

tan5 βminus 3r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D8)

Ch0H+Hminus =m2h0

vo

(2δ213r0tanβ

+2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1minus

2m2Hplusmn

tan4 βm2h0

minus4m2

Hplusmn

tan2 βm2h0

minus2m2

Hplusmn

m2h0

) (D9)

References










ndash 32 ndash























ndash 33 ndash






















ndash 34 ndash








ndash 35 ndash

1 Introduction

2 The Model








42 Direct Detection


5 Summary

A Model Parameters










∣∣∣∣∣ξS0

Z0

ξh0

Z0

∣∣∣∣∣2


)equiv σSM


sin (β minus α)


) (33)



on∣∣∣ξS0

Z0




radicmmicrome


0

lmlv0



ndash 8 ndash

mS0(GeV) 12 15 20 25 30 35 40 45 50 55 60 65∣∣∣ξS0

Z0

∣∣∣ 285 316 398 530 751 1132 1028 457 260 199 169 093


Z0


574

5 10 20 24 30 40

10-6

10-5

10-4

10-3

10-2

10-1

100

101485

100 G

eV

2

50 G

eV

2

30 G

eV

2

20 G

eV

2

10 G

eV

2

H0rarr

τ+τ- F

orb

idd

en

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

Forbidden

(a) mH0 = 400 GeV mA0 = 200 GeV

574

5 10 20 24 30 40

10-6

10-5

10-4

10-3

10-2

10-1

100

101485

100 G

eV

2

50 G

eV

2

30 G

eV

2

20 G

eV

2

10 GeV2

H0rarr

τ+τ- F

orb

idd

en

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

Forbidden

(b) mH0 = 400 GeV mA0 = 400 GeV

574

5 10 20 24 30 40

10-6

10-5

10-4

10-3

10-2

10-1

100

101485

100 G

eV

2

50 G

eV

2

30 G

eV

2

20 G

eV

2

10 GeV2

H0rarr

τ+τ- F

orb

idd

en

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

Forbidden

(c) mH0 = 400 GeV mA0 = 600 GeV

574

5 10 20 24 30 40

10-6

10-5

10-4

10-3

10-2

10-1

100

101485

100 G

eV

2

50 G

eV

2

30 G

eV

2

20 G

eV

2

10 GeV2

H0rarr

τ+τ- F

orb

idd

en

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

Forbidden

(d) mH0 = 600 GeV mA0 = 400 GeV



12 = 0 GeV2




ndash 9 ndash

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2

30 GeV2

20 GeV2

10 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 400 GeV

mA0 = 200 GeV

(a)

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2

30 GeV2

20 GeV2

10 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 400 GeV

mA0 = 400 GeV

(b)

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2 30 GeV

2

20 GeV2

10 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 400 GeV

mA0 = 600 GeV

(c)

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2

30 GeV2

20 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 600 GeV

mA0 = 400 GeV

(d)







0


0


0



2

ndash 10 ndash

5 10 20 30 40 50 60200

300

400

500

600

700

800

900

1000m

H0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 20 GeV

2

(a)

5 10 20 30 40 50 60200

300

400

500

600

700

800

900

1000

1100

mH

0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 30 GeV

2

(b)

5 10 20 30 40 50 60200

300

400

500

600

700

800

900

1000

1100

1200

mH

0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 50 GeV

2

(c)

5 10 20 30 40 50 60100

200

300

400

500

600

700

800

900

1000

mH

0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 100 GeV

2

(d)


0






32πmh0

radic1minus

4m2S0

m2h0

(34)






ndash 11 ndash





12 ge10 GeV2







)minus 1 =


minus 1 (35)








ndash 12 ndash









dnχdt

+ 3a


(n2χ minus n2

χeq

)(42)

where aa =

radic8πρ


n2χeq = g

(mχT2π

) 32

exp[minusmχT




MPl


xF)

(43)


mχTF

is given by

xF = ln

c (c+ 2)

radic45

8

gMPl mχ

(a+ 6 b

xF

)2π3radic


(44)

ndash 13 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 50 GeV

2

(f)






ndash 14 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 50 GeV

2

(f)





ndash 15 ndash


12

)(

200 GeV 30 GeV2)(200 GeV 50 GeV2

)(400 GeV 30 GeV2

)(

400 GeV 50 GeV2)(600 GeV 30 GeV2

)and

(600 GeV 50 GeV2

)


42 Direct Detection



σγγN =

(αemZ

π

)2[micro2N

π

(αemZ

πm2S0

)2](

π2

12

)2(microNv

mτ

)2

2

(gχS0ξS

0

l

mτ

v0

)2

(45)



LS0gg

eff = minusξS

0

q

12π

αsvo

sumq=cbt

Iq




12π

ξS0

q gχS0

vom2S0

sumq=cbt

Iq


ndash 16 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 50 GeV

2

(f)




σggN =

(2ξS

0

q gχS0mN

m2S027vo


Iq

∣∣∣∣∣∣2

2

π(mχ +mN )2m2Nm

2χ (48)

ndash 17 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 50 GeV

2

(f)





2N

m2N

(ξS

0

τ

ξS0

q

)2(9

8

)2 v2


ndash 18 ndash




GamicroνGamicroν



Since mN equivsum



F gN = 1minussumuds

FqiNS (q2)

mN= minus 1

mN









ndash 19 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





ndash 20 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





ndash 21 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)




the reference [56]


f

π Ff (x) log

(s(1minusx)m2f


ndash 22 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)






ndash 23 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





x(413)

ndash 24 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





rang

ndash 25 ndash








ndash 26 ndash


5 Summary









ndash 27 ndash





Acknowledgments


ndash 28 ndash

Appendix

A Model Parameters


12

m211 = minus1

2

[m2H0 cos2 α+m2

h0 sin2 α+


h0)minus 2m2

12

tanβ

](A1)

m222 = minus1

2

[m2h0 cos2 α+m2

H0 sin2 α+


h0)minus 2m2

12

cotβ

](A2)

λ1 =1

v2o cos2 β

[m2H0 cos2 α+m2


](A3)

λ2 =1

v2o sin2 β

[m2h0 cos2 α+m2


](A4)

λ3 =2

v2o sin (2β)

[sinα cosα

(m2H0 minusm2

h0)minusm2

12 + m2H+ sin (2β)

](A5)

λ4 =1

v2o sin (2β)

[2m2

12 +(m2A0 minus 2m2

H+

)sin (2β)

](A6)

λ5 =1

v2o sin (2β)

[2m2


](A7)



Γ(S0 rarr f f) =Nc

8π

(ξSfmf

vo

)2

mS0

(1minus

4m2f

m2S0

)32




0

V )2

16π v2o

m3S0

(1minus

4m2W

m2S0

)12[

12

(mW

mS0

)4

minus 4

(mW

mS0

)2

+ 1





8πmS0

(1minus

4m2χ

m2S0

)32



Γ(S0 rarr gg) =

(mtξ

S0

q

vo

)2α2s

72π3

m3S0

m2t


Iq

∣∣∣∣∣∣2

(B5)

ndash 29 ndash



16πv20

(αemπ

)2∣∣∣∣∣sumq

ξS0

q Q2qIq +

suml

ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn

∣∣∣∣∣2







f(λ) as

f(λ) = minus2

(sinminus1 1

2radicλ

)2

for λ gt1

4

=1

2

(lnη+

ηminus

)2

minus π2

2minus iπ η

+

ηminus for λ lt

1

4(B8)


radic14 minus λ




=

(mfξ

S0

f

vo

)2

g2χS0

1

4π

(1minus

m2l

m2χ

) 32 m2

χ

(4m2χ minusm2

φ)2

(3

xf

)θ (mχ minusmf )


)vrang

=

(ξS

0

V

vo

)2g2χS0

8π

radic1minus

m2Z

m2χ

(16m4χ + 12m4

Z minus 16m2χm

2Z)

(4m2χ minusm2

S0)2

(3

xf


σ(χχrarrW+Wminus

)vrang

=

(ξS

0

V

vo

)2g2χS0

16π

radic1minus

m2W

m2χ

(16m4χ + 12m4

W minus 16m2χm

2W )

(4m2χ minusm2

S0)2

(3

xf



(ξS

0

q αs gχS0

3π32vo

)2m4χ

(4m2χ minusm2

S0)2 +m2S0Γ

(3

2xf


Iq

∣∣∣∣∣∣2

(C4)


2em

2π3v2o

m4χ


q Q2qIq +

suml ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn


S0)2 +m2S0Γ2

times(

3

xf

)(C5)

ndash 30 ndash


rang= c0


C2S0HiHj

g2χS0

16πλ

12

(1m2Hi

4m2χ

m2Hj

4m2χ

)

times 1

(4m2χ minusm2

φ)2

(3

xf

)(C6)




)vrang

=3g4χS0

64πm2χ

(3

xf





m2h0

and s0 =m2

12

m2h0 All


Ch0S0S0 =δ213m

2h0

vo

(minus4δ213r

20

tanβ+

2δ213r0tanβ

minus 8r30tan4 β

+8r20s0tan3 β

+4r20

tan4 βminus 8r0s0

tan3 βminus 8r0s0

tanβ

+2r0

tan4 βminus 2r0

tan2 β+

2s0tan3 β


minus 1

tan4 βminus 2

tan2 βminus 1

)(D1)

CS0h0h0 =δ13m

2h0

vo

(minus4δ213r

20

tan2 β+

2δ213r0tan2 β


tan3 βminus 4r0

tanβ

)(D2)

CS0H0H0 =δ13m

2h0

vo

(minus8δ213r

30

tan2 β+

12δ213r20


tan2 βminus 6r20

tan5 βminus 4r20

tan3 β+

2r20tanβ

+6r0s0tan4 β

+4r0s0tan2 β

minus2r0s0 +3r0

tan5 β+

r0tan3 β


minus 3s0tan4 β


+ 3s0

)(D3)

CS0S0H0 =δ213m

2h0

vo

(minus8δ213r

30

tan2 β+

8δ213r20


tan2 β+

12r30tan5 β

+4r30


tan4 βminus 4r20s0

tan2 βminus 12r20

tan5 β

+8r20

tanβ+

12r0s0tan4 β

+8r0s0tan2 β

minus 4r0s0 +3r0

tan5 βminus r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D4)

CS0H0h0 =δ13m

2h0

vo

(minus4δ213r

30

tan3 β+

4δ213r20


20

tanβminus δ213r0

tan3 β+

3δ213r0tanβ

+4r20

tan4 β+

4r20tan2 β

minus 4r0s0tan3 β

minus4r0s0tanβ

minus 3r0tan2 β

minus r0 +2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1

)(D5)

ndash 31 ndash

CS0H+Hminus =δ13m

2h0

vo

(minus 2r20

tan5 β+

2r20tanβ

+2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0 +r0

tan5 βminus r0


minus 5r0tanβ

minus s0tan4 β


+ s0 minus4m2

Hplusmnr0

tan3 βm2h0

minus4m2

Hplusmnr0

tanβm2h0

)(D6)

CS0A0A0 =δ13m

2h0

vo

(minus

4m2A0r0

tan3 βm2h0

minus4m2

A0r0tanβm2

h0

minus 2r20tan5 β

+2r20

tanβ+

2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0

+r0

tan5 βminus r0


tanβminus s0


tan2 β+ s0

)(D7)

CS0S0S0 =δ313m

2h0

vo

(minus 24r40

tan5 β+

24r30s0tan4 β

+36r30

tan5 βminus 12r30



tan2 βminus 18r20

tan5 β+

12r20tan3 β

+18r20tanβ

+18r0s0tan4 β

+12r0s0tan2 β

minus 6r0s0 +3r0

tan5 βminus 3r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D8)

Ch0H+Hminus =m2h0

vo

(2δ213r0tanβ

+2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1minus

2m2Hplusmn

tan4 βm2h0

minus4m2

Hplusmn

tan2 βm2h0

minus2m2

Hplusmn

m2h0

) (D9)

References










ndash 32 ndash























ndash 33 ndash






















ndash 34 ndash








ndash 35 ndash

1 Introduction

2 The Model








42 Direct Detection


5 Summary

A Model Parameters




mS0(GeV) 12 15 20 25 30 35 40 45 50 55 60 65∣∣∣ξS0

Z0

∣∣∣ 285 316 398 530 751 1132 1028 457 260 199 169 093


Z0


574

5 10 20 24 30 40

10-6

10-5

10-4

10-3

10-2

10-1

100

101485

100 G

eV

2

50 G

eV

2

30 G

eV

2

20 G

eV

2

10 G

eV

2

H0rarr

τ+τ- F

orb

idd

en

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

Forbidden

(a) mH0 = 400 GeV mA0 = 200 GeV

574

5 10 20 24 30 40

10-6

10-5

10-4

10-3

10-2

10-1

100

101485

100 G

eV

2

50 G

eV

2

30 G

eV

2

20 G

eV

2

10 GeV2

H0rarr

τ+τ- F

orb

idd

en

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

Forbidden

(b) mH0 = 400 GeV mA0 = 400 GeV

574

5 10 20 24 30 40

10-6

10-5

10-4

10-3

10-2

10-1

100

101485

100 G

eV

2

50 G

eV

2

30 G

eV

2

20 G

eV

2

10 GeV2

H0rarr

τ+τ- F

orb

idd

en

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

Forbidden

(c) mH0 = 400 GeV mA0 = 600 GeV

574

5 10 20 24 30 40

10-6

10-5

10-4

10-3

10-2

10-1

100

101485

100 G

eV

2

50 G

eV

2

30 G

eV

2

20 G

eV

2

10 GeV2

H0rarr

τ+τ- F

orb

idd

en

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

Forbidden

(d) mH0 = 600 GeV mA0 = 400 GeV



12 = 0 GeV2




ndash 9 ndash

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2

30 GeV2

20 GeV2

10 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 400 GeV

mA0 = 200 GeV

(a)

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2

30 GeV2

20 GeV2

10 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 400 GeV

mA0 = 400 GeV

(b)

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2 30 GeV

2

20 GeV2

10 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 400 GeV

mA0 = 600 GeV

(c)

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2

30 GeV2

20 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 600 GeV

mA0 = 400 GeV

(d)







0


0


0



2

ndash 10 ndash

5 10 20 30 40 50 60200

300

400

500

600

700

800

900

1000m

H0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 20 GeV

2

(a)

5 10 20 30 40 50 60200

300

400

500

600

700

800

900

1000

1100

mH

0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 30 GeV

2

(b)

5 10 20 30 40 50 60200

300

400

500

600

700

800

900

1000

1100

1200

mH

0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 50 GeV

2

(c)

5 10 20 30 40 50 60100

200

300

400

500

600

700

800

900

1000

mH

0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 100 GeV

2

(d)


0






32πmh0

radic1minus

4m2S0

m2h0

(34)






ndash 11 ndash





12 ge10 GeV2







)minus 1 =


minus 1 (35)








ndash 12 ndash









dnχdt

+ 3a


(n2χ minus n2

χeq

)(42)

where aa =

radic8πρ


n2χeq = g

(mχT2π

) 32

exp[minusmχT




MPl


xF)

(43)


mχTF

is given by

xF = ln

c (c+ 2)

radic45

8

gMPl mχ

(a+ 6 b

xF

)2π3radic


(44)

ndash 13 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 50 GeV

2

(f)






ndash 14 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 50 GeV

2

(f)





ndash 15 ndash


12

)(

200 GeV 30 GeV2)(200 GeV 50 GeV2

)(400 GeV 30 GeV2

)(

400 GeV 50 GeV2)(600 GeV 30 GeV2

)and

(600 GeV 50 GeV2

)


42 Direct Detection



σγγN =

(αemZ

π

)2[micro2N

π

(αemZ

πm2S0

)2](

π2

12

)2(microNv

mτ

)2

2

(gχS0ξS

0

l

mτ

v0

)2

(45)



LS0gg

eff = minusξS

0

q

12π

αsvo

sumq=cbt

Iq




12π

ξS0

q gχS0

vom2S0

sumq=cbt

Iq


ndash 16 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 50 GeV

2

(f)




σggN =

(2ξS

0

q gχS0mN

m2S027vo


Iq

∣∣∣∣∣∣2

2

π(mχ +mN )2m2Nm

2χ (48)

ndash 17 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 50 GeV

2

(f)





2N

m2N

(ξS

0

τ

ξS0

q

)2(9

8

)2 v2


ndash 18 ndash




GamicroνGamicroν



Since mN equivsum



F gN = 1minussumuds

FqiNS (q2)

mN= minus 1

mN









ndash 19 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





ndash 20 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





ndash 21 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)




the reference [56]


f

π Ff (x) log

(s(1minusx)m2f


ndash 22 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)






ndash 23 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





x(413)

ndash 24 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





rang

ndash 25 ndash








ndash 26 ndash


5 Summary









ndash 27 ndash





Acknowledgments


ndash 28 ndash

Appendix

A Model Parameters


12

m211 = minus1

2

[m2H0 cos2 α+m2

h0 sin2 α+


h0)minus 2m2

12

tanβ

](A1)

m222 = minus1

2

[m2h0 cos2 α+m2

H0 sin2 α+


h0)minus 2m2

12

cotβ

](A2)

λ1 =1

v2o cos2 β

[m2H0 cos2 α+m2


](A3)

λ2 =1

v2o sin2 β

[m2h0 cos2 α+m2


](A4)

λ3 =2

v2o sin (2β)

[sinα cosα

(m2H0 minusm2

h0)minusm2

12 + m2H+ sin (2β)

](A5)

λ4 =1

v2o sin (2β)

[2m2

12 +(m2A0 minus 2m2

H+

)sin (2β)

](A6)

λ5 =1

v2o sin (2β)

[2m2


](A7)



Γ(S0 rarr f f) =Nc

8π

(ξSfmf

vo

)2

mS0

(1minus

4m2f

m2S0

)32




0

V )2

16π v2o

m3S0

(1minus

4m2W

m2S0

)12[

12

(mW

mS0

)4

minus 4

(mW

mS0

)2

+ 1





8πmS0

(1minus

4m2χ

m2S0

)32



Γ(S0 rarr gg) =

(mtξ

S0

q

vo

)2α2s

72π3

m3S0

m2t


Iq

∣∣∣∣∣∣2

(B5)

ndash 29 ndash



16πv20

(αemπ

)2∣∣∣∣∣sumq

ξS0

q Q2qIq +

suml

ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn

∣∣∣∣∣2







f(λ) as

f(λ) = minus2

(sinminus1 1

2radicλ

)2

for λ gt1

4

=1

2

(lnη+

ηminus

)2

minus π2

2minus iπ η

+

ηminus for λ lt

1

4(B8)


radic14 minus λ




=

(mfξ

S0

f

vo

)2

g2χS0

1

4π

(1minus

m2l

m2χ

) 32 m2

χ

(4m2χ minusm2

φ)2

(3

xf

)θ (mχ minusmf )


)vrang

=

(ξS

0

V

vo

)2g2χS0

8π

radic1minus

m2Z

m2χ

(16m4χ + 12m4

Z minus 16m2χm

2Z)

(4m2χ minusm2

S0)2

(3

xf


σ(χχrarrW+Wminus

)vrang

=

(ξS

0

V

vo

)2g2χS0

16π

radic1minus

m2W

m2χ

(16m4χ + 12m4

W minus 16m2χm

2W )

(4m2χ minusm2

S0)2

(3

xf



(ξS

0

q αs gχS0

3π32vo

)2m4χ

(4m2χ minusm2

S0)2 +m2S0Γ

(3

2xf


Iq

∣∣∣∣∣∣2

(C4)


2em

2π3v2o

m4χ


q Q2qIq +

suml ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn


S0)2 +m2S0Γ2

times(

3

xf

)(C5)

ndash 30 ndash


rang= c0


C2S0HiHj

g2χS0

16πλ

12

(1m2Hi

4m2χ

m2Hj

4m2χ

)

times 1

(4m2χ minusm2

φ)2

(3

xf

)(C6)




)vrang

=3g4χS0

64πm2χ

(3

xf





m2h0

and s0 =m2

12

m2h0 All


Ch0S0S0 =δ213m

2h0

vo

(minus4δ213r

20

tanβ+

2δ213r0tanβ

minus 8r30tan4 β

+8r20s0tan3 β

+4r20

tan4 βminus 8r0s0

tan3 βminus 8r0s0

tanβ

+2r0

tan4 βminus 2r0

tan2 β+

2s0tan3 β


minus 1

tan4 βminus 2

tan2 βminus 1

)(D1)

CS0h0h0 =δ13m

2h0

vo

(minus4δ213r

20

tan2 β+

2δ213r0tan2 β


tan3 βminus 4r0

tanβ

)(D2)

CS0H0H0 =δ13m

2h0

vo

(minus8δ213r

30

tan2 β+

12δ213r20


tan2 βminus 6r20

tan5 βminus 4r20

tan3 β+

2r20tanβ

+6r0s0tan4 β

+4r0s0tan2 β

minus2r0s0 +3r0

tan5 β+

r0tan3 β


minus 3s0tan4 β


+ 3s0

)(D3)

CS0S0H0 =δ213m

2h0

vo

(minus8δ213r

30

tan2 β+

8δ213r20


tan2 β+

12r30tan5 β

+4r30


tan4 βminus 4r20s0

tan2 βminus 12r20

tan5 β

+8r20

tanβ+

12r0s0tan4 β

+8r0s0tan2 β

minus 4r0s0 +3r0

tan5 βminus r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D4)

CS0H0h0 =δ13m

2h0

vo

(minus4δ213r

30

tan3 β+

4δ213r20


20

tanβminus δ213r0

tan3 β+

3δ213r0tanβ

+4r20

tan4 β+

4r20tan2 β

minus 4r0s0tan3 β

minus4r0s0tanβ

minus 3r0tan2 β

minus r0 +2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1

)(D5)

ndash 31 ndash

CS0H+Hminus =δ13m

2h0

vo

(minus 2r20

tan5 β+

2r20tanβ

+2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0 +r0

tan5 βminus r0


minus 5r0tanβ

minus s0tan4 β


+ s0 minus4m2

Hplusmnr0

tan3 βm2h0

minus4m2

Hplusmnr0

tanβm2h0

)(D6)

CS0A0A0 =δ13m

2h0

vo

(minus

4m2A0r0

tan3 βm2h0

minus4m2

A0r0tanβm2

h0

minus 2r20tan5 β

+2r20

tanβ+

2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0

+r0

tan5 βminus r0


tanβminus s0


tan2 β+ s0

)(D7)

CS0S0S0 =δ313m

2h0

vo

(minus 24r40

tan5 β+

24r30s0tan4 β

+36r30

tan5 βminus 12r30



tan2 βminus 18r20

tan5 β+

12r20tan3 β

+18r20tanβ

+18r0s0tan4 β

+12r0s0tan2 β

minus 6r0s0 +3r0

tan5 βminus 3r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D8)

Ch0H+Hminus =m2h0

vo

(2δ213r0tanβ

+2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1minus

2m2Hplusmn

tan4 βm2h0

minus4m2

Hplusmn

tan2 βm2h0

minus2m2

Hplusmn

m2h0

) (D9)

References










ndash 32 ndash























ndash 33 ndash






















ndash 34 ndash








ndash 35 ndash

1 Introduction

2 The Model








42 Direct Detection


5 Summary

A Model Parameters




574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2

30 GeV2

20 GeV2

10 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 400 GeV

mA0 = 200 GeV

(a)

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2

30 GeV2

20 GeV2

10 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 400 GeV

mA0 = 400 GeV

(b)

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2 30 GeV

2

20 GeV2

10 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 400 GeV

mA0 = 600 GeV

(c)

574

5 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

10155 100 150 200 300 350 400 450

100 GeV2

50 GeV2

30 GeV2

20 GeV2

Γ(h

0 rarr

S0 +

S0)

in M

eV

mS0 in GeV

tanβ

0 GeV2

ForbiddenmH

0 = 600 GeV

mA0 = 400 GeV

(d)







0


0


0



2

ndash 10 ndash

5 10 20 30 40 50 60200

300

400

500

600

700

800

900

1000m

H0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 20 GeV

2

(a)

5 10 20 30 40 50 60200

300

400

500

600

700

800

900

1000

1100

mH

0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 30 GeV

2

(b)

5 10 20 30 40 50 60200

300

400

500

600

700

800

900

1000

1100

1200

mH

0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 50 GeV

2

(c)

5 10 20 30 40 50 60100

200

300

400

500

600

700

800

900

1000

mH

0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 100 GeV

2

(d)


0






32πmh0

radic1minus

4m2S0

m2h0

(34)






ndash 11 ndash





12 ge10 GeV2







)minus 1 =


minus 1 (35)








ndash 12 ndash









dnχdt

+ 3a


(n2χ minus n2

χeq

)(42)

where aa =

radic8πρ


n2χeq = g

(mχT2π

) 32

exp[minusmχT




MPl


xF)

(43)


mχTF

is given by

xF = ln

c (c+ 2)

radic45

8

gMPl mχ

(a+ 6 b

xF

)2π3radic


(44)

ndash 13 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 50 GeV

2

(f)






ndash 14 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 50 GeV

2

(f)





ndash 15 ndash


12

)(

200 GeV 30 GeV2)(200 GeV 50 GeV2

)(400 GeV 30 GeV2

)(

400 GeV 50 GeV2)(600 GeV 30 GeV2

)and

(600 GeV 50 GeV2

)


42 Direct Detection



σγγN =

(αemZ

π

)2[micro2N

π

(αemZ

πm2S0

)2](

π2

12

)2(microNv

mτ

)2

2

(gχS0ξS

0

l

mτ

v0

)2

(45)



LS0gg

eff = minusξS

0

q

12π

αsvo

sumq=cbt

Iq




12π

ξS0

q gχS0

vom2S0

sumq=cbt

Iq


ndash 16 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 50 GeV

2

(f)




σggN =

(2ξS

0

q gχS0mN

m2S027vo


Iq

∣∣∣∣∣∣2

2

π(mχ +mN )2m2Nm

2χ (48)

ndash 17 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 50 GeV

2

(f)





2N

m2N

(ξS

0

τ

ξS0

q

)2(9

8

)2 v2


ndash 18 ndash




GamicroνGamicroν



Since mN equivsum



F gN = 1minussumuds

FqiNS (q2)

mN= minus 1

mN









ndash 19 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





ndash 20 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





ndash 21 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)




the reference [56]


f

π Ff (x) log

(s(1minusx)m2f


ndash 22 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)






ndash 23 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





x(413)

ndash 24 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





rang

ndash 25 ndash








ndash 26 ndash


5 Summary









ndash 27 ndash





Acknowledgments


ndash 28 ndash

Appendix

A Model Parameters


12

m211 = minus1

2

[m2H0 cos2 α+m2

h0 sin2 α+


h0)minus 2m2

12

tanβ

](A1)

m222 = minus1

2

[m2h0 cos2 α+m2

H0 sin2 α+


h0)minus 2m2

12

cotβ

](A2)

λ1 =1

v2o cos2 β

[m2H0 cos2 α+m2


](A3)

λ2 =1

v2o sin2 β

[m2h0 cos2 α+m2


](A4)

λ3 =2

v2o sin (2β)

[sinα cosα

(m2H0 minusm2

h0)minusm2

12 + m2H+ sin (2β)

](A5)

λ4 =1

v2o sin (2β)

[2m2

12 +(m2A0 minus 2m2

H+

)sin (2β)

](A6)

λ5 =1

v2o sin (2β)

[2m2


](A7)



Γ(S0 rarr f f) =Nc

8π

(ξSfmf

vo

)2

mS0

(1minus

4m2f

m2S0

)32




0

V )2

16π v2o

m3S0

(1minus

4m2W

m2S0

)12[

12

(mW

mS0

)4

minus 4

(mW

mS0

)2

+ 1





8πmS0

(1minus

4m2χ

m2S0

)32



Γ(S0 rarr gg) =

(mtξ

S0

q

vo

)2α2s

72π3

m3S0

m2t


Iq

∣∣∣∣∣∣2

(B5)

ndash 29 ndash



16πv20

(αemπ

)2∣∣∣∣∣sumq

ξS0

q Q2qIq +

suml

ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn

∣∣∣∣∣2







f(λ) as

f(λ) = minus2

(sinminus1 1

2radicλ

)2

for λ gt1

4

=1

2

(lnη+

ηminus

)2

minus π2

2minus iπ η

+

ηminus for λ lt

1

4(B8)


radic14 minus λ




=

(mfξ

S0

f

vo

)2

g2χS0

1

4π

(1minus

m2l

m2χ

) 32 m2

χ

(4m2χ minusm2

φ)2

(3

xf

)θ (mχ minusmf )


)vrang

=

(ξS

0

V

vo

)2g2χS0

8π

radic1minus

m2Z

m2χ

(16m4χ + 12m4

Z minus 16m2χm

2Z)

(4m2χ minusm2

S0)2

(3

xf


σ(χχrarrW+Wminus

)vrang

=

(ξS

0

V

vo

)2g2χS0

16π

radic1minus

m2W

m2χ

(16m4χ + 12m4

W minus 16m2χm

2W )

(4m2χ minusm2

S0)2

(3

xf



(ξS

0

q αs gχS0

3π32vo

)2m4χ

(4m2χ minusm2

S0)2 +m2S0Γ

(3

2xf


Iq

∣∣∣∣∣∣2

(C4)


2em

2π3v2o

m4χ


q Q2qIq +

suml ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn


S0)2 +m2S0Γ2

times(

3

xf

)(C5)

ndash 30 ndash


rang= c0


C2S0HiHj

g2χS0

16πλ

12

(1m2Hi

4m2χ

m2Hj

4m2χ

)

times 1

(4m2χ minusm2

φ)2

(3

xf

)(C6)




)vrang

=3g4χS0

64πm2χ

(3

xf





m2h0

and s0 =m2

12

m2h0 All


Ch0S0S0 =δ213m

2h0

vo

(minus4δ213r

20

tanβ+

2δ213r0tanβ

minus 8r30tan4 β

+8r20s0tan3 β

+4r20

tan4 βminus 8r0s0

tan3 βminus 8r0s0

tanβ

+2r0

tan4 βminus 2r0

tan2 β+

2s0tan3 β


minus 1

tan4 βminus 2

tan2 βminus 1

)(D1)

CS0h0h0 =δ13m

2h0

vo

(minus4δ213r

20

tan2 β+

2δ213r0tan2 β


tan3 βminus 4r0

tanβ

)(D2)

CS0H0H0 =δ13m

2h0

vo

(minus8δ213r

30

tan2 β+

12δ213r20


tan2 βminus 6r20

tan5 βminus 4r20

tan3 β+

2r20tanβ

+6r0s0tan4 β

+4r0s0tan2 β

minus2r0s0 +3r0

tan5 β+

r0tan3 β


minus 3s0tan4 β


+ 3s0

)(D3)

CS0S0H0 =δ213m

2h0

vo

(minus8δ213r

30

tan2 β+

8δ213r20


tan2 β+

12r30tan5 β

+4r30


tan4 βminus 4r20s0

tan2 βminus 12r20

tan5 β

+8r20

tanβ+

12r0s0tan4 β

+8r0s0tan2 β

minus 4r0s0 +3r0

tan5 βminus r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D4)

CS0H0h0 =δ13m

2h0

vo

(minus4δ213r

30

tan3 β+

4δ213r20


20

tanβminus δ213r0

tan3 β+

3δ213r0tanβ

+4r20

tan4 β+

4r20tan2 β

minus 4r0s0tan3 β

minus4r0s0tanβ

minus 3r0tan2 β

minus r0 +2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1

)(D5)

ndash 31 ndash

CS0H+Hminus =δ13m

2h0

vo

(minus 2r20

tan5 β+

2r20tanβ

+2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0 +r0

tan5 βminus r0


minus 5r0tanβ

minus s0tan4 β


+ s0 minus4m2

Hplusmnr0

tan3 βm2h0

minus4m2

Hplusmnr0

tanβm2h0

)(D6)

CS0A0A0 =δ13m

2h0

vo

(minus

4m2A0r0

tan3 βm2h0

minus4m2

A0r0tanβm2

h0

minus 2r20tan5 β

+2r20

tanβ+

2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0

+r0

tan5 βminus r0


tanβminus s0


tan2 β+ s0

)(D7)

CS0S0S0 =δ313m

2h0

vo

(minus 24r40

tan5 β+

24r30s0tan4 β

+36r30

tan5 βminus 12r30



tan2 βminus 18r20

tan5 β+

12r20tan3 β

+18r20tanβ

+18r0s0tan4 β

+12r0s0tan2 β

minus 6r0s0 +3r0

tan5 βminus 3r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D8)

Ch0H+Hminus =m2h0

vo

(2δ213r0tanβ

+2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1minus

2m2Hplusmn

tan4 βm2h0

minus4m2

Hplusmn

tan2 βm2h0

minus2m2

Hplusmn

m2h0

) (D9)

References










ndash 32 ndash























ndash 33 ndash






















ndash 34 ndash








ndash 35 ndash

1 Introduction

2 The Model








42 Direct Detection


5 Summary

A Model Parameters




5 10 20 30 40 50 60200

300

400

500

600

700

800

900

1000m

H0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 20 GeV

2

(a)

5 10 20 30 40 50 60200

300

400

500

600

700

800

900

1000

1100

mH

0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 30 GeV

2

(b)

5 10 20 30 40 50 60200

300

400

500

600

700

800

900

1000

1100

1200

mH

0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 50 GeV

2

(c)

5 10 20 30 40 50 60100

200

300

400

500

600

700

800

900

1000

mH

0 in

GeV

mS0 in GeV

mA0 = 200 GeV

mA0 = 400 GeV

mA0 = 600 GeV

m12

2 = 100 GeV

2

(d)


0






32πmh0

radic1minus

4m2S0

m2h0

(34)






ndash 11 ndash





12 ge10 GeV2







)minus 1 =


minus 1 (35)








ndash 12 ndash









dnχdt

+ 3a


(n2χ minus n2

χeq

)(42)

where aa =

radic8πρ


n2χeq = g

(mχT2π

) 32

exp[minusmχT




MPl


xF)

(43)


mχTF

is given by

xF = ln

c (c+ 2)

radic45

8

gMPl mχ

(a+ 6 b

xF

)2π3radic


(44)

ndash 13 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 50 GeV

2

(f)






ndash 14 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 50 GeV

2

(f)





ndash 15 ndash


12

)(

200 GeV 30 GeV2)(200 GeV 50 GeV2

)(400 GeV 30 GeV2

)(

400 GeV 50 GeV2)(600 GeV 30 GeV2

)and

(600 GeV 50 GeV2

)


42 Direct Detection



σγγN =

(αemZ

π

)2[micro2N

π

(αemZ

πm2S0

)2](

π2

12

)2(microNv

mτ

)2

2

(gχS0ξS

0

l

mτ

v0

)2

(45)



LS0gg

eff = minusξS

0

q

12π

αsvo

sumq=cbt

Iq




12π

ξS0

q gχS0

vom2S0

sumq=cbt

Iq


ndash 16 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 50 GeV

2

(f)




σggN =

(2ξS

0

q gχS0mN

m2S027vo


Iq

∣∣∣∣∣∣2

2

π(mχ +mN )2m2Nm

2χ (48)

ndash 17 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 50 GeV

2

(f)





2N

m2N

(ξS

0

τ

ξS0

q

)2(9

8

)2 v2


ndash 18 ndash




GamicroνGamicroν



Since mN equivsum



F gN = 1minussumuds

FqiNS (q2)

mN= minus 1

mN









ndash 19 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





ndash 20 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





ndash 21 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)




the reference [56]


f

π Ff (x) log

(s(1minusx)m2f


ndash 22 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)






ndash 23 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





x(413)

ndash 24 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





rang

ndash 25 ndash








ndash 26 ndash


5 Summary









ndash 27 ndash





Acknowledgments


ndash 28 ndash

Appendix

A Model Parameters


12

m211 = minus1

2

[m2H0 cos2 α+m2

h0 sin2 α+


h0)minus 2m2

12

tanβ

](A1)

m222 = minus1

2

[m2h0 cos2 α+m2

H0 sin2 α+


h0)minus 2m2

12

cotβ

](A2)

λ1 =1

v2o cos2 β

[m2H0 cos2 α+m2


](A3)

λ2 =1

v2o sin2 β

[m2h0 cos2 α+m2


](A4)

λ3 =2

v2o sin (2β)

[sinα cosα

(m2H0 minusm2

h0)minusm2

12 + m2H+ sin (2β)

](A5)

λ4 =1

v2o sin (2β)

[2m2

12 +(m2A0 minus 2m2

H+

)sin (2β)

](A6)

λ5 =1

v2o sin (2β)

[2m2


](A7)



Γ(S0 rarr f f) =Nc

8π

(ξSfmf

vo

)2

mS0

(1minus

4m2f

m2S0

)32




0

V )2

16π v2o

m3S0

(1minus

4m2W

m2S0

)12[

12

(mW

mS0

)4

minus 4

(mW

mS0

)2

+ 1





8πmS0

(1minus

4m2χ

m2S0

)32



Γ(S0 rarr gg) =

(mtξ

S0

q

vo

)2α2s

72π3

m3S0

m2t


Iq

∣∣∣∣∣∣2

(B5)

ndash 29 ndash



16πv20

(αemπ

)2∣∣∣∣∣sumq

ξS0

q Q2qIq +

suml

ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn

∣∣∣∣∣2







f(λ) as

f(λ) = minus2

(sinminus1 1

2radicλ

)2

for λ gt1

4

=1

2

(lnη+

ηminus

)2

minus π2

2minus iπ η

+

ηminus for λ lt

1

4(B8)


radic14 minus λ




=

(mfξ

S0

f

vo

)2

g2χS0

1

4π

(1minus

m2l

m2χ

) 32 m2

χ

(4m2χ minusm2

φ)2

(3

xf

)θ (mχ minusmf )


)vrang

=

(ξS

0

V

vo

)2g2χS0

8π

radic1minus

m2Z

m2χ

(16m4χ + 12m4

Z minus 16m2χm

2Z)

(4m2χ minusm2

S0)2

(3

xf


σ(χχrarrW+Wminus

)vrang

=

(ξS

0

V

vo

)2g2χS0

16π

radic1minus

m2W

m2χ

(16m4χ + 12m4

W minus 16m2χm

2W )

(4m2χ minusm2

S0)2

(3

xf



(ξS

0

q αs gχS0

3π32vo

)2m4χ

(4m2χ minusm2

S0)2 +m2S0Γ

(3

2xf


Iq

∣∣∣∣∣∣2

(C4)


2em

2π3v2o

m4χ


q Q2qIq +

suml ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn


S0)2 +m2S0Γ2

times(

3

xf

)(C5)

ndash 30 ndash


rang= c0


C2S0HiHj

g2χS0

16πλ

12

(1m2Hi

4m2χ

m2Hj

4m2χ

)

times 1

(4m2χ minusm2

φ)2

(3

xf

)(C6)




)vrang

=3g4χS0

64πm2χ

(3

xf





m2h0

and s0 =m2

12

m2h0 All


Ch0S0S0 =δ213m

2h0

vo

(minus4δ213r

20

tanβ+

2δ213r0tanβ

minus 8r30tan4 β

+8r20s0tan3 β

+4r20

tan4 βminus 8r0s0

tan3 βminus 8r0s0

tanβ

+2r0

tan4 βminus 2r0

tan2 β+

2s0tan3 β


minus 1

tan4 βminus 2

tan2 βminus 1

)(D1)

CS0h0h0 =δ13m

2h0

vo

(minus4δ213r

20

tan2 β+

2δ213r0tan2 β


tan3 βminus 4r0

tanβ

)(D2)

CS0H0H0 =δ13m

2h0

vo

(minus8δ213r

30

tan2 β+

12δ213r20


tan2 βminus 6r20

tan5 βminus 4r20

tan3 β+

2r20tanβ

+6r0s0tan4 β

+4r0s0tan2 β

minus2r0s0 +3r0

tan5 β+

r0tan3 β


minus 3s0tan4 β


+ 3s0

)(D3)

CS0S0H0 =δ213m

2h0

vo

(minus8δ213r

30

tan2 β+

8δ213r20


tan2 β+

12r30tan5 β

+4r30


tan4 βminus 4r20s0

tan2 βminus 12r20

tan5 β

+8r20

tanβ+

12r0s0tan4 β

+8r0s0tan2 β

minus 4r0s0 +3r0

tan5 βminus r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D4)

CS0H0h0 =δ13m

2h0

vo

(minus4δ213r

30

tan3 β+

4δ213r20


20

tanβminus δ213r0

tan3 β+

3δ213r0tanβ

+4r20

tan4 β+

4r20tan2 β

minus 4r0s0tan3 β

minus4r0s0tanβ

minus 3r0tan2 β

minus r0 +2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1

)(D5)

ndash 31 ndash

CS0H+Hminus =δ13m

2h0

vo

(minus 2r20

tan5 β+

2r20tanβ

+2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0 +r0

tan5 βminus r0


minus 5r0tanβ

minus s0tan4 β


+ s0 minus4m2

Hplusmnr0

tan3 βm2h0

minus4m2

Hplusmnr0

tanβm2h0

)(D6)

CS0A0A0 =δ13m

2h0

vo

(minus

4m2A0r0

tan3 βm2h0

minus4m2

A0r0tanβm2

h0

minus 2r20tan5 β

+2r20

tanβ+

2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0

+r0

tan5 βminus r0


tanβminus s0


tan2 β+ s0

)(D7)

CS0S0S0 =δ313m

2h0

vo

(minus 24r40

tan5 β+

24r30s0tan4 β

+36r30

tan5 βminus 12r30



tan2 βminus 18r20

tan5 β+

12r20tan3 β

+18r20tanβ

+18r0s0tan4 β

+12r0s0tan2 β

minus 6r0s0 +3r0

tan5 βminus 3r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D8)

Ch0H+Hminus =m2h0

vo

(2δ213r0tanβ

+2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1minus

2m2Hplusmn

tan4 βm2h0

minus4m2

Hplusmn

tan2 βm2h0

minus2m2

Hplusmn

m2h0

) (D9)

References










ndash 32 ndash























ndash 33 ndash






















ndash 34 ndash








ndash 35 ndash

1 Introduction

2 The Model








42 Direct Detection


5 Summary

A Model Parameters








12 ge10 GeV2







)minus 1 =


minus 1 (35)








ndash 12 ndash









dnχdt

+ 3a


(n2χ minus n2

χeq

)(42)

where aa =

radic8πρ


n2χeq = g

(mχT2π

) 32

exp[minusmχT




MPl


xF)

(43)


mχTF

is given by

xF = ln

c (c+ 2)

radic45

8

gMPl mχ

(a+ 6 b

xF

)2π3radic


(44)

ndash 13 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 50 GeV

2

(f)






ndash 14 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 50 GeV

2

(f)





ndash 15 ndash


12

)(

200 GeV 30 GeV2)(200 GeV 50 GeV2

)(400 GeV 30 GeV2

)(

400 GeV 50 GeV2)(600 GeV 30 GeV2

)and

(600 GeV 50 GeV2

)


42 Direct Detection



σγγN =

(αemZ

π

)2[micro2N

π

(αemZ

πm2S0

)2](

π2

12

)2(microNv

mτ

)2

2

(gχS0ξS

0

l

mτ

v0

)2

(45)



LS0gg

eff = minusξS

0

q

12π

αsvo

sumq=cbt

Iq




12π

ξS0

q gχS0

vom2S0

sumq=cbt

Iq


ndash 16 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 50 GeV

2

(f)




σggN =

(2ξS

0

q gχS0mN

m2S027vo


Iq

∣∣∣∣∣∣2

2

π(mχ +mN )2m2Nm

2χ (48)

ndash 17 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 50 GeV

2

(f)





2N

m2N

(ξS

0

τ

ξS0

q

)2(9

8

)2 v2


ndash 18 ndash




GamicroνGamicroν



Since mN equivsum



F gN = 1minussumuds

FqiNS (q2)

mN= minus 1

mN









ndash 19 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





ndash 20 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





ndash 21 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)




the reference [56]


f

π Ff (x) log

(s(1minusx)m2f


ndash 22 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)






ndash 23 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





x(413)

ndash 24 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





rang

ndash 25 ndash








ndash 26 ndash


5 Summary









ndash 27 ndash





Acknowledgments


ndash 28 ndash

Appendix

A Model Parameters


12

m211 = minus1

2

[m2H0 cos2 α+m2

h0 sin2 α+


h0)minus 2m2

12

tanβ

](A1)

m222 = minus1

2

[m2h0 cos2 α+m2

H0 sin2 α+


h0)minus 2m2

12

cotβ

](A2)

λ1 =1

v2o cos2 β

[m2H0 cos2 α+m2


](A3)

λ2 =1

v2o sin2 β

[m2h0 cos2 α+m2


](A4)

λ3 =2

v2o sin (2β)

[sinα cosα

(m2H0 minusm2

h0)minusm2

12 + m2H+ sin (2β)

](A5)

λ4 =1

v2o sin (2β)

[2m2

12 +(m2A0 minus 2m2

H+

)sin (2β)

](A6)

λ5 =1

v2o sin (2β)

[2m2


](A7)



Γ(S0 rarr f f) =Nc

8π

(ξSfmf

vo

)2

mS0

(1minus

4m2f

m2S0

)32




0

V )2

16π v2o

m3S0

(1minus

4m2W

m2S0

)12[

12

(mW

mS0

)4

minus 4

(mW

mS0

)2

+ 1





8πmS0

(1minus

4m2χ

m2S0

)32



Γ(S0 rarr gg) =

(mtξ

S0

q

vo

)2α2s

72π3

m3S0

m2t


Iq

∣∣∣∣∣∣2

(B5)

ndash 29 ndash



16πv20

(αemπ

)2∣∣∣∣∣sumq

ξS0

q Q2qIq +

suml

ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn

∣∣∣∣∣2







f(λ) as

f(λ) = minus2

(sinminus1 1

2radicλ

)2

for λ gt1

4

=1

2

(lnη+

ηminus

)2

minus π2

2minus iπ η

+

ηminus for λ lt

1

4(B8)


radic14 minus λ




=

(mfξ

S0

f

vo

)2

g2χS0

1

4π

(1minus

m2l

m2χ

) 32 m2

χ

(4m2χ minusm2

φ)2

(3

xf

)θ (mχ minusmf )


)vrang

=

(ξS

0

V

vo

)2g2χS0

8π

radic1minus

m2Z

m2χ

(16m4χ + 12m4

Z minus 16m2χm

2Z)

(4m2χ minusm2

S0)2

(3

xf


σ(χχrarrW+Wminus

)vrang

=

(ξS

0

V

vo

)2g2χS0

16π

radic1minus

m2W

m2χ

(16m4χ + 12m4

W minus 16m2χm

2W )

(4m2χ minusm2

S0)2

(3

xf



(ξS

0

q αs gχS0

3π32vo

)2m4χ

(4m2χ minusm2

S0)2 +m2S0Γ

(3

2xf


Iq

∣∣∣∣∣∣2

(C4)


2em

2π3v2o

m4χ


q Q2qIq +

suml ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn


S0)2 +m2S0Γ2

times(

3

xf

)(C5)

ndash 30 ndash


rang= c0


C2S0HiHj

g2χS0

16πλ

12

(1m2Hi

4m2χ

m2Hj

4m2χ

)

times 1

(4m2χ minusm2

φ)2

(3

xf

)(C6)




)vrang

=3g4χS0

64πm2χ

(3

xf





m2h0

and s0 =m2

12

m2h0 All


Ch0S0S0 =δ213m

2h0

vo

(minus4δ213r

20

tanβ+

2δ213r0tanβ

minus 8r30tan4 β

+8r20s0tan3 β

+4r20

tan4 βminus 8r0s0

tan3 βminus 8r0s0

tanβ

+2r0

tan4 βminus 2r0

tan2 β+

2s0tan3 β


minus 1

tan4 βminus 2

tan2 βminus 1

)(D1)

CS0h0h0 =δ13m

2h0

vo

(minus4δ213r

20

tan2 β+

2δ213r0tan2 β


tan3 βminus 4r0

tanβ

)(D2)

CS0H0H0 =δ13m

2h0

vo

(minus8δ213r

30

tan2 β+

12δ213r20


tan2 βminus 6r20

tan5 βminus 4r20

tan3 β+

2r20tanβ

+6r0s0tan4 β

+4r0s0tan2 β

minus2r0s0 +3r0

tan5 β+

r0tan3 β


minus 3s0tan4 β


+ 3s0

)(D3)

CS0S0H0 =δ213m

2h0

vo

(minus8δ213r

30

tan2 β+

8δ213r20


tan2 β+

12r30tan5 β

+4r30


tan4 βminus 4r20s0

tan2 βminus 12r20

tan5 β

+8r20

tanβ+

12r0s0tan4 β

+8r0s0tan2 β

minus 4r0s0 +3r0

tan5 βminus r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D4)

CS0H0h0 =δ13m

2h0

vo

(minus4δ213r

30

tan3 β+

4δ213r20


20

tanβminus δ213r0

tan3 β+

3δ213r0tanβ

+4r20

tan4 β+

4r20tan2 β

minus 4r0s0tan3 β

minus4r0s0tanβ

minus 3r0tan2 β

minus r0 +2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1

)(D5)

ndash 31 ndash

CS0H+Hminus =δ13m

2h0

vo

(minus 2r20

tan5 β+

2r20tanβ

+2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0 +r0

tan5 βminus r0


minus 5r0tanβ

minus s0tan4 β


+ s0 minus4m2

Hplusmnr0

tan3 βm2h0

minus4m2

Hplusmnr0

tanβm2h0

)(D6)

CS0A0A0 =δ13m

2h0

vo

(minus

4m2A0r0

tan3 βm2h0

minus4m2

A0r0tanβm2

h0

minus 2r20tan5 β

+2r20

tanβ+

2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0

+r0

tan5 βminus r0


tanβminus s0


tan2 β+ s0

)(D7)

CS0S0S0 =δ313m

2h0

vo

(minus 24r40

tan5 β+

24r30s0tan4 β

+36r30

tan5 βminus 12r30



tan2 βminus 18r20

tan5 β+

12r20tan3 β

+18r20tanβ

+18r0s0tan4 β

+12r0s0tan2 β

minus 6r0s0 +3r0

tan5 βminus 3r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D8)

Ch0H+Hminus =m2h0

vo

(2δ213r0tanβ

+2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1minus

2m2Hplusmn

tan4 βm2h0

minus4m2

Hplusmn

tan2 βm2h0

minus2m2

Hplusmn

m2h0

) (D9)

References










ndash 32 ndash























ndash 33 ndash






















ndash 34 ndash








ndash 35 ndash

1 Introduction

2 The Model








42 Direct Detection


5 Summary

A Model Parameters












dnχdt

+ 3a


(n2χ minus n2

χeq

)(42)

where aa =

radic8πρ


n2χeq = g

(mχT2π

) 32

exp[minusmχT




MPl


xF)

(43)


mχTF

is given by

xF = ln

c (c+ 2)

radic45

8

gMPl mχ

(a+ 6 b

xF

)2π3radic


(44)

ndash 13 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 50 GeV

2

(f)






ndash 14 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 50 GeV

2

(f)





ndash 15 ndash


12

)(

200 GeV 30 GeV2)(200 GeV 50 GeV2

)(400 GeV 30 GeV2

)(

400 GeV 50 GeV2)(600 GeV 30 GeV2

)and

(600 GeV 50 GeV2

)


42 Direct Detection



σγγN =

(αemZ

π

)2[micro2N

π

(αemZ

πm2S0

)2](

π2

12

)2(microNv

mτ

)2

2

(gχS0ξS

0

l

mτ

v0

)2

(45)



LS0gg

eff = minusξS

0

q

12π

αsvo

sumq=cbt

Iq




12π

ξS0

q gχS0

vom2S0

sumq=cbt

Iq


ndash 16 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 50 GeV

2

(f)




σggN =

(2ξS

0

q gχS0mN

m2S027vo


Iq

∣∣∣∣∣∣2

2

π(mχ +mN )2m2Nm

2χ (48)

ndash 17 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 50 GeV

2

(f)





2N

m2N

(ξS

0

τ

ξS0

q

)2(9

8

)2 v2


ndash 18 ndash




GamicroνGamicroν



Since mN equivsum



F gN = 1minussumuds

FqiNS (q2)

mN= minus 1

mN









ndash 19 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





ndash 20 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





ndash 21 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)




the reference [56]


f

π Ff (x) log

(s(1minusx)m2f


ndash 22 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)






ndash 23 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





x(413)

ndash 24 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





rang

ndash 25 ndash








ndash 26 ndash


5 Summary









ndash 27 ndash





Acknowledgments


ndash 28 ndash

Appendix

A Model Parameters


12

m211 = minus1

2

[m2H0 cos2 α+m2

h0 sin2 α+


h0)minus 2m2

12

tanβ

](A1)

m222 = minus1

2

[m2h0 cos2 α+m2

H0 sin2 α+


h0)minus 2m2

12

cotβ

](A2)

λ1 =1

v2o cos2 β

[m2H0 cos2 α+m2


](A3)

λ2 =1

v2o sin2 β

[m2h0 cos2 α+m2


](A4)

λ3 =2

v2o sin (2β)

[sinα cosα

(m2H0 minusm2

h0)minusm2

12 + m2H+ sin (2β)

](A5)

λ4 =1

v2o sin (2β)

[2m2

12 +(m2A0 minus 2m2

H+

)sin (2β)

](A6)

λ5 =1

v2o sin (2β)

[2m2


](A7)



Γ(S0 rarr f f) =Nc

8π

(ξSfmf

vo

)2

mS0

(1minus

4m2f

m2S0

)32




0

V )2

16π v2o

m3S0

(1minus

4m2W

m2S0

)12[

12

(mW

mS0

)4

minus 4

(mW

mS0

)2

+ 1





8πmS0

(1minus

4m2χ

m2S0

)32



Γ(S0 rarr gg) =

(mtξ

S0

q

vo

)2α2s

72π3

m3S0

m2t


Iq

∣∣∣∣∣∣2

(B5)

ndash 29 ndash



16πv20

(αemπ

)2∣∣∣∣∣sumq

ξS0

q Q2qIq +

suml

ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn

∣∣∣∣∣2







f(λ) as

f(λ) = minus2

(sinminus1 1

2radicλ

)2

for λ gt1

4

=1

2

(lnη+

ηminus

)2

minus π2

2minus iπ η

+

ηminus for λ lt

1

4(B8)


radic14 minus λ




=

(mfξ

S0

f

vo

)2

g2χS0

1

4π

(1minus

m2l

m2χ

) 32 m2

χ

(4m2χ minusm2

φ)2

(3

xf

)θ (mχ minusmf )


)vrang

=

(ξS

0

V

vo

)2g2χS0

8π

radic1minus

m2Z

m2χ

(16m4χ + 12m4

Z minus 16m2χm

2Z)

(4m2χ minusm2

S0)2

(3

xf


σ(χχrarrW+Wminus

)vrang

=

(ξS

0

V

vo

)2g2χS0

16π

radic1minus

m2W

m2χ

(16m4χ + 12m4

W minus 16m2χm

2W )

(4m2χ minusm2

S0)2

(3

xf



(ξS

0

q αs gχS0

3π32vo

)2m4χ

(4m2χ minusm2

S0)2 +m2S0Γ

(3

2xf


Iq

∣∣∣∣∣∣2

(C4)


2em

2π3v2o

m4χ


q Q2qIq +

suml ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn


S0)2 +m2S0Γ2

times(

3

xf

)(C5)

ndash 30 ndash


rang= c0


C2S0HiHj

g2χS0

16πλ

12

(1m2Hi

4m2χ

m2Hj

4m2χ

)

times 1

(4m2χ minusm2

φ)2

(3

xf

)(C6)




)vrang

=3g4χS0

64πm2χ

(3

xf





m2h0

and s0 =m2

12

m2h0 All


Ch0S0S0 =δ213m

2h0

vo

(minus4δ213r

20

tanβ+

2δ213r0tanβ

minus 8r30tan4 β

+8r20s0tan3 β

+4r20

tan4 βminus 8r0s0

tan3 βminus 8r0s0

tanβ

+2r0

tan4 βminus 2r0

tan2 β+

2s0tan3 β


minus 1

tan4 βminus 2

tan2 βminus 1

)(D1)

CS0h0h0 =δ13m

2h0

vo

(minus4δ213r

20

tan2 β+

2δ213r0tan2 β


tan3 βminus 4r0

tanβ

)(D2)

CS0H0H0 =δ13m

2h0

vo

(minus8δ213r

30

tan2 β+

12δ213r20


tan2 βminus 6r20

tan5 βminus 4r20

tan3 β+

2r20tanβ

+6r0s0tan4 β

+4r0s0tan2 β

minus2r0s0 +3r0

tan5 β+

r0tan3 β


minus 3s0tan4 β


+ 3s0

)(D3)

CS0S0H0 =δ213m

2h0

vo

(minus8δ213r

30

tan2 β+

8δ213r20


tan2 β+

12r30tan5 β

+4r30


tan4 βminus 4r20s0

tan2 βminus 12r20

tan5 β

+8r20

tanβ+

12r0s0tan4 β

+8r0s0tan2 β

minus 4r0s0 +3r0

tan5 βminus r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D4)

CS0H0h0 =δ13m

2h0

vo

(minus4δ213r

30

tan3 β+

4δ213r20


20

tanβminus δ213r0

tan3 β+

3δ213r0tanβ

+4r20

tan4 β+

4r20tan2 β

minus 4r0s0tan3 β

minus4r0s0tanβ

minus 3r0tan2 β

minus r0 +2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1

)(D5)

ndash 31 ndash

CS0H+Hminus =δ13m

2h0

vo

(minus 2r20

tan5 β+

2r20tanβ

+2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0 +r0

tan5 βminus r0


minus 5r0tanβ

minus s0tan4 β


+ s0 minus4m2

Hplusmnr0

tan3 βm2h0

minus4m2

Hplusmnr0

tanβm2h0

)(D6)

CS0A0A0 =δ13m

2h0

vo

(minus

4m2A0r0

tan3 βm2h0

minus4m2

A0r0tanβm2

h0

minus 2r20tan5 β

+2r20

tanβ+

2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0

+r0

tan5 βminus r0


tanβminus s0


tan2 β+ s0

)(D7)

CS0S0S0 =δ313m

2h0

vo

(minus 24r40

tan5 β+

24r30s0tan4 β

+36r30

tan5 βminus 12r30



tan2 βminus 18r20

tan5 β+

12r20tan3 β

+18r20tanβ

+18r0s0tan4 β

+12r0s0tan2 β

minus 6r0s0 +3r0

tan5 βminus 3r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D8)

Ch0H+Hminus =m2h0

vo

(2δ213r0tanβ

+2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1minus

2m2Hplusmn

tan4 βm2h0

minus4m2

Hplusmn

tan2 βm2h0

minus2m2

Hplusmn

m2h0

) (D9)

References










ndash 32 ndash























ndash 33 ndash






















ndash 34 ndash








ndash 35 ndash

1 Introduction

2 The Model








42 Direct Detection


5 Summary

A Model Parameters




005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-22e-2

5e-21e-1

2e-1

5e-1

1e0

2e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 50 GeV

2

(f)






ndash 14 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 50 GeV

2

(f)





ndash 15 ndash


12

)(

200 GeV 30 GeV2)(200 GeV 50 GeV2

)(400 GeV 30 GeV2

)(

400 GeV 50 GeV2)(600 GeV 30 GeV2

)and

(600 GeV 50 GeV2

)


42 Direct Detection



σγγN =

(αemZ

π

)2[micro2N

π

(αemZ

πm2S0

)2](

π2

12

)2(microNv

mτ

)2

2

(gχS0ξS

0

l

mτ

v0

)2

(45)



LS0gg

eff = minusξS

0

q

12π

αsvo

sumq=cbt

Iq




12π

ξS0

q gχS0

vom2S0

sumq=cbt

Iq


ndash 16 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 50 GeV

2

(f)




σggN =

(2ξS

0

q gχS0mN

m2S027vo


Iq

∣∣∣∣∣∣2

2

π(mχ +mN )2m2Nm

2χ (48)

ndash 17 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 50 GeV

2

(f)





2N

m2N

(ξS

0

τ

ξS0

q

)2(9

8

)2 v2


ndash 18 ndash




GamicroνGamicroν



Since mN equivsum



F gN = 1minussumuds

FqiNS (q2)

mN= minus 1

mN









ndash 19 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





ndash 20 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





ndash 21 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)




the reference [56]


f

π Ff (x) log

(s(1minusx)m2f


ndash 22 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)






ndash 23 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





x(413)

ndash 24 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





rang

ndash 25 ndash








ndash 26 ndash


5 Summary









ndash 27 ndash





Acknowledgments


ndash 28 ndash

Appendix

A Model Parameters


12

m211 = minus1

2

[m2H0 cos2 α+m2

h0 sin2 α+


h0)minus 2m2

12

tanβ

](A1)

m222 = minus1

2

[m2h0 cos2 α+m2

H0 sin2 α+


h0)minus 2m2

12

cotβ

](A2)

λ1 =1

v2o cos2 β

[m2H0 cos2 α+m2


](A3)

λ2 =1

v2o sin2 β

[m2h0 cos2 α+m2


](A4)

λ3 =2

v2o sin (2β)

[sinα cosα

(m2H0 minusm2

h0)minusm2

12 + m2H+ sin (2β)

](A5)

λ4 =1

v2o sin (2β)

[2m2

12 +(m2A0 minus 2m2

H+

)sin (2β)

](A6)

λ5 =1

v2o sin (2β)

[2m2


](A7)



Γ(S0 rarr f f) =Nc

8π

(ξSfmf

vo

)2

mS0

(1minus

4m2f

m2S0

)32




0

V )2

16π v2o

m3S0

(1minus

4m2W

m2S0

)12[

12

(mW

mS0

)4

minus 4

(mW

mS0

)2

+ 1





8πmS0

(1minus

4m2χ

m2S0

)32



Γ(S0 rarr gg) =

(mtξ

S0

q

vo

)2α2s

72π3

m3S0

m2t


Iq

∣∣∣∣∣∣2

(B5)

ndash 29 ndash



16πv20

(αemπ

)2∣∣∣∣∣sumq

ξS0

q Q2qIq +

suml

ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn

∣∣∣∣∣2







f(λ) as

f(λ) = minus2

(sinminus1 1

2radicλ

)2

for λ gt1

4

=1

2

(lnη+

ηminus

)2

minus π2

2minus iπ η

+

ηminus for λ lt

1

4(B8)


radic14 minus λ




=

(mfξ

S0

f

vo

)2

g2χS0

1

4π

(1minus

m2l

m2χ

) 32 m2

χ

(4m2χ minusm2

φ)2

(3

xf

)θ (mχ minusmf )


)vrang

=

(ξS

0

V

vo

)2g2χS0

8π

radic1minus

m2Z

m2χ

(16m4χ + 12m4

Z minus 16m2χm

2Z)

(4m2χ minusm2

S0)2

(3

xf


σ(χχrarrW+Wminus

)vrang

=

(ξS

0

V

vo

)2g2χS0

16π

radic1minus

m2W

m2χ

(16m4χ + 12m4

W minus 16m2χm

2W )

(4m2χ minusm2

S0)2

(3

xf



(ξS

0

q αs gχS0

3π32vo

)2m4χ

(4m2χ minusm2

S0)2 +m2S0Γ

(3

2xf


Iq

∣∣∣∣∣∣2

(C4)


2em

2π3v2o

m4χ


q Q2qIq +

suml ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn


S0)2 +m2S0Γ2

times(

3

xf

)(C5)

ndash 30 ndash


rang= c0


C2S0HiHj

g2χS0

16πλ

12

(1m2Hi

4m2χ

m2Hj

4m2χ

)

times 1

(4m2χ minusm2

φ)2

(3

xf

)(C6)




)vrang

=3g4χS0

64πm2χ

(3

xf





m2h0

and s0 =m2

12

m2h0 All


Ch0S0S0 =δ213m

2h0

vo

(minus4δ213r

20

tanβ+

2δ213r0tanβ

minus 8r30tan4 β

+8r20s0tan3 β

+4r20

tan4 βminus 8r0s0

tan3 βminus 8r0s0

tanβ

+2r0

tan4 βminus 2r0

tan2 β+

2s0tan3 β


minus 1

tan4 βminus 2

tan2 βminus 1

)(D1)

CS0h0h0 =δ13m

2h0

vo

(minus4δ213r

20

tan2 β+

2δ213r0tan2 β


tan3 βminus 4r0

tanβ

)(D2)

CS0H0H0 =δ13m

2h0

vo

(minus8δ213r

30

tan2 β+

12δ213r20


tan2 βminus 6r20

tan5 βminus 4r20

tan3 β+

2r20tanβ

+6r0s0tan4 β

+4r0s0tan2 β

minus2r0s0 +3r0

tan5 β+

r0tan3 β


minus 3s0tan4 β


+ 3s0

)(D3)

CS0S0H0 =δ213m

2h0

vo

(minus8δ213r

30

tan2 β+

8δ213r20


tan2 β+

12r30tan5 β

+4r30


tan4 βminus 4r20s0

tan2 βminus 12r20

tan5 β

+8r20

tanβ+

12r0s0tan4 β

+8r0s0tan2 β

minus 4r0s0 +3r0

tan5 βminus r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D4)

CS0H0h0 =δ13m

2h0

vo

(minus4δ213r

30

tan3 β+

4δ213r20


20

tanβminus δ213r0

tan3 β+

3δ213r0tanβ

+4r20

tan4 β+

4r20tan2 β

minus 4r0s0tan3 β

minus4r0s0tanβ

minus 3r0tan2 β

minus r0 +2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1

)(D5)

ndash 31 ndash

CS0H+Hminus =δ13m

2h0

vo

(minus 2r20

tan5 β+

2r20tanβ

+2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0 +r0

tan5 βminus r0


minus 5r0tanβ

minus s0tan4 β


+ s0 minus4m2

Hplusmnr0

tan3 βm2h0

minus4m2

Hplusmnr0

tanβm2h0

)(D6)

CS0A0A0 =δ13m

2h0

vo

(minus

4m2A0r0

tan3 βm2h0

minus4m2

A0r0tanβm2

h0

minus 2r20tan5 β

+2r20

tanβ+

2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0

+r0

tan5 βminus r0


tanβminus s0


tan2 β+ s0

)(D7)

CS0S0S0 =δ313m

2h0

vo

(minus 24r40

tan5 β+

24r30s0tan4 β

+36r30

tan5 βminus 12r30



tan2 βminus 18r20

tan5 β+

12r20tan3 β

+18r20tanβ

+18r0s0tan4 β

+12r0s0tan2 β

minus 6r0s0 +3r0

tan5 βminus 3r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D8)

Ch0H+Hminus =m2h0

vo

(2δ213r0tanβ

+2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1minus

2m2Hplusmn

tan4 βm2h0

minus4m2

Hplusmn

tan2 βm2h0

minus2m2

Hplusmn

m2h0

) (D9)

References










ndash 32 ndash























ndash 33 ndash






















ndash 34 ndash








ndash 35 ndash

1 Introduction

2 The Model








42 Direct Detection


5 Summary

A Model Parameters




005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 751e-4

2e-4

5e-4

1e-3

2e-3

5e-3

1e-2

2e-2

5e-2

1e-1

2e-1

5e-1

1e0

gχS

0

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV

mA0 = 600 GeV

m122 = 50 GeV

2

(f)





ndash 15 ndash


12

)(

200 GeV 30 GeV2)(200 GeV 50 GeV2

)(400 GeV 30 GeV2

)(

400 GeV 50 GeV2)(600 GeV 30 GeV2

)and

(600 GeV 50 GeV2

)


42 Direct Detection



σγγN =

(αemZ

π

)2[micro2N

π

(αemZ

πm2S0

)2](

π2

12

)2(microNv

mτ

)2

2

(gχS0ξS

0

l

mτ

v0

)2

(45)



LS0gg

eff = minusξS

0

q

12π

αsvo

sumq=cbt

Iq




12π

ξS0

q gχS0

vom2S0

sumq=cbt

Iq


ndash 16 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 50 GeV

2

(f)




σggN =

(2ξS

0

q gχS0mN

m2S027vo


Iq

∣∣∣∣∣∣2

2

π(mχ +mN )2m2Nm

2χ (48)

ndash 17 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 50 GeV

2

(f)





2N

m2N

(ξS

0

τ

ξS0

q

)2(9

8

)2 v2


ndash 18 ndash




GamicroνGamicroν



Since mN equivsum



F gN = 1minussumuds

FqiNS (q2)

mN= minus 1

mN









ndash 19 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





ndash 20 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





ndash 21 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)




the reference [56]


f

π Ff (x) log

(s(1minusx)m2f


ndash 22 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)






ndash 23 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





x(413)

ndash 24 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





rang

ndash 25 ndash








ndash 26 ndash


5 Summary









ndash 27 ndash





Acknowledgments


ndash 28 ndash

Appendix

A Model Parameters


12

m211 = minus1

2

[m2H0 cos2 α+m2

h0 sin2 α+


h0)minus 2m2

12

tanβ

](A1)

m222 = minus1

2

[m2h0 cos2 α+m2

H0 sin2 α+


h0)minus 2m2

12

cotβ

](A2)

λ1 =1

v2o cos2 β

[m2H0 cos2 α+m2


](A3)

λ2 =1

v2o sin2 β

[m2h0 cos2 α+m2


](A4)

λ3 =2

v2o sin (2β)

[sinα cosα

(m2H0 minusm2

h0)minusm2

12 + m2H+ sin (2β)

](A5)

λ4 =1

v2o sin (2β)

[2m2

12 +(m2A0 minus 2m2

H+

)sin (2β)

](A6)

λ5 =1

v2o sin (2β)

[2m2


](A7)



Γ(S0 rarr f f) =Nc

8π

(ξSfmf

vo

)2

mS0

(1minus

4m2f

m2S0

)32




0

V )2

16π v2o

m3S0

(1minus

4m2W

m2S0

)12[

12

(mW

mS0

)4

minus 4

(mW

mS0

)2

+ 1





8πmS0

(1minus

4m2χ

m2S0

)32



Γ(S0 rarr gg) =

(mtξ

S0

q

vo

)2α2s

72π3

m3S0

m2t


Iq

∣∣∣∣∣∣2

(B5)

ndash 29 ndash



16πv20

(αemπ

)2∣∣∣∣∣sumq

ξS0

q Q2qIq +

suml

ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn

∣∣∣∣∣2







f(λ) as

f(λ) = minus2

(sinminus1 1

2radicλ

)2

for λ gt1

4

=1

2

(lnη+

ηminus

)2

minus π2

2minus iπ η

+

ηminus for λ lt

1

4(B8)


radic14 minus λ




=

(mfξ

S0

f

vo

)2

g2χS0

1

4π

(1minus

m2l

m2χ

) 32 m2

χ

(4m2χ minusm2

φ)2

(3

xf

)θ (mχ minusmf )


)vrang

=

(ξS

0

V

vo

)2g2χS0

8π

radic1minus

m2Z

m2χ

(16m4χ + 12m4

Z minus 16m2χm

2Z)

(4m2χ minusm2

S0)2

(3

xf


σ(χχrarrW+Wminus

)vrang

=

(ξS

0

V

vo

)2g2χS0

16π

radic1minus

m2W

m2χ

(16m4χ + 12m4

W minus 16m2χm

2W )

(4m2χ minusm2

S0)2

(3

xf



(ξS

0

q αs gχS0

3π32vo

)2m4χ

(4m2χ minusm2

S0)2 +m2S0Γ

(3

2xf


Iq

∣∣∣∣∣∣2

(C4)


2em

2π3v2o

m4χ


q Q2qIq +

suml ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn


S0)2 +m2S0Γ2

times(

3

xf

)(C5)

ndash 30 ndash


rang= c0


C2S0HiHj

g2χS0

16πλ

12

(1m2Hi

4m2χ

m2Hj

4m2χ

)

times 1

(4m2χ minusm2

φ)2

(3

xf

)(C6)




)vrang

=3g4χS0

64πm2χ

(3

xf





m2h0

and s0 =m2

12

m2h0 All


Ch0S0S0 =δ213m

2h0

vo

(minus4δ213r

20

tanβ+

2δ213r0tanβ

minus 8r30tan4 β

+8r20s0tan3 β

+4r20

tan4 βminus 8r0s0

tan3 βminus 8r0s0

tanβ

+2r0

tan4 βminus 2r0

tan2 β+

2s0tan3 β


minus 1

tan4 βminus 2

tan2 βminus 1

)(D1)

CS0h0h0 =δ13m

2h0

vo

(minus4δ213r

20

tan2 β+

2δ213r0tan2 β


tan3 βminus 4r0

tanβ

)(D2)

CS0H0H0 =δ13m

2h0

vo

(minus8δ213r

30

tan2 β+

12δ213r20


tan2 βminus 6r20

tan5 βminus 4r20

tan3 β+

2r20tanβ

+6r0s0tan4 β

+4r0s0tan2 β

minus2r0s0 +3r0

tan5 β+

r0tan3 β


minus 3s0tan4 β


+ 3s0

)(D3)

CS0S0H0 =δ213m

2h0

vo

(minus8δ213r

30

tan2 β+

8δ213r20


tan2 β+

12r30tan5 β

+4r30


tan4 βminus 4r20s0

tan2 βminus 12r20

tan5 β

+8r20

tanβ+

12r0s0tan4 β

+8r0s0tan2 β

minus 4r0s0 +3r0

tan5 βminus r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D4)

CS0H0h0 =δ13m

2h0

vo

(minus4δ213r

30

tan3 β+

4δ213r20


20

tanβminus δ213r0

tan3 β+

3δ213r0tanβ

+4r20

tan4 β+

4r20tan2 β

minus 4r0s0tan3 β

minus4r0s0tanβ

minus 3r0tan2 β

minus r0 +2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1

)(D5)

ndash 31 ndash

CS0H+Hminus =δ13m

2h0

vo

(minus 2r20

tan5 β+

2r20tanβ

+2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0 +r0

tan5 βminus r0


minus 5r0tanβ

minus s0tan4 β


+ s0 minus4m2

Hplusmnr0

tan3 βm2h0

minus4m2

Hplusmnr0

tanβm2h0

)(D6)

CS0A0A0 =δ13m

2h0

vo

(minus

4m2A0r0

tan3 βm2h0

minus4m2

A0r0tanβm2

h0

minus 2r20tan5 β

+2r20

tanβ+

2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0

+r0

tan5 βminus r0


tanβminus s0


tan2 β+ s0

)(D7)

CS0S0S0 =δ313m

2h0

vo

(minus 24r40

tan5 β+

24r30s0tan4 β

+36r30

tan5 βminus 12r30



tan2 βminus 18r20

tan5 β+

12r20tan3 β

+18r20tanβ

+18r0s0tan4 β

+12r0s0tan2 β

minus 6r0s0 +3r0

tan5 βminus 3r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D8)

Ch0H+Hminus =m2h0

vo

(2δ213r0tanβ

+2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1minus

2m2Hplusmn

tan4 βm2h0

minus4m2

Hplusmn

tan2 βm2h0

minus2m2

Hplusmn

m2h0

) (D9)

References










ndash 32 ndash























ndash 33 ndash






















ndash 34 ndash








ndash 35 ndash

1 Introduction

2 The Model








42 Direct Detection


5 Summary

A Model Parameters





12

)(

200 GeV 30 GeV2)(200 GeV 50 GeV2

)(400 GeV 30 GeV2

)(

400 GeV 50 GeV2)(600 GeV 30 GeV2

)and

(600 GeV 50 GeV2

)


42 Direct Detection



σγγN =

(αemZ

π

)2[micro2N

π

(αemZ

πm2S0

)2](

π2

12

)2(microNv

mτ

)2

2

(gχS0ξS

0

l

mτ

v0

)2

(45)



LS0gg

eff = minusξS

0

q

12π

αsvo

sumq=cbt

Iq




12π

ξS0

q gχS0

vom2S0

sumq=cbt

Iq


ndash 16 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 50 GeV

2

(f)




σggN =

(2ξS

0

q gχS0mN

m2S027vo


Iq

∣∣∣∣∣∣2

2

π(mχ +mN )2m2Nm

2χ (48)

ndash 17 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 50 GeV

2

(f)





2N

m2N

(ξS

0

τ

ξS0

q

)2(9

8

)2 v2


ndash 18 ndash




GamicroνGamicroν



Since mN equivsum



F gN = 1minussumuds

FqiNS (q2)

mN= minus 1

mN









ndash 19 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





ndash 20 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





ndash 21 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)




the reference [56]


f

π Ff (x) log

(s(1minusx)m2f


ndash 22 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)






ndash 23 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





x(413)

ndash 24 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





rang

ndash 25 ndash








ndash 26 ndash


5 Summary









ndash 27 ndash





Acknowledgments


ndash 28 ndash

Appendix

A Model Parameters


12

m211 = minus1

2

[m2H0 cos2 α+m2

h0 sin2 α+


h0)minus 2m2

12

tanβ

](A1)

m222 = minus1

2

[m2h0 cos2 α+m2

H0 sin2 α+


h0)minus 2m2

12

cotβ

](A2)

λ1 =1

v2o cos2 β

[m2H0 cos2 α+m2


](A3)

λ2 =1

v2o sin2 β

[m2h0 cos2 α+m2


](A4)

λ3 =2

v2o sin (2β)

[sinα cosα

(m2H0 minusm2

h0)minusm2

12 + m2H+ sin (2β)

](A5)

λ4 =1

v2o sin (2β)

[2m2

12 +(m2A0 minus 2m2

H+

)sin (2β)

](A6)

λ5 =1

v2o sin (2β)

[2m2


](A7)



Γ(S0 rarr f f) =Nc

8π

(ξSfmf

vo

)2

mS0

(1minus

4m2f

m2S0

)32




0

V )2

16π v2o

m3S0

(1minus

4m2W

m2S0

)12[

12

(mW

mS0

)4

minus 4

(mW

mS0

)2

+ 1





8πmS0

(1minus

4m2χ

m2S0

)32



Γ(S0 rarr gg) =

(mtξ

S0

q

vo

)2α2s

72π3

m3S0

m2t


Iq

∣∣∣∣∣∣2

(B5)

ndash 29 ndash



16πv20

(αemπ

)2∣∣∣∣∣sumq

ξS0

q Q2qIq +

suml

ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn

∣∣∣∣∣2







f(λ) as

f(λ) = minus2

(sinminus1 1

2radicλ

)2

for λ gt1

4

=1

2

(lnη+

ηminus

)2

minus π2

2minus iπ η

+

ηminus for λ lt

1

4(B8)


radic14 minus λ




=

(mfξ

S0

f

vo

)2

g2χS0

1

4π

(1minus

m2l

m2χ

) 32 m2

χ

(4m2χ minusm2

φ)2

(3

xf

)θ (mχ minusmf )


)vrang

=

(ξS

0

V

vo

)2g2χS0

8π

radic1minus

m2Z

m2χ

(16m4χ + 12m4

Z minus 16m2χm

2Z)

(4m2χ minusm2

S0)2

(3

xf


σ(χχrarrW+Wminus

)vrang

=

(ξS

0

V

vo

)2g2χS0

16π

radic1minus

m2W

m2χ

(16m4χ + 12m4

W minus 16m2χm

2W )

(4m2χ minusm2

S0)2

(3

xf



(ξS

0

q αs gχS0

3π32vo

)2m4χ

(4m2χ minusm2

S0)2 +m2S0Γ

(3

2xf


Iq

∣∣∣∣∣∣2

(C4)


2em

2π3v2o

m4χ


q Q2qIq +

suml ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn


S0)2 +m2S0Γ2

times(

3

xf

)(C5)

ndash 30 ndash


rang= c0


C2S0HiHj

g2χS0

16πλ

12

(1m2Hi

4m2χ

m2Hj

4m2χ

)

times 1

(4m2χ minusm2

φ)2

(3

xf

)(C6)




)vrang

=3g4χS0

64πm2χ

(3

xf





m2h0

and s0 =m2

12

m2h0 All


Ch0S0S0 =δ213m

2h0

vo

(minus4δ213r

20

tanβ+

2δ213r0tanβ

minus 8r30tan4 β

+8r20s0tan3 β

+4r20

tan4 βminus 8r0s0

tan3 βminus 8r0s0

tanβ

+2r0

tan4 βminus 2r0

tan2 β+

2s0tan3 β


minus 1

tan4 βminus 2

tan2 βminus 1

)(D1)

CS0h0h0 =δ13m

2h0

vo

(minus4δ213r

20

tan2 β+

2δ213r0tan2 β


tan3 βminus 4r0

tanβ

)(D2)

CS0H0H0 =δ13m

2h0

vo

(minus8δ213r

30

tan2 β+

12δ213r20


tan2 βminus 6r20

tan5 βminus 4r20

tan3 β+

2r20tanβ

+6r0s0tan4 β

+4r0s0tan2 β

minus2r0s0 +3r0

tan5 β+

r0tan3 β


minus 3s0tan4 β


+ 3s0

)(D3)

CS0S0H0 =δ213m

2h0

vo

(minus8δ213r

30

tan2 β+

8δ213r20


tan2 β+

12r30tan5 β

+4r30


tan4 βminus 4r20s0

tan2 βminus 12r20

tan5 β

+8r20

tanβ+

12r0s0tan4 β

+8r0s0tan2 β

minus 4r0s0 +3r0

tan5 βminus r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D4)

CS0H0h0 =δ13m

2h0

vo

(minus4δ213r

30

tan3 β+

4δ213r20


20

tanβminus δ213r0

tan3 β+

3δ213r0tanβ

+4r20

tan4 β+

4r20tan2 β

minus 4r0s0tan3 β

minus4r0s0tanβ

minus 3r0tan2 β

minus r0 +2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1

)(D5)

ndash 31 ndash

CS0H+Hminus =δ13m

2h0

vo

(minus 2r20

tan5 β+

2r20tanβ

+2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0 +r0

tan5 βminus r0


minus 5r0tanβ

minus s0tan4 β


+ s0 minus4m2

Hplusmnr0

tan3 βm2h0

minus4m2

Hplusmnr0

tanβm2h0

)(D6)

CS0A0A0 =δ13m

2h0

vo

(minus

4m2A0r0

tan3 βm2h0

minus4m2

A0r0tanβm2

h0

minus 2r20tan5 β

+2r20

tanβ+

2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0

+r0

tan5 βminus r0


tanβminus s0


tan2 β+ s0

)(D7)

CS0S0S0 =δ313m

2h0

vo

(minus 24r40

tan5 β+

24r30s0tan4 β

+36r30

tan5 βminus 12r30



tan2 βminus 18r20

tan5 β+

12r20tan3 β

+18r20tanβ

+18r0s0tan4 β

+12r0s0tan2 β

minus 6r0s0 +3r0

tan5 βminus 3r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D8)

Ch0H+Hminus =m2h0

vo

(2δ213r0tanβ

+2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1minus

2m2Hplusmn

tan4 βm2h0

minus4m2

Hplusmn

tan2 βm2h0

minus2m2

Hplusmn

m2h0

) (D9)

References










ndash 32 ndash























ndash 33 ndash






















ndash 34 ndash








ndash 35 ndash

1 Introduction

2 The Model








42 Direct Detection


5 Summary

A Model Parameters




005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 50 GeV

2

(f)




σggN =

(2ξS

0

q gχS0mN

m2S027vo


Iq

∣∣∣∣∣∣2

2

π(mχ +mN )2m2Nm

2χ (48)

ndash 17 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 50 GeV

2

(f)





2N

m2N

(ξS

0

τ

ξS0

q

)2(9

8

)2 v2


ndash 18 ndash




GamicroνGamicroν



Since mN equivsum



F gN = 1minussumuds

FqiNS (q2)

mN= minus 1

mN









ndash 19 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





ndash 20 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





ndash 21 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)




the reference [56]


f

π Ff (x) log

(s(1minusx)m2f


ndash 22 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)






ndash 23 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





x(413)

ndash 24 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





rang

ndash 25 ndash








ndash 26 ndash


5 Summary









ndash 27 ndash





Acknowledgments


ndash 28 ndash

Appendix

A Model Parameters


12

m211 = minus1

2

[m2H0 cos2 α+m2

h0 sin2 α+


h0)minus 2m2

12

tanβ

](A1)

m222 = minus1

2

[m2h0 cos2 α+m2

H0 sin2 α+


h0)minus 2m2

12

cotβ

](A2)

λ1 =1

v2o cos2 β

[m2H0 cos2 α+m2


](A3)

λ2 =1

v2o sin2 β

[m2h0 cos2 α+m2


](A4)

λ3 =2

v2o sin (2β)

[sinα cosα

(m2H0 minusm2

h0)minusm2

12 + m2H+ sin (2β)

](A5)

λ4 =1

v2o sin (2β)

[2m2

12 +(m2A0 minus 2m2

H+

)sin (2β)

](A6)

λ5 =1

v2o sin (2β)

[2m2


](A7)



Γ(S0 rarr f f) =Nc

8π

(ξSfmf

vo

)2

mS0

(1minus

4m2f

m2S0

)32




0

V )2

16π v2o

m3S0

(1minus

4m2W

m2S0

)12[

12

(mW

mS0

)4

minus 4

(mW

mS0

)2

+ 1





8πmS0

(1minus

4m2χ

m2S0

)32



Γ(S0 rarr gg) =

(mtξ

S0

q

vo

)2α2s

72π3

m3S0

m2t


Iq

∣∣∣∣∣∣2

(B5)

ndash 29 ndash



16πv20

(αemπ

)2∣∣∣∣∣sumq

ξS0

q Q2qIq +

suml

ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn

∣∣∣∣∣2







f(λ) as

f(λ) = minus2

(sinminus1 1

2radicλ

)2

for λ gt1

4

=1

2

(lnη+

ηminus

)2

minus π2

2minus iπ η

+

ηminus for λ lt

1

4(B8)


radic14 minus λ




=

(mfξ

S0

f

vo

)2

g2χS0

1

4π

(1minus

m2l

m2χ

) 32 m2

χ

(4m2χ minusm2

φ)2

(3

xf

)θ (mχ minusmf )


)vrang

=

(ξS

0

V

vo

)2g2χS0

8π

radic1minus

m2Z

m2χ

(16m4χ + 12m4

Z minus 16m2χm

2Z)

(4m2χ minusm2

S0)2

(3

xf


σ(χχrarrW+Wminus

)vrang

=

(ξS

0

V

vo

)2g2χS0

16π

radic1minus

m2W

m2χ

(16m4χ + 12m4

W minus 16m2χm

2W )

(4m2χ minusm2

S0)2

(3

xf



(ξS

0

q αs gχS0

3π32vo

)2m4χ

(4m2χ minusm2

S0)2 +m2S0Γ

(3

2xf


Iq

∣∣∣∣∣∣2

(C4)


2em

2π3v2o

m4χ


q Q2qIq +

suml ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn


S0)2 +m2S0Γ2

times(

3

xf

)(C5)

ndash 30 ndash


rang= c0


C2S0HiHj

g2χS0

16πλ

12

(1m2Hi

4m2χ

m2Hj

4m2χ

)

times 1

(4m2χ minusm2

φ)2

(3

xf

)(C6)




)vrang

=3g4χS0

64πm2χ

(3

xf





m2h0

and s0 =m2

12

m2h0 All


Ch0S0S0 =δ213m

2h0

vo

(minus4δ213r

20

tanβ+

2δ213r0tanβ

minus 8r30tan4 β

+8r20s0tan3 β

+4r20

tan4 βminus 8r0s0

tan3 βminus 8r0s0

tanβ

+2r0

tan4 βminus 2r0

tan2 β+

2s0tan3 β


minus 1

tan4 βminus 2

tan2 βminus 1

)(D1)

CS0h0h0 =δ13m

2h0

vo

(minus4δ213r

20

tan2 β+

2δ213r0tan2 β


tan3 βminus 4r0

tanβ

)(D2)

CS0H0H0 =δ13m

2h0

vo

(minus8δ213r

30

tan2 β+

12δ213r20


tan2 βminus 6r20

tan5 βminus 4r20

tan3 β+

2r20tanβ

+6r0s0tan4 β

+4r0s0tan2 β

minus2r0s0 +3r0

tan5 β+

r0tan3 β


minus 3s0tan4 β


+ 3s0

)(D3)

CS0S0H0 =δ213m

2h0

vo

(minus8δ213r

30

tan2 β+

8δ213r20


tan2 β+

12r30tan5 β

+4r30


tan4 βminus 4r20s0

tan2 βminus 12r20

tan5 β

+8r20

tanβ+

12r0s0tan4 β

+8r0s0tan2 β

minus 4r0s0 +3r0

tan5 βminus r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D4)

CS0H0h0 =δ13m

2h0

vo

(minus4δ213r

30

tan3 β+

4δ213r20


20

tanβminus δ213r0

tan3 β+

3δ213r0tanβ

+4r20

tan4 β+

4r20tan2 β

minus 4r0s0tan3 β

minus4r0s0tanβ

minus 3r0tan2 β

minus r0 +2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1

)(D5)

ndash 31 ndash

CS0H+Hminus =δ13m

2h0

vo

(minus 2r20

tan5 β+

2r20tanβ

+2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0 +r0

tan5 βminus r0


minus 5r0tanβ

minus s0tan4 β


+ s0 minus4m2

Hplusmnr0

tan3 βm2h0

minus4m2

Hplusmnr0

tanβm2h0

)(D6)

CS0A0A0 =δ13m

2h0

vo

(minus

4m2A0r0

tan3 βm2h0

minus4m2

A0r0tanβm2

h0

minus 2r20tan5 β

+2r20

tanβ+

2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0

+r0

tan5 βminus r0


tanβminus s0


tan2 β+ s0

)(D7)

CS0S0S0 =δ313m

2h0

vo

(minus 24r40

tan5 β+

24r30s0tan4 β

+36r30

tan5 βminus 12r30



tan2 βminus 18r20

tan5 β+

12r20tan3 β

+18r20tanβ

+18r0s0tan4 β

+12r0s0tan2 β

minus 6r0s0 +3r0

tan5 βminus 3r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D8)

Ch0H+Hminus =m2h0

vo

(2δ213r0tanβ

+2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1minus

2m2Hplusmn

tan4 βm2h0

minus4m2

Hplusmn

tan2 βm2h0

minus2m2

Hplusmn

m2h0

) (D9)

References










ndash 32 ndash























ndash 33 ndash






















ndash 34 ndash








ndash 35 ndash

1 Introduction

2 The Model








42 Direct Detection


5 Summary

A Model Parameters




005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 30 GeV

2

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 200 GeV

m122 = 50 GeV

2

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 30 GeV

2

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 400 GeV

m122 = 50 GeV

2

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 30 GeV

2

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-51

10-50

10-49

10-48

10-47

10-46

10-45

10-44

10-43

σ(χ

N rarr

χ N

) in

cm

2

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


PANDA2X-II 2017

mA0 = 600 GeV

m122 = 50 GeV

2

(f)





2N

m2N

(ξS

0

τ

ξS0

q

)2(9

8

)2 v2


ndash 18 ndash




GamicroνGamicroν



Since mN equivsum



F gN = 1minussumuds

FqiNS (q2)

mN= minus 1

mN









ndash 19 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





ndash 20 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





ndash 21 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)




the reference [56]


f

π Ff (x) log

(s(1minusx)m2f


ndash 22 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)






ndash 23 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





x(413)

ndash 24 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





rang

ndash 25 ndash








ndash 26 ndash


5 Summary









ndash 27 ndash





Acknowledgments


ndash 28 ndash

Appendix

A Model Parameters


12

m211 = minus1

2

[m2H0 cos2 α+m2

h0 sin2 α+


h0)minus 2m2

12

tanβ

](A1)

m222 = minus1

2

[m2h0 cos2 α+m2

H0 sin2 α+


h0)minus 2m2

12

cotβ

](A2)

λ1 =1

v2o cos2 β

[m2H0 cos2 α+m2


](A3)

λ2 =1

v2o sin2 β

[m2h0 cos2 α+m2


](A4)

λ3 =2

v2o sin (2β)

[sinα cosα

(m2H0 minusm2

h0)minusm2

12 + m2H+ sin (2β)

](A5)

λ4 =1

v2o sin (2β)

[2m2

12 +(m2A0 minus 2m2

H+

)sin (2β)

](A6)

λ5 =1

v2o sin (2β)

[2m2


](A7)



Γ(S0 rarr f f) =Nc

8π

(ξSfmf

vo

)2

mS0

(1minus

4m2f

m2S0

)32




0

V )2

16π v2o

m3S0

(1minus

4m2W

m2S0

)12[

12

(mW

mS0

)4

minus 4

(mW

mS0

)2

+ 1





8πmS0

(1minus

4m2χ

m2S0

)32



Γ(S0 rarr gg) =

(mtξ

S0

q

vo

)2α2s

72π3

m3S0

m2t


Iq

∣∣∣∣∣∣2

(B5)

ndash 29 ndash



16πv20

(αemπ

)2∣∣∣∣∣sumq

ξS0

q Q2qIq +

suml

ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn

∣∣∣∣∣2







f(λ) as

f(λ) = minus2

(sinminus1 1

2radicλ

)2

for λ gt1

4

=1

2

(lnη+

ηminus

)2

minus π2

2minus iπ η

+

ηminus for λ lt

1

4(B8)


radic14 minus λ




=

(mfξ

S0

f

vo

)2

g2χS0

1

4π

(1minus

m2l

m2χ

) 32 m2

χ

(4m2χ minusm2

φ)2

(3

xf

)θ (mχ minusmf )


)vrang

=

(ξS

0

V

vo

)2g2χS0

8π

radic1minus

m2Z

m2χ

(16m4χ + 12m4

Z minus 16m2χm

2Z)

(4m2χ minusm2

S0)2

(3

xf


σ(χχrarrW+Wminus

)vrang

=

(ξS

0

V

vo

)2g2χS0

16π

radic1minus

m2W

m2χ

(16m4χ + 12m4

W minus 16m2χm

2W )

(4m2χ minusm2

S0)2

(3

xf



(ξS

0

q αs gχS0

3π32vo

)2m4χ

(4m2χ minusm2

S0)2 +m2S0Γ

(3

2xf


Iq

∣∣∣∣∣∣2

(C4)


2em

2π3v2o

m4χ


q Q2qIq +

suml ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn


S0)2 +m2S0Γ2

times(

3

xf

)(C5)

ndash 30 ndash


rang= c0


C2S0HiHj

g2χS0

16πλ

12

(1m2Hi

4m2χ

m2Hj

4m2χ

)

times 1

(4m2χ minusm2

φ)2

(3

xf

)(C6)




)vrang

=3g4χS0

64πm2χ

(3

xf





m2h0

and s0 =m2

12

m2h0 All


Ch0S0S0 =δ213m

2h0

vo

(minus4δ213r

20

tanβ+

2δ213r0tanβ

minus 8r30tan4 β

+8r20s0tan3 β

+4r20

tan4 βminus 8r0s0

tan3 βminus 8r0s0

tanβ

+2r0

tan4 βminus 2r0

tan2 β+

2s0tan3 β


minus 1

tan4 βminus 2

tan2 βminus 1

)(D1)

CS0h0h0 =δ13m

2h0

vo

(minus4δ213r

20

tan2 β+

2δ213r0tan2 β


tan3 βminus 4r0

tanβ

)(D2)

CS0H0H0 =δ13m

2h0

vo

(minus8δ213r

30

tan2 β+

12δ213r20


tan2 βminus 6r20

tan5 βminus 4r20

tan3 β+

2r20tanβ

+6r0s0tan4 β

+4r0s0tan2 β

minus2r0s0 +3r0

tan5 β+

r0tan3 β


minus 3s0tan4 β


+ 3s0

)(D3)

CS0S0H0 =δ213m

2h0

vo

(minus8δ213r

30

tan2 β+

8δ213r20


tan2 β+

12r30tan5 β

+4r30


tan4 βminus 4r20s0

tan2 βminus 12r20

tan5 β

+8r20

tanβ+

12r0s0tan4 β

+8r0s0tan2 β

minus 4r0s0 +3r0

tan5 βminus r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D4)

CS0H0h0 =δ13m

2h0

vo

(minus4δ213r

30

tan3 β+

4δ213r20


20

tanβminus δ213r0

tan3 β+

3δ213r0tanβ

+4r20

tan4 β+

4r20tan2 β

minus 4r0s0tan3 β

minus4r0s0tanβ

minus 3r0tan2 β

minus r0 +2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1

)(D5)

ndash 31 ndash

CS0H+Hminus =δ13m

2h0

vo

(minus 2r20

tan5 β+

2r20tanβ

+2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0 +r0

tan5 βminus r0


minus 5r0tanβ

minus s0tan4 β


+ s0 minus4m2

Hplusmnr0

tan3 βm2h0

minus4m2

Hplusmnr0

tanβm2h0

)(D6)

CS0A0A0 =δ13m

2h0

vo

(minus

4m2A0r0

tan3 βm2h0

minus4m2

A0r0tanβm2

h0

minus 2r20tan5 β

+2r20

tanβ+

2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0

+r0

tan5 βminus r0


tanβminus s0


tan2 β+ s0

)(D7)

CS0S0S0 =δ313m

2h0

vo

(minus 24r40

tan5 β+

24r30s0tan4 β

+36r30

tan5 βminus 12r30



tan2 βminus 18r20

tan5 β+

12r20tan3 β

+18r20tanβ

+18r0s0tan4 β

+12r0s0tan2 β

minus 6r0s0 +3r0

tan5 βminus 3r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D8)

Ch0H+Hminus =m2h0

vo

(2δ213r0tanβ

+2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1minus

2m2Hplusmn

tan4 βm2h0

minus4m2

Hplusmn

tan2 βm2h0

minus2m2

Hplusmn

m2h0

) (D9)

References










ndash 32 ndash























ndash 33 ndash






















ndash 34 ndash








ndash 35 ndash

1 Introduction

2 The Model








42 Direct Detection


5 Summary

A Model Parameters







GamicroνGamicroν



Since mN equivsum



F gN = 1minussumuds

FqiNS (q2)

mN= minus 1

mN









ndash 19 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





ndash 20 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





ndash 21 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)




the reference [56]


f

π Ff (x) log

(s(1minusx)m2f


ndash 22 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)






ndash 23 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





x(413)

ndash 24 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





rang

ndash 25 ndash








ndash 26 ndash


5 Summary









ndash 27 ndash





Acknowledgments


ndash 28 ndash

Appendix

A Model Parameters


12

m211 = minus1

2

[m2H0 cos2 α+m2

h0 sin2 α+


h0)minus 2m2

12

tanβ

](A1)

m222 = minus1

2

[m2h0 cos2 α+m2

H0 sin2 α+


h0)minus 2m2

12

cotβ

](A2)

λ1 =1

v2o cos2 β

[m2H0 cos2 α+m2


](A3)

λ2 =1

v2o sin2 β

[m2h0 cos2 α+m2


](A4)

λ3 =2

v2o sin (2β)

[sinα cosα

(m2H0 minusm2

h0)minusm2

12 + m2H+ sin (2β)

](A5)

λ4 =1

v2o sin (2β)

[2m2

12 +(m2A0 minus 2m2

H+

)sin (2β)

](A6)

λ5 =1

v2o sin (2β)

[2m2


](A7)



Γ(S0 rarr f f) =Nc

8π

(ξSfmf

vo

)2

mS0

(1minus

4m2f

m2S0

)32




0

V )2

16π v2o

m3S0

(1minus

4m2W

m2S0

)12[

12

(mW

mS0

)4

minus 4

(mW

mS0

)2

+ 1





8πmS0

(1minus

4m2χ

m2S0

)32



Γ(S0 rarr gg) =

(mtξ

S0

q

vo

)2α2s

72π3

m3S0

m2t


Iq

∣∣∣∣∣∣2

(B5)

ndash 29 ndash



16πv20

(αemπ

)2∣∣∣∣∣sumq

ξS0

q Q2qIq +

suml

ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn

∣∣∣∣∣2







f(λ) as

f(λ) = minus2

(sinminus1 1

2radicλ

)2

for λ gt1

4

=1

2

(lnη+

ηminus

)2

minus π2

2minus iπ η

+

ηminus for λ lt

1

4(B8)


radic14 minus λ




=

(mfξ

S0

f

vo

)2

g2χS0

1

4π

(1minus

m2l

m2χ

) 32 m2

χ

(4m2χ minusm2

φ)2

(3

xf

)θ (mχ minusmf )


)vrang

=

(ξS

0

V

vo

)2g2χS0

8π

radic1minus

m2Z

m2χ

(16m4χ + 12m4

Z minus 16m2χm

2Z)

(4m2χ minusm2

S0)2

(3

xf


σ(χχrarrW+Wminus

)vrang

=

(ξS

0

V

vo

)2g2χS0

16π

radic1minus

m2W

m2χ

(16m4χ + 12m4

W minus 16m2χm

2W )

(4m2χ minusm2

S0)2

(3

xf



(ξS

0

q αs gχS0

3π32vo

)2m4χ

(4m2χ minusm2

S0)2 +m2S0Γ

(3

2xf


Iq

∣∣∣∣∣∣2

(C4)


2em

2π3v2o

m4χ


q Q2qIq +

suml ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn


S0)2 +m2S0Γ2

times(

3

xf

)(C5)

ndash 30 ndash


rang= c0


C2S0HiHj

g2χS0

16πλ

12

(1m2Hi

4m2χ

m2Hj

4m2χ

)

times 1

(4m2χ minusm2

φ)2

(3

xf

)(C6)




)vrang

=3g4χS0

64πm2χ

(3

xf





m2h0

and s0 =m2

12

m2h0 All


Ch0S0S0 =δ213m

2h0

vo

(minus4δ213r

20

tanβ+

2δ213r0tanβ

minus 8r30tan4 β

+8r20s0tan3 β

+4r20

tan4 βminus 8r0s0

tan3 βminus 8r0s0

tanβ

+2r0

tan4 βminus 2r0

tan2 β+

2s0tan3 β


minus 1

tan4 βminus 2

tan2 βminus 1

)(D1)

CS0h0h0 =δ13m

2h0

vo

(minus4δ213r

20

tan2 β+

2δ213r0tan2 β


tan3 βminus 4r0

tanβ

)(D2)

CS0H0H0 =δ13m

2h0

vo

(minus8δ213r

30

tan2 β+

12δ213r20


tan2 βminus 6r20

tan5 βminus 4r20

tan3 β+

2r20tanβ

+6r0s0tan4 β

+4r0s0tan2 β

minus2r0s0 +3r0

tan5 β+

r0tan3 β


minus 3s0tan4 β


+ 3s0

)(D3)

CS0S0H0 =δ213m

2h0

vo

(minus8δ213r

30

tan2 β+

8δ213r20


tan2 β+

12r30tan5 β

+4r30


tan4 βminus 4r20s0

tan2 βminus 12r20

tan5 β

+8r20

tanβ+

12r0s0tan4 β

+8r0s0tan2 β

minus 4r0s0 +3r0

tan5 βminus r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D4)

CS0H0h0 =δ13m

2h0

vo

(minus4δ213r

30

tan3 β+

4δ213r20


20

tanβminus δ213r0

tan3 β+

3δ213r0tanβ

+4r20

tan4 β+

4r20tan2 β

minus 4r0s0tan3 β

minus4r0s0tanβ

minus 3r0tan2 β

minus r0 +2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1

)(D5)

ndash 31 ndash

CS0H+Hminus =δ13m

2h0

vo

(minus 2r20

tan5 β+

2r20tanβ

+2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0 +r0

tan5 βminus r0


minus 5r0tanβ

minus s0tan4 β


+ s0 minus4m2

Hplusmnr0

tan3 βm2h0

minus4m2

Hplusmnr0

tanβm2h0

)(D6)

CS0A0A0 =δ13m

2h0

vo

(minus

4m2A0r0

tan3 βm2h0

minus4m2

A0r0tanβm2

h0

minus 2r20tan5 β

+2r20

tanβ+

2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0

+r0

tan5 βminus r0


tanβminus s0


tan2 β+ s0

)(D7)

CS0S0S0 =δ313m

2h0

vo

(minus 24r40

tan5 β+

24r30s0tan4 β

+36r30

tan5 βminus 12r30



tan2 βminus 18r20

tan5 β+

12r20tan3 β

+18r20tanβ

+18r0s0tan4 β

+12r0s0tan2 β

minus 6r0s0 +3r0

tan5 βminus 3r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D8)

Ch0H+Hminus =m2h0

vo

(2δ213r0tanβ

+2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1minus

2m2Hplusmn

tan4 βm2h0

minus4m2

Hplusmn

tan2 βm2h0

minus2m2

Hplusmn

m2h0

) (D9)

References










ndash 32 ndash























ndash 33 ndash






















ndash 34 ndash








ndash 35 ndash

1 Introduction

2 The Model








42 Direct Detection


5 Summary

A Model Parameters




005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





ndash 20 ndash

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





ndash 21 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)




the reference [56]


f

π Ff (x) log

(s(1minusx)m2f


ndash 22 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)






ndash 23 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





x(413)

ndash 24 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





rang

ndash 25 ndash








ndash 26 ndash


5 Summary









ndash 27 ndash





Acknowledgments


ndash 28 ndash

Appendix

A Model Parameters


12

m211 = minus1

2

[m2H0 cos2 α+m2

h0 sin2 α+


h0)minus 2m2

12

tanβ

](A1)

m222 = minus1

2

[m2h0 cos2 α+m2

H0 sin2 α+


h0)minus 2m2

12

cotβ

](A2)

λ1 =1

v2o cos2 β

[m2H0 cos2 α+m2


](A3)

λ2 =1

v2o sin2 β

[m2h0 cos2 α+m2


](A4)

λ3 =2

v2o sin (2β)

[sinα cosα

(m2H0 minusm2

h0)minusm2

12 + m2H+ sin (2β)

](A5)

λ4 =1

v2o sin (2β)

[2m2

12 +(m2A0 minus 2m2

H+

)sin (2β)

](A6)

λ5 =1

v2o sin (2β)

[2m2


](A7)



Γ(S0 rarr f f) =Nc

8π

(ξSfmf

vo

)2

mS0

(1minus

4m2f

m2S0

)32




0

V )2

16π v2o

m3S0

(1minus

4m2W

m2S0

)12[

12

(mW

mS0

)4

minus 4

(mW

mS0

)2

+ 1





8πmS0

(1minus

4m2χ

m2S0

)32



Γ(S0 rarr gg) =

(mtξ

S0

q

vo

)2α2s

72π3

m3S0

m2t


Iq

∣∣∣∣∣∣2

(B5)

ndash 29 ndash



16πv20

(αemπ

)2∣∣∣∣∣sumq

ξS0

q Q2qIq +

suml

ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn

∣∣∣∣∣2







f(λ) as

f(λ) = minus2

(sinminus1 1

2radicλ

)2

for λ gt1

4

=1

2

(lnη+

ηminus

)2

minus π2

2minus iπ η

+

ηminus for λ lt

1

4(B8)


radic14 minus λ




=

(mfξ

S0

f

vo

)2

g2χS0

1

4π

(1minus

m2l

m2χ

) 32 m2

χ

(4m2χ minusm2

φ)2

(3

xf

)θ (mχ minusmf )


)vrang

=

(ξS

0

V

vo

)2g2χS0

8π

radic1minus

m2Z

m2χ

(16m4χ + 12m4

Z minus 16m2χm

2Z)

(4m2χ minusm2

S0)2

(3

xf


σ(χχrarrW+Wminus

)vrang

=

(ξS

0

V

vo

)2g2χS0

16π

radic1minus

m2W

m2χ

(16m4χ + 12m4

W minus 16m2χm

2W )

(4m2χ minusm2

S0)2

(3

xf



(ξS

0

q αs gχS0

3π32vo

)2m4χ

(4m2χ minusm2

S0)2 +m2S0Γ

(3

2xf


Iq

∣∣∣∣∣∣2

(C4)


2em

2π3v2o

m4χ


q Q2qIq +

suml ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn


S0)2 +m2S0Γ2

times(

3

xf

)(C5)

ndash 30 ndash


rang= c0


C2S0HiHj

g2χS0

16πλ

12

(1m2Hi

4m2χ

m2Hj

4m2χ

)

times 1

(4m2χ minusm2

φ)2

(3

xf

)(C6)




)vrang

=3g4χS0

64πm2χ

(3

xf





m2h0

and s0 =m2

12

m2h0 All


Ch0S0S0 =δ213m

2h0

vo

(minus4δ213r

20

tanβ+

2δ213r0tanβ

minus 8r30tan4 β

+8r20s0tan3 β

+4r20

tan4 βminus 8r0s0

tan3 βminus 8r0s0

tanβ

+2r0

tan4 βminus 2r0

tan2 β+

2s0tan3 β


minus 1

tan4 βminus 2

tan2 βminus 1

)(D1)

CS0h0h0 =δ13m

2h0

vo

(minus4δ213r

20

tan2 β+

2δ213r0tan2 β


tan3 βminus 4r0

tanβ

)(D2)

CS0H0H0 =δ13m

2h0

vo

(minus8δ213r

30

tan2 β+

12δ213r20


tan2 βminus 6r20

tan5 βminus 4r20

tan3 β+

2r20tanβ

+6r0s0tan4 β

+4r0s0tan2 β

minus2r0s0 +3r0

tan5 β+

r0tan3 β


minus 3s0tan4 β


+ 3s0

)(D3)

CS0S0H0 =δ213m

2h0

vo

(minus8δ213r

30

tan2 β+

8δ213r20


tan2 β+

12r30tan5 β

+4r30


tan4 βminus 4r20s0

tan2 βminus 12r20

tan5 β

+8r20

tanβ+

12r0s0tan4 β

+8r0s0tan2 β

minus 4r0s0 +3r0

tan5 βminus r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D4)

CS0H0h0 =δ13m

2h0

vo

(minus4δ213r

30

tan3 β+

4δ213r20


20

tanβminus δ213r0

tan3 β+

3δ213r0tanβ

+4r20

tan4 β+

4r20tan2 β

minus 4r0s0tan3 β

minus4r0s0tanβ

minus 3r0tan2 β

minus r0 +2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1

)(D5)

ndash 31 ndash

CS0H+Hminus =δ13m

2h0

vo

(minus 2r20

tan5 β+

2r20tanβ

+2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0 +r0

tan5 βminus r0


minus 5r0tanβ

minus s0tan4 β


+ s0 minus4m2

Hplusmnr0

tan3 βm2h0

minus4m2

Hplusmnr0

tanβm2h0

)(D6)

CS0A0A0 =δ13m

2h0

vo

(minus

4m2A0r0

tan3 βm2h0

minus4m2

A0r0tanβm2

h0

minus 2r20tan5 β

+2r20

tanβ+

2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0

+r0

tan5 βminus r0


tanβminus s0


tan2 β+ s0

)(D7)

CS0S0S0 =δ313m

2h0

vo

(minus 24r40

tan5 β+

24r30s0tan4 β

+36r30

tan5 βminus 12r30



tan2 βminus 18r20

tan5 β+

12r20tan3 β

+18r20tanβ

+18r0s0tan4 β

+12r0s0tan2 β

minus 6r0s0 +3r0

tan5 βminus 3r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D8)

Ch0H+Hminus =m2h0

vo

(2δ213r0tanβ

+2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1minus

2m2Hplusmn

tan4 βm2h0

minus4m2

Hplusmn

tan2 βm2h0

minus2m2

Hplusmn

m2h0

) (D9)

References










ndash 32 ndash























ndash 33 ndash






















ndash 34 ndash








ndash 35 ndash

1 Introduction

2 The Model








42 Direct Detection


5 Summary

A Model Parameters




005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

005 01 02 05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





ndash 21 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)




the reference [56]


f

π Ff (x) log

(s(1minusx)m2f


ndash 22 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)






ndash 23 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





x(413)

ndash 24 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





rang

ndash 25 ndash








ndash 26 ndash


5 Summary









ndash 27 ndash





Acknowledgments


ndash 28 ndash

Appendix

A Model Parameters


12

m211 = minus1

2

[m2H0 cos2 α+m2

h0 sin2 α+


h0)minus 2m2

12

tanβ

](A1)

m222 = minus1

2

[m2h0 cos2 α+m2

H0 sin2 α+


h0)minus 2m2

12

cotβ

](A2)

λ1 =1

v2o cos2 β

[m2H0 cos2 α+m2


](A3)

λ2 =1

v2o sin2 β

[m2h0 cos2 α+m2


](A4)

λ3 =2

v2o sin (2β)

[sinα cosα

(m2H0 minusm2

h0)minusm2

12 + m2H+ sin (2β)

](A5)

λ4 =1

v2o sin (2β)

[2m2

12 +(m2A0 minus 2m2

H+

)sin (2β)

](A6)

λ5 =1

v2o sin (2β)

[2m2


](A7)



Γ(S0 rarr f f) =Nc

8π

(ξSfmf

vo

)2

mS0

(1minus

4m2f

m2S0

)32




0

V )2

16π v2o

m3S0

(1minus

4m2W

m2S0

)12[

12

(mW

mS0

)4

minus 4

(mW

mS0

)2

+ 1





8πmS0

(1minus

4m2χ

m2S0

)32



Γ(S0 rarr gg) =

(mtξ

S0

q

vo

)2α2s

72π3

m3S0

m2t


Iq

∣∣∣∣∣∣2

(B5)

ndash 29 ndash



16πv20

(αemπ

)2∣∣∣∣∣sumq

ξS0

q Q2qIq +

suml

ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn

∣∣∣∣∣2







f(λ) as

f(λ) = minus2

(sinminus1 1

2radicλ

)2

for λ gt1

4

=1

2

(lnη+

ηminus

)2

minus π2

2minus iπ η

+

ηminus for λ lt

1

4(B8)


radic14 minus λ




=

(mfξ

S0

f

vo

)2

g2χS0

1

4π

(1minus

m2l

m2χ

) 32 m2

χ

(4m2χ minusm2

φ)2

(3

xf

)θ (mχ minusmf )


)vrang

=

(ξS

0

V

vo

)2g2χS0

8π

radic1minus

m2Z

m2χ

(16m4χ + 12m4

Z minus 16m2χm

2Z)

(4m2χ minusm2

S0)2

(3

xf


σ(χχrarrW+Wminus

)vrang

=

(ξS

0

V

vo

)2g2χS0

16π

radic1minus

m2W

m2χ

(16m4χ + 12m4

W minus 16m2χm

2W )

(4m2χ minusm2

S0)2

(3

xf



(ξS

0

q αs gχS0

3π32vo

)2m4χ

(4m2χ minusm2

S0)2 +m2S0Γ

(3

2xf


Iq

∣∣∣∣∣∣2

(C4)


2em

2π3v2o

m4χ


q Q2qIq +

suml ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn


S0)2 +m2S0Γ2

times(

3

xf

)(C5)

ndash 30 ndash


rang= c0


C2S0HiHj

g2χS0

16πλ

12

(1m2Hi

4m2χ

m2Hj

4m2χ

)

times 1

(4m2χ minusm2

φ)2

(3

xf

)(C6)




)vrang

=3g4χS0

64πm2χ

(3

xf





m2h0

and s0 =m2

12

m2h0 All


Ch0S0S0 =δ213m

2h0

vo

(minus4δ213r

20

tanβ+

2δ213r0tanβ

minus 8r30tan4 β

+8r20s0tan3 β

+4r20

tan4 βminus 8r0s0

tan3 βminus 8r0s0

tanβ

+2r0

tan4 βminus 2r0

tan2 β+

2s0tan3 β


minus 1

tan4 βminus 2

tan2 βminus 1

)(D1)

CS0h0h0 =δ13m

2h0

vo

(minus4δ213r

20

tan2 β+

2δ213r0tan2 β


tan3 βminus 4r0

tanβ

)(D2)

CS0H0H0 =δ13m

2h0

vo

(minus8δ213r

30

tan2 β+

12δ213r20


tan2 βminus 6r20

tan5 βminus 4r20

tan3 β+

2r20tanβ

+6r0s0tan4 β

+4r0s0tan2 β

minus2r0s0 +3r0

tan5 β+

r0tan3 β


minus 3s0tan4 β


+ 3s0

)(D3)

CS0S0H0 =δ213m

2h0

vo

(minus8δ213r

30

tan2 β+

8δ213r20


tan2 β+

12r30tan5 β

+4r30


tan4 βminus 4r20s0

tan2 βminus 12r20

tan5 β

+8r20

tanβ+

12r0s0tan4 β

+8r0s0tan2 β

minus 4r0s0 +3r0

tan5 βminus r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D4)

CS0H0h0 =δ13m

2h0

vo

(minus4δ213r

30

tan3 β+

4δ213r20


20

tanβminus δ213r0

tan3 β+

3δ213r0tanβ

+4r20

tan4 β+

4r20tan2 β

minus 4r0s0tan3 β

minus4r0s0tanβ

minus 3r0tan2 β

minus r0 +2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1

)(D5)

ndash 31 ndash

CS0H+Hminus =δ13m

2h0

vo

(minus 2r20

tan5 β+

2r20tanβ

+2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0 +r0

tan5 βminus r0


minus 5r0tanβ

minus s0tan4 β


+ s0 minus4m2

Hplusmnr0

tan3 βm2h0

minus4m2

Hplusmnr0

tanβm2h0

)(D6)

CS0A0A0 =δ13m

2h0

vo

(minus

4m2A0r0

tan3 βm2h0

minus4m2

A0r0tanβm2

h0

minus 2r20tan5 β

+2r20

tanβ+

2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0

+r0

tan5 βminus r0


tanβminus s0


tan2 β+ s0

)(D7)

CS0S0S0 =δ313m

2h0

vo

(minus 24r40

tan5 β+

24r30s0tan4 β

+36r30

tan5 βminus 12r30



tan2 βminus 18r20

tan5 β+

12r20tan3 β

+18r20tanβ

+18r0s0tan4 β

+12r0s0tan2 β

minus 6r0s0 +3r0

tan5 βminus 3r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D8)

Ch0H+Hminus =m2h0

vo

(2δ213r0tanβ

+2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1minus

2m2Hplusmn

tan4 βm2h0

minus4m2

Hplusmn

tan2 βm2h0

minus2m2

Hplusmn

m2h0

) (D9)

References










ndash 32 ndash























ndash 33 ndash






















ndash 34 ndash








ndash 35 ndash

1 Introduction

2 The Model








42 Direct Detection


5 Summary

A Model Parameters




1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)




the reference [56]


f

π Ff (x) log

(s(1minusx)m2f


ndash 22 ndash

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)






ndash 23 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





x(413)

ndash 24 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





rang

ndash 25 ndash








ndash 26 ndash


5 Summary









ndash 27 ndash





Acknowledgments


ndash 28 ndash

Appendix

A Model Parameters


12

m211 = minus1

2

[m2H0 cos2 α+m2

h0 sin2 α+


h0)minus 2m2

12

tanβ

](A1)

m222 = minus1

2

[m2h0 cos2 α+m2

H0 sin2 α+


h0)minus 2m2

12

cotβ

](A2)

λ1 =1

v2o cos2 β

[m2H0 cos2 α+m2


](A3)

λ2 =1

v2o sin2 β

[m2h0 cos2 α+m2


](A4)

λ3 =2

v2o sin (2β)

[sinα cosα

(m2H0 minusm2

h0)minusm2

12 + m2H+ sin (2β)

](A5)

λ4 =1

v2o sin (2β)

[2m2

12 +(m2A0 minus 2m2

H+

)sin (2β)

](A6)

λ5 =1

v2o sin (2β)

[2m2


](A7)



Γ(S0 rarr f f) =Nc

8π

(ξSfmf

vo

)2

mS0

(1minus

4m2f

m2S0

)32




0

V )2

16π v2o

m3S0

(1minus

4m2W

m2S0

)12[

12

(mW

mS0

)4

minus 4

(mW

mS0

)2

+ 1





8πmS0

(1minus

4m2χ

m2S0

)32



Γ(S0 rarr gg) =

(mtξ

S0

q

vo

)2α2s

72π3

m3S0

m2t


Iq

∣∣∣∣∣∣2

(B5)

ndash 29 ndash



16πv20

(αemπ

)2∣∣∣∣∣sumq

ξS0

q Q2qIq +

suml

ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn

∣∣∣∣∣2







f(λ) as

f(λ) = minus2

(sinminus1 1

2radicλ

)2

for λ gt1

4

=1

2

(lnη+

ηminus

)2

minus π2

2minus iπ η

+

ηminus for λ lt

1

4(B8)


radic14 minus λ




=

(mfξ

S0

f

vo

)2

g2χS0

1

4π

(1minus

m2l

m2χ

) 32 m2

χ

(4m2χ minusm2

φ)2

(3

xf

)θ (mχ minusmf )


)vrang

=

(ξS

0

V

vo

)2g2χS0

8π

radic1minus

m2Z

m2χ

(16m4χ + 12m4

Z minus 16m2χm

2Z)

(4m2χ minusm2

S0)2

(3

xf


σ(χχrarrW+Wminus

)vrang

=

(ξS

0

V

vo

)2g2χS0

16π

radic1minus

m2W

m2χ

(16m4χ + 12m4

W minus 16m2χm

2W )

(4m2χ minusm2

S0)2

(3

xf



(ξS

0

q αs gχS0

3π32vo

)2m4χ

(4m2χ minusm2

S0)2 +m2S0Γ

(3

2xf


Iq

∣∣∣∣∣∣2

(C4)


2em

2π3v2o

m4χ


q Q2qIq +

suml ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn


S0)2 +m2S0Γ2

times(

3

xf

)(C5)

ndash 30 ndash


rang= c0


C2S0HiHj

g2χS0

16πλ

12

(1m2Hi

4m2χ

m2Hj

4m2χ

)

times 1

(4m2χ minusm2

φ)2

(3

xf

)(C6)




)vrang

=3g4χS0

64πm2χ

(3

xf





m2h0

and s0 =m2

12

m2h0 All


Ch0S0S0 =δ213m

2h0

vo

(minus4δ213r

20

tanβ+

2δ213r0tanβ

minus 8r30tan4 β

+8r20s0tan3 β

+4r20

tan4 βminus 8r0s0

tan3 βminus 8r0s0

tanβ

+2r0

tan4 βminus 2r0

tan2 β+

2s0tan3 β


minus 1

tan4 βminus 2

tan2 βminus 1

)(D1)

CS0h0h0 =δ13m

2h0

vo

(minus4δ213r

20

tan2 β+

2δ213r0tan2 β


tan3 βminus 4r0

tanβ

)(D2)

CS0H0H0 =δ13m

2h0

vo

(minus8δ213r

30

tan2 β+

12δ213r20


tan2 βminus 6r20

tan5 βminus 4r20

tan3 β+

2r20tanβ

+6r0s0tan4 β

+4r0s0tan2 β

minus2r0s0 +3r0

tan5 β+

r0tan3 β


minus 3s0tan4 β


+ 3s0

)(D3)

CS0S0H0 =δ213m

2h0

vo

(minus8δ213r

30

tan2 β+

8δ213r20


tan2 β+

12r30tan5 β

+4r30


tan4 βminus 4r20s0

tan2 βminus 12r20

tan5 β

+8r20

tanβ+

12r0s0tan4 β

+8r0s0tan2 β

minus 4r0s0 +3r0

tan5 βminus r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D4)

CS0H0h0 =δ13m

2h0

vo

(minus4δ213r

30

tan3 β+

4δ213r20


20

tanβminus δ213r0

tan3 β+

3δ213r0tanβ

+4r20

tan4 β+

4r20tan2 β

minus 4r0s0tan3 β

minus4r0s0tanβ

minus 3r0tan2 β

minus r0 +2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1

)(D5)

ndash 31 ndash

CS0H+Hminus =δ13m

2h0

vo

(minus 2r20

tan5 β+

2r20tanβ

+2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0 +r0

tan5 βminus r0


minus 5r0tanβ

minus s0tan4 β


+ s0 minus4m2

Hplusmnr0

tan3 βm2h0

minus4m2

Hplusmnr0

tanβm2h0

)(D6)

CS0A0A0 =δ13m

2h0

vo

(minus

4m2A0r0

tan3 βm2h0

minus4m2

A0r0tanβm2

h0

minus 2r20tan5 β

+2r20

tanβ+

2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0

+r0

tan5 βminus r0


tanβminus s0


tan2 β+ s0

)(D7)

CS0S0S0 =δ313m

2h0

vo

(minus 24r40

tan5 β+

24r30s0tan4 β

+36r30

tan5 βminus 12r30



tan2 βminus 18r20

tan5 β+

12r20tan3 β

+18r20tanβ

+18r0s0tan4 β

+12r0s0tan2 β

minus 6r0s0 +3r0

tan5 βminus 3r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D8)

Ch0H+Hminus =m2h0

vo

(2δ213r0tanβ

+2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1minus

2m2Hplusmn

tan4 βm2h0

minus4m2

Hplusmn

tan2 βm2h0

minus2m2

Hplusmn

m2h0

) (D9)

References










ndash 32 ndash























ndash 33 ndash






















ndash 34 ndash








ndash 35 ndash

1 Introduction

2 The Model








42 Direct Detection


5 Summary

A Model Parameters




1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)






ndash 23 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





x(413)

ndash 24 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





rang

ndash 25 ndash








ndash 26 ndash


5 Summary









ndash 27 ndash





Acknowledgments


ndash 28 ndash

Appendix

A Model Parameters


12

m211 = minus1

2

[m2H0 cos2 α+m2

h0 sin2 α+


h0)minus 2m2

12

tanβ

](A1)

m222 = minus1

2

[m2h0 cos2 α+m2

H0 sin2 α+


h0)minus 2m2

12

cotβ

](A2)

λ1 =1

v2o cos2 β

[m2H0 cos2 α+m2


](A3)

λ2 =1

v2o sin2 β

[m2h0 cos2 α+m2


](A4)

λ3 =2

v2o sin (2β)

[sinα cosα

(m2H0 minusm2

h0)minusm2

12 + m2H+ sin (2β)

](A5)

λ4 =1

v2o sin (2β)

[2m2

12 +(m2A0 minus 2m2

H+

)sin (2β)

](A6)

λ5 =1

v2o sin (2β)

[2m2


](A7)



Γ(S0 rarr f f) =Nc

8π

(ξSfmf

vo

)2

mS0

(1minus

4m2f

m2S0

)32




0

V )2

16π v2o

m3S0

(1minus

4m2W

m2S0

)12[

12

(mW

mS0

)4

minus 4

(mW

mS0

)2

+ 1





8πmS0

(1minus

4m2χ

m2S0

)32



Γ(S0 rarr gg) =

(mtξ

S0

q

vo

)2α2s

72π3

m3S0

m2t


Iq

∣∣∣∣∣∣2

(B5)

ndash 29 ndash



16πv20

(αemπ

)2∣∣∣∣∣sumq

ξS0

q Q2qIq +

suml

ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn

∣∣∣∣∣2







f(λ) as

f(λ) = minus2

(sinminus1 1

2radicλ

)2

for λ gt1

4

=1

2

(lnη+

ηminus

)2

minus π2

2minus iπ η

+

ηminus for λ lt

1

4(B8)


radic14 minus λ




=

(mfξ

S0

f

vo

)2

g2χS0

1

4π

(1minus

m2l

m2χ

) 32 m2

χ

(4m2χ minusm2

φ)2

(3

xf

)θ (mχ minusmf )


)vrang

=

(ξS

0

V

vo

)2g2χS0

8π

radic1minus

m2Z

m2χ

(16m4χ + 12m4

Z minus 16m2χm

2Z)

(4m2χ minusm2

S0)2

(3

xf


σ(χχrarrW+Wminus

)vrang

=

(ξS

0

V

vo

)2g2χS0

16π

radic1minus

m2W

m2χ

(16m4χ + 12m4

W minus 16m2χm

2W )

(4m2χ minusm2

S0)2

(3

xf



(ξS

0

q αs gχS0

3π32vo

)2m4χ

(4m2χ minusm2

S0)2 +m2S0Γ

(3

2xf


Iq

∣∣∣∣∣∣2

(C4)


2em

2π3v2o

m4χ


q Q2qIq +

suml ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn


S0)2 +m2S0Γ2

times(

3

xf

)(C5)

ndash 30 ndash


rang= c0


C2S0HiHj

g2χS0

16πλ

12

(1m2Hi

4m2χ

m2Hj

4m2χ

)

times 1

(4m2χ minusm2

φ)2

(3

xf

)(C6)




)vrang

=3g4χS0

64πm2χ

(3

xf





m2h0

and s0 =m2

12

m2h0 All


Ch0S0S0 =δ213m

2h0

vo

(minus4δ213r

20

tanβ+

2δ213r0tanβ

minus 8r30tan4 β

+8r20s0tan3 β

+4r20

tan4 βminus 8r0s0

tan3 βminus 8r0s0

tanβ

+2r0

tan4 βminus 2r0

tan2 β+

2s0tan3 β


minus 1

tan4 βminus 2

tan2 βminus 1

)(D1)

CS0h0h0 =δ13m

2h0

vo

(minus4δ213r

20

tan2 β+

2δ213r0tan2 β


tan3 βminus 4r0

tanβ

)(D2)

CS0H0H0 =δ13m

2h0

vo

(minus8δ213r

30

tan2 β+

12δ213r20


tan2 βminus 6r20

tan5 βminus 4r20

tan3 β+

2r20tanβ

+6r0s0tan4 β

+4r0s0tan2 β

minus2r0s0 +3r0

tan5 β+

r0tan3 β


minus 3s0tan4 β


+ 3s0

)(D3)

CS0S0H0 =δ213m

2h0

vo

(minus8δ213r

30

tan2 β+

8δ213r20


tan2 β+

12r30tan5 β

+4r30


tan4 βminus 4r20s0

tan2 βminus 12r20

tan5 β

+8r20

tanβ+

12r0s0tan4 β

+8r0s0tan2 β

minus 4r0s0 +3r0

tan5 βminus r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D4)

CS0H0h0 =δ13m

2h0

vo

(minus4δ213r

30

tan3 β+

4δ213r20


20

tanβminus δ213r0

tan3 β+

3δ213r0tanβ

+4r20

tan4 β+

4r20tan2 β

minus 4r0s0tan3 β

minus4r0s0tanβ

minus 3r0tan2 β

minus r0 +2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1

)(D5)

ndash 31 ndash

CS0H+Hminus =δ13m

2h0

vo

(minus 2r20

tan5 β+

2r20tanβ

+2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0 +r0

tan5 βminus r0


minus 5r0tanβ

minus s0tan4 β


+ s0 minus4m2

Hplusmnr0

tan3 βm2h0

minus4m2

Hplusmnr0

tanβm2h0

)(D6)

CS0A0A0 =δ13m

2h0

vo

(minus

4m2A0r0

tan3 βm2h0

minus4m2

A0r0tanβm2

h0

minus 2r20tan5 β

+2r20

tanβ+

2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0

+r0

tan5 βminus r0


tanβminus s0


tan2 β+ s0

)(D7)

CS0S0S0 =δ313m

2h0

vo

(minus 24r40

tan5 β+

24r30s0tan4 β

+36r30

tan5 βminus 12r30



tan2 βminus 18r20

tan5 β+

12r20tan3 β

+18r20tanβ

+18r0s0tan4 β

+12r0s0tan2 β

minus 6r0s0 +3r0

tan5 βminus 3r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D8)

Ch0H+Hminus =m2h0

vo

(2δ213r0tanβ

+2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1minus

2m2Hplusmn

tan4 βm2h0

minus4m2

Hplusmn

tan2 βm2h0

minus2m2

Hplusmn

m2h0

) (D9)

References










ndash 32 ndash























ndash 33 ndash






















ndash 34 ndash








ndash 35 ndash

1 Introduction

2 The Model








42 Direct Detection


5 Summary

A Model Parameters




05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 20 GeV mH

0 = 200 GeV

mS0 = 10 GeV mH

0 = 400 GeV

mS0 = 20 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





x(413)

ndash 24 ndash

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





rang

ndash 25 ndash








ndash 26 ndash


5 Summary









ndash 27 ndash





Acknowledgments


ndash 28 ndash

Appendix

A Model Parameters


12

m211 = minus1

2

[m2H0 cos2 α+m2

h0 sin2 α+


h0)minus 2m2

12

tanβ

](A1)

m222 = minus1

2

[m2h0 cos2 α+m2

H0 sin2 α+


h0)minus 2m2

12

cotβ

](A2)

λ1 =1

v2o cos2 β

[m2H0 cos2 α+m2


](A3)

λ2 =1

v2o sin2 β

[m2h0 cos2 α+m2


](A4)

λ3 =2

v2o sin (2β)

[sinα cosα

(m2H0 minusm2

h0)minusm2

12 + m2H+ sin (2β)

](A5)

λ4 =1

v2o sin (2β)

[2m2

12 +(m2A0 minus 2m2

H+

)sin (2β)

](A6)

λ5 =1

v2o sin (2β)

[2m2


](A7)



Γ(S0 rarr f f) =Nc

8π

(ξSfmf

vo

)2

mS0

(1minus

4m2f

m2S0

)32




0

V )2

16π v2o

m3S0

(1minus

4m2W

m2S0

)12[

12

(mW

mS0

)4

minus 4

(mW

mS0

)2

+ 1





8πmS0

(1minus

4m2χ

m2S0

)32



Γ(S0 rarr gg) =

(mtξ

S0

q

vo

)2α2s

72π3

m3S0

m2t


Iq

∣∣∣∣∣∣2

(B5)

ndash 29 ndash



16πv20

(αemπ

)2∣∣∣∣∣sumq

ξS0

q Q2qIq +

suml

ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn

∣∣∣∣∣2







f(λ) as

f(λ) = minus2

(sinminus1 1

2radicλ

)2

for λ gt1

4

=1

2

(lnη+

ηminus

)2

minus π2

2minus iπ η

+

ηminus for λ lt

1

4(B8)


radic14 minus λ




=

(mfξ

S0

f

vo

)2

g2χS0

1

4π

(1minus

m2l

m2χ

) 32 m2

χ

(4m2χ minusm2

φ)2

(3

xf

)θ (mχ minusmf )


)vrang

=

(ξS

0

V

vo

)2g2χS0

8π

radic1minus

m2Z

m2χ

(16m4χ + 12m4

Z minus 16m2χm

2Z)

(4m2χ minusm2

S0)2

(3

xf


σ(χχrarrW+Wminus

)vrang

=

(ξS

0

V

vo

)2g2χS0

16π

radic1minus

m2W

m2χ

(16m4χ + 12m4

W minus 16m2χm

2W )

(4m2χ minusm2

S0)2

(3

xf



(ξS

0

q αs gχS0

3π32vo

)2m4χ

(4m2χ minusm2

S0)2 +m2S0Γ

(3

2xf


Iq

∣∣∣∣∣∣2

(C4)


2em

2π3v2o

m4χ


q Q2qIq +

suml ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn


S0)2 +m2S0Γ2

times(

3

xf

)(C5)

ndash 30 ndash


rang= c0


C2S0HiHj

g2χS0

16πλ

12

(1m2Hi

4m2χ

m2Hj

4m2χ

)

times 1

(4m2χ minusm2

φ)2

(3

xf

)(C6)




)vrang

=3g4χS0

64πm2χ

(3

xf





m2h0

and s0 =m2

12

m2h0 All


Ch0S0S0 =δ213m

2h0

vo

(minus4δ213r

20

tanβ+

2δ213r0tanβ

minus 8r30tan4 β

+8r20s0tan3 β

+4r20

tan4 βminus 8r0s0

tan3 βminus 8r0s0

tanβ

+2r0

tan4 βminus 2r0

tan2 β+

2s0tan3 β


minus 1

tan4 βminus 2

tan2 βminus 1

)(D1)

CS0h0h0 =δ13m

2h0

vo

(minus4δ213r

20

tan2 β+

2δ213r0tan2 β


tan3 βminus 4r0

tanβ

)(D2)

CS0H0H0 =δ13m

2h0

vo

(minus8δ213r

30

tan2 β+

12δ213r20


tan2 βminus 6r20

tan5 βminus 4r20

tan3 β+

2r20tanβ

+6r0s0tan4 β

+4r0s0tan2 β

minus2r0s0 +3r0

tan5 β+

r0tan3 β


minus 3s0tan4 β


+ 3s0

)(D3)

CS0S0H0 =δ213m

2h0

vo

(minus8δ213r

30

tan2 β+

8δ213r20


tan2 β+

12r30tan5 β

+4r30


tan4 βminus 4r20s0

tan2 βminus 12r20

tan5 β

+8r20

tanβ+

12r0s0tan4 β

+8r0s0tan2 β

minus 4r0s0 +3r0

tan5 βminus r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D4)

CS0H0h0 =δ13m

2h0

vo

(minus4δ213r

30

tan3 β+

4δ213r20


20

tanβminus δ213r0

tan3 β+

3δ213r0tanβ

+4r20

tan4 β+

4r20tan2 β

minus 4r0s0tan3 β

minus4r0s0tanβ

minus 3r0tan2 β

minus r0 +2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1

)(D5)

ndash 31 ndash

CS0H+Hminus =δ13m

2h0

vo

(minus 2r20

tan5 β+

2r20tanβ

+2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0 +r0

tan5 βminus r0


minus 5r0tanβ

minus s0tan4 β


+ s0 minus4m2

Hplusmnr0

tan3 βm2h0

minus4m2

Hplusmnr0

tanβm2h0

)(D6)

CS0A0A0 =δ13m

2h0

vo

(minus

4m2A0r0

tan3 βm2h0

minus4m2

A0r0tanβm2

h0

minus 2r20tan5 β

+2r20

tanβ+

2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0

+r0

tan5 βminus r0


tanβminus s0


tan2 β+ s0

)(D7)

CS0S0S0 =δ313m

2h0

vo

(minus 24r40

tan5 β+

24r30s0tan4 β

+36r30

tan5 βminus 12r30



tan2 βminus 18r20

tan5 β+

12r20tan3 β

+18r20tanβ

+18r0s0tan4 β

+12r0s0tan2 β

minus 6r0s0 +3r0

tan5 βminus 3r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D8)

Ch0H+Hminus =m2h0

vo

(2δ213r0tanβ

+2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1minus

2m2Hplusmn

tan4 βm2h0

minus4m2

Hplusmn

tan2 βm2h0

minus2m2

Hplusmn

m2h0

) (D9)

References










ndash 32 ndash























ndash 33 ndash






















ndash 34 ndash








ndash 35 ndash

1 Introduction

2 The Model








42 Direct Detection


5 Summary

A Model Parameters




05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(a)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 200 GeV

(b)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(c)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 400 GeV

(d)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(e)

05 1 2 3 5 7 1 2 3 5 75

10-39

10-37

10-35

10-33

10-31

10-29

10-27

10-25

10-23

ltσ

vgt

in

cm

3 s

-1

mχ in TeV

mS0 = 10 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 200 GeV

mS0 = 50 GeV mH

0 = 200 GeV

mS0 = 30 GeV mH

0 = 400 GeV

mS0 = 50 GeV mH

0 = 400 GeV


2

mA0 = 600 GeV

(f)





rang

ndash 25 ndash








ndash 26 ndash


5 Summary









ndash 27 ndash





Acknowledgments


ndash 28 ndash

Appendix

A Model Parameters


12

m211 = minus1

2

[m2H0 cos2 α+m2

h0 sin2 α+


h0)minus 2m2

12

tanβ

](A1)

m222 = minus1

2

[m2h0 cos2 α+m2

H0 sin2 α+


h0)minus 2m2

12

cotβ

](A2)

λ1 =1

v2o cos2 β

[m2H0 cos2 α+m2


](A3)

λ2 =1

v2o sin2 β

[m2h0 cos2 α+m2


](A4)

λ3 =2

v2o sin (2β)

[sinα cosα

(m2H0 minusm2

h0)minusm2

12 + m2H+ sin (2β)

](A5)

λ4 =1

v2o sin (2β)

[2m2

12 +(m2A0 minus 2m2

H+

)sin (2β)

](A6)

λ5 =1

v2o sin (2β)

[2m2


](A7)



Γ(S0 rarr f f) =Nc

8π

(ξSfmf

vo

)2

mS0

(1minus

4m2f

m2S0

)32




0

V )2

16π v2o

m3S0

(1minus

4m2W

m2S0

)12[

12

(mW

mS0

)4

minus 4

(mW

mS0

)2

+ 1





8πmS0

(1minus

4m2χ

m2S0

)32



Γ(S0 rarr gg) =

(mtξ

S0

q

vo

)2α2s

72π3

m3S0

m2t


Iq

∣∣∣∣∣∣2

(B5)

ndash 29 ndash



16πv20

(αemπ

)2∣∣∣∣∣sumq

ξS0

q Q2qIq +

suml

ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn

∣∣∣∣∣2







f(λ) as

f(λ) = minus2

(sinminus1 1

2radicλ

)2

for λ gt1

4

=1

2

(lnη+

ηminus

)2

minus π2

2minus iπ η

+

ηminus for λ lt

1

4(B8)


radic14 minus λ




=

(mfξ

S0

f

vo

)2

g2χS0

1

4π

(1minus

m2l

m2χ

) 32 m2

χ

(4m2χ minusm2

φ)2

(3

xf

)θ (mχ minusmf )


)vrang

=

(ξS

0

V

vo

)2g2χS0

8π

radic1minus

m2Z

m2χ

(16m4χ + 12m4

Z minus 16m2χm

2Z)

(4m2χ minusm2

S0)2

(3

xf


σ(χχrarrW+Wminus

)vrang

=

(ξS

0

V

vo

)2g2χS0

16π

radic1minus

m2W

m2χ

(16m4χ + 12m4

W minus 16m2χm

2W )

(4m2χ minusm2

S0)2

(3

xf



(ξS

0

q αs gχS0

3π32vo

)2m4χ

(4m2χ minusm2

S0)2 +m2S0Γ

(3

2xf


Iq

∣∣∣∣∣∣2

(C4)


2em

2π3v2o

m4χ


q Q2qIq +

suml ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn


S0)2 +m2S0Γ2

times(

3

xf

)(C5)

ndash 30 ndash


rang= c0


C2S0HiHj

g2χS0

16πλ

12

(1m2Hi

4m2χ

m2Hj

4m2χ

)

times 1

(4m2χ minusm2

φ)2

(3

xf

)(C6)




)vrang

=3g4χS0

64πm2χ

(3

xf





m2h0

and s0 =m2

12

m2h0 All


Ch0S0S0 =δ213m

2h0

vo

(minus4δ213r

20

tanβ+

2δ213r0tanβ

minus 8r30tan4 β

+8r20s0tan3 β

+4r20

tan4 βminus 8r0s0

tan3 βminus 8r0s0

tanβ

+2r0

tan4 βminus 2r0

tan2 β+

2s0tan3 β


minus 1

tan4 βminus 2

tan2 βminus 1

)(D1)

CS0h0h0 =δ13m

2h0

vo

(minus4δ213r

20

tan2 β+

2δ213r0tan2 β


tan3 βminus 4r0

tanβ

)(D2)

CS0H0H0 =δ13m

2h0

vo

(minus8δ213r

30

tan2 β+

12δ213r20


tan2 βminus 6r20

tan5 βminus 4r20

tan3 β+

2r20tanβ

+6r0s0tan4 β

+4r0s0tan2 β

minus2r0s0 +3r0

tan5 β+

r0tan3 β


minus 3s0tan4 β


+ 3s0

)(D3)

CS0S0H0 =δ213m

2h0

vo

(minus8δ213r

30

tan2 β+

8δ213r20


tan2 β+

12r30tan5 β

+4r30


tan4 βminus 4r20s0

tan2 βminus 12r20

tan5 β

+8r20

tanβ+

12r0s0tan4 β

+8r0s0tan2 β

minus 4r0s0 +3r0

tan5 βminus r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D4)

CS0H0h0 =δ13m

2h0

vo

(minus4δ213r

30

tan3 β+

4δ213r20


20

tanβminus δ213r0

tan3 β+

3δ213r0tanβ

+4r20

tan4 β+

4r20tan2 β

minus 4r0s0tan3 β

minus4r0s0tanβ

minus 3r0tan2 β

minus r0 +2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1

)(D5)

ndash 31 ndash

CS0H+Hminus =δ13m

2h0

vo

(minus 2r20

tan5 β+

2r20tanβ

+2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0 +r0

tan5 βminus r0


minus 5r0tanβ

minus s0tan4 β


+ s0 minus4m2

Hplusmnr0

tan3 βm2h0

minus4m2

Hplusmnr0

tanβm2h0

)(D6)

CS0A0A0 =δ13m

2h0

vo

(minus

4m2A0r0

tan3 βm2h0

minus4m2

A0r0tanβm2

h0

minus 2r20tan5 β

+2r20

tanβ+

2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0

+r0

tan5 βminus r0


tanβminus s0


tan2 β+ s0

)(D7)

CS0S0S0 =δ313m

2h0

vo

(minus 24r40

tan5 β+

24r30s0tan4 β

+36r30

tan5 βminus 12r30



tan2 βminus 18r20

tan5 β+

12r20tan3 β

+18r20tanβ

+18r0s0tan4 β

+12r0s0tan2 β

minus 6r0s0 +3r0

tan5 βminus 3r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D8)

Ch0H+Hminus =m2h0

vo

(2δ213r0tanβ

+2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1minus

2m2Hplusmn

tan4 βm2h0

minus4m2

Hplusmn

tan2 βm2h0

minus2m2

Hplusmn

m2h0

) (D9)

References










ndash 32 ndash























ndash 33 ndash






















ndash 34 ndash








ndash 35 ndash

1 Introduction

2 The Model








42 Direct Detection


5 Summary

A Model Parameters











ndash 26 ndash


5 Summary









ndash 27 ndash





Acknowledgments


ndash 28 ndash

Appendix

A Model Parameters


12

m211 = minus1

2

[m2H0 cos2 α+m2

h0 sin2 α+


h0)minus 2m2

12

tanβ

](A1)

m222 = minus1

2

[m2h0 cos2 α+m2

H0 sin2 α+


h0)minus 2m2

12

cotβ

](A2)

λ1 =1

v2o cos2 β

[m2H0 cos2 α+m2


](A3)

λ2 =1

v2o sin2 β

[m2h0 cos2 α+m2


](A4)

λ3 =2

v2o sin (2β)

[sinα cosα

(m2H0 minusm2

h0)minusm2

12 + m2H+ sin (2β)

](A5)

λ4 =1

v2o sin (2β)

[2m2

12 +(m2A0 minus 2m2

H+

)sin (2β)

](A6)

λ5 =1

v2o sin (2β)

[2m2


](A7)



Γ(S0 rarr f f) =Nc

8π

(ξSfmf

vo

)2

mS0

(1minus

4m2f

m2S0

)32




0

V )2

16π v2o

m3S0

(1minus

4m2W

m2S0

)12[

12

(mW

mS0

)4

minus 4

(mW

mS0

)2

+ 1





8πmS0

(1minus

4m2χ

m2S0

)32



Γ(S0 rarr gg) =

(mtξ

S0

q

vo

)2α2s

72π3

m3S0

m2t


Iq

∣∣∣∣∣∣2

(B5)

ndash 29 ndash



16πv20

(αemπ

)2∣∣∣∣∣sumq

ξS0

q Q2qIq +

suml

ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn

∣∣∣∣∣2







f(λ) as

f(λ) = minus2

(sinminus1 1

2radicλ

)2

for λ gt1

4

=1

2

(lnη+

ηminus

)2

minus π2

2minus iπ η

+

ηminus for λ lt

1

4(B8)


radic14 minus λ




=

(mfξ

S0

f

vo

)2

g2χS0

1

4π

(1minus

m2l

m2χ

) 32 m2

χ

(4m2χ minusm2

φ)2

(3

xf

)θ (mχ minusmf )


)vrang

=

(ξS

0

V

vo

)2g2χS0

8π

radic1minus

m2Z

m2χ

(16m4χ + 12m4

Z minus 16m2χm

2Z)

(4m2χ minusm2

S0)2

(3

xf


σ(χχrarrW+Wminus

)vrang

=

(ξS

0

V

vo

)2g2χS0

16π

radic1minus

m2W

m2χ

(16m4χ + 12m4

W minus 16m2χm

2W )

(4m2χ minusm2

S0)2

(3

xf



(ξS

0

q αs gχS0

3π32vo

)2m4χ

(4m2χ minusm2

S0)2 +m2S0Γ

(3

2xf


Iq

∣∣∣∣∣∣2

(C4)


2em

2π3v2o

m4χ


q Q2qIq +

suml ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn


S0)2 +m2S0Γ2

times(

3

xf

)(C5)

ndash 30 ndash


rang= c0


C2S0HiHj

g2χS0

16πλ

12

(1m2Hi

4m2χ

m2Hj

4m2χ

)

times 1

(4m2χ minusm2

φ)2

(3

xf

)(C6)




)vrang

=3g4χS0

64πm2χ

(3

xf





m2h0

and s0 =m2

12

m2h0 All


Ch0S0S0 =δ213m

2h0

vo

(minus4δ213r

20

tanβ+

2δ213r0tanβ

minus 8r30tan4 β

+8r20s0tan3 β

+4r20

tan4 βminus 8r0s0

tan3 βminus 8r0s0

tanβ

+2r0

tan4 βminus 2r0

tan2 β+

2s0tan3 β


minus 1

tan4 βminus 2

tan2 βminus 1

)(D1)

CS0h0h0 =δ13m

2h0

vo

(minus4δ213r

20

tan2 β+

2δ213r0tan2 β


tan3 βminus 4r0

tanβ

)(D2)

CS0H0H0 =δ13m

2h0

vo

(minus8δ213r

30

tan2 β+

12δ213r20


tan2 βminus 6r20

tan5 βminus 4r20

tan3 β+

2r20tanβ

+6r0s0tan4 β

+4r0s0tan2 β

minus2r0s0 +3r0

tan5 β+

r0tan3 β


minus 3s0tan4 β


+ 3s0

)(D3)

CS0S0H0 =δ213m

2h0

vo

(minus8δ213r

30

tan2 β+

8δ213r20


tan2 β+

12r30tan5 β

+4r30


tan4 βminus 4r20s0

tan2 βminus 12r20

tan5 β

+8r20

tanβ+

12r0s0tan4 β

+8r0s0tan2 β

minus 4r0s0 +3r0

tan5 βminus r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D4)

CS0H0h0 =δ13m

2h0

vo

(minus4δ213r

30

tan3 β+

4δ213r20


20

tanβminus δ213r0

tan3 β+

3δ213r0tanβ

+4r20

tan4 β+

4r20tan2 β

minus 4r0s0tan3 β

minus4r0s0tanβ

minus 3r0tan2 β

minus r0 +2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1

)(D5)

ndash 31 ndash

CS0H+Hminus =δ13m

2h0

vo

(minus 2r20

tan5 β+

2r20tanβ

+2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0 +r0

tan5 βminus r0


minus 5r0tanβ

minus s0tan4 β


+ s0 minus4m2

Hplusmnr0

tan3 βm2h0

minus4m2

Hplusmnr0

tanβm2h0

)(D6)

CS0A0A0 =δ13m

2h0

vo

(minus

4m2A0r0

tan3 βm2h0

minus4m2

A0r0tanβm2

h0

minus 2r20tan5 β

+2r20

tanβ+

2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0

+r0

tan5 βminus r0


tanβminus s0


tan2 β+ s0

)(D7)

CS0S0S0 =δ313m

2h0

vo

(minus 24r40

tan5 β+

24r30s0tan4 β

+36r30

tan5 βminus 12r30



tan2 βminus 18r20

tan5 β+

12r20tan3 β

+18r20tanβ

+18r0s0tan4 β

+12r0s0tan2 β

minus 6r0s0 +3r0

tan5 βminus 3r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D8)

Ch0H+Hminus =m2h0

vo

(2δ213r0tanβ

+2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1minus

2m2Hplusmn

tan4 βm2h0

minus4m2

Hplusmn

tan2 βm2h0

minus2m2

Hplusmn

m2h0

) (D9)

References










ndash 32 ndash























ndash 33 ndash






















ndash 34 ndash








ndash 35 ndash

1 Introduction

2 The Model








42 Direct Detection


5 Summary

A Model Parameters





5 Summary









ndash 27 ndash





Acknowledgments


ndash 28 ndash

Appendix

A Model Parameters


12

m211 = minus1

2

[m2H0 cos2 α+m2

h0 sin2 α+


h0)minus 2m2

12

tanβ

](A1)

m222 = minus1

2

[m2h0 cos2 α+m2

H0 sin2 α+


h0)minus 2m2

12

cotβ

](A2)

λ1 =1

v2o cos2 β

[m2H0 cos2 α+m2


](A3)

λ2 =1

v2o sin2 β

[m2h0 cos2 α+m2


](A4)

λ3 =2

v2o sin (2β)

[sinα cosα

(m2H0 minusm2

h0)minusm2

12 + m2H+ sin (2β)

](A5)

λ4 =1

v2o sin (2β)

[2m2

12 +(m2A0 minus 2m2

H+

)sin (2β)

](A6)

λ5 =1

v2o sin (2β)

[2m2


](A7)



Γ(S0 rarr f f) =Nc

8π

(ξSfmf

vo

)2

mS0

(1minus

4m2f

m2S0

)32




0

V )2

16π v2o

m3S0

(1minus

4m2W

m2S0

)12[

12

(mW

mS0

)4

minus 4

(mW

mS0

)2

+ 1





8πmS0

(1minus

4m2χ

m2S0

)32



Γ(S0 rarr gg) =

(mtξ

S0

q

vo

)2α2s

72π3

m3S0

m2t


Iq

∣∣∣∣∣∣2

(B5)

ndash 29 ndash



16πv20

(αemπ

)2∣∣∣∣∣sumq

ξS0

q Q2qIq +

suml

ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn

∣∣∣∣∣2







f(λ) as

f(λ) = minus2

(sinminus1 1

2radicλ

)2

for λ gt1

4

=1

2

(lnη+

ηminus

)2

minus π2

2minus iπ η

+

ηminus for λ lt

1

4(B8)


radic14 minus λ




=

(mfξ

S0

f

vo

)2

g2χS0

1

4π

(1minus

m2l

m2χ

) 32 m2

χ

(4m2χ minusm2

φ)2

(3

xf

)θ (mχ minusmf )


)vrang

=

(ξS

0

V

vo

)2g2χS0

8π

radic1minus

m2Z

m2χ

(16m4χ + 12m4

Z minus 16m2χm

2Z)

(4m2χ minusm2

S0)2

(3

xf


σ(χχrarrW+Wminus

)vrang

=

(ξS

0

V

vo

)2g2χS0

16π

radic1minus

m2W

m2χ

(16m4χ + 12m4

W minus 16m2χm

2W )

(4m2χ minusm2

S0)2

(3

xf



(ξS

0

q αs gχS0

3π32vo

)2m4χ

(4m2χ minusm2

S0)2 +m2S0Γ

(3

2xf


Iq

∣∣∣∣∣∣2

(C4)


2em

2π3v2o

m4χ


q Q2qIq +

suml ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn


S0)2 +m2S0Γ2

times(

3

xf

)(C5)

ndash 30 ndash


rang= c0


C2S0HiHj

g2χS0

16πλ

12

(1m2Hi

4m2χ

m2Hj

4m2χ

)

times 1

(4m2χ minusm2

φ)2

(3

xf

)(C6)




)vrang

=3g4χS0

64πm2χ

(3

xf





m2h0

and s0 =m2

12

m2h0 All


Ch0S0S0 =δ213m

2h0

vo

(minus4δ213r

20

tanβ+

2δ213r0tanβ

minus 8r30tan4 β

+8r20s0tan3 β

+4r20

tan4 βminus 8r0s0

tan3 βminus 8r0s0

tanβ

+2r0

tan4 βminus 2r0

tan2 β+

2s0tan3 β


minus 1

tan4 βminus 2

tan2 βminus 1

)(D1)

CS0h0h0 =δ13m

2h0

vo

(minus4δ213r

20

tan2 β+

2δ213r0tan2 β


tan3 βminus 4r0

tanβ

)(D2)

CS0H0H0 =δ13m

2h0

vo

(minus8δ213r

30

tan2 β+

12δ213r20


tan2 βminus 6r20

tan5 βminus 4r20

tan3 β+

2r20tanβ

+6r0s0tan4 β

+4r0s0tan2 β

minus2r0s0 +3r0

tan5 β+

r0tan3 β


minus 3s0tan4 β


+ 3s0

)(D3)

CS0S0H0 =δ213m

2h0

vo

(minus8δ213r

30

tan2 β+

8δ213r20


tan2 β+

12r30tan5 β

+4r30


tan4 βminus 4r20s0

tan2 βminus 12r20

tan5 β

+8r20

tanβ+

12r0s0tan4 β

+8r0s0tan2 β

minus 4r0s0 +3r0

tan5 βminus r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D4)

CS0H0h0 =δ13m

2h0

vo

(minus4δ213r

30

tan3 β+

4δ213r20


20

tanβminus δ213r0

tan3 β+

3δ213r0tanβ

+4r20

tan4 β+

4r20tan2 β

minus 4r0s0tan3 β

minus4r0s0tanβ

minus 3r0tan2 β

minus r0 +2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1

)(D5)

ndash 31 ndash

CS0H+Hminus =δ13m

2h0

vo

(minus 2r20

tan5 β+

2r20tanβ

+2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0 +r0

tan5 βminus r0


minus 5r0tanβ

minus s0tan4 β


+ s0 minus4m2

Hplusmnr0

tan3 βm2h0

minus4m2

Hplusmnr0

tanβm2h0

)(D6)

CS0A0A0 =δ13m

2h0

vo

(minus

4m2A0r0

tan3 βm2h0

minus4m2

A0r0tanβm2

h0

minus 2r20tan5 β

+2r20

tanβ+

2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0

+r0

tan5 βminus r0


tanβminus s0


tan2 β+ s0

)(D7)

CS0S0S0 =δ313m

2h0

vo

(minus 24r40

tan5 β+

24r30s0tan4 β

+36r30

tan5 βminus 12r30



tan2 βminus 18r20

tan5 β+

12r20tan3 β

+18r20tanβ

+18r0s0tan4 β

+12r0s0tan2 β

minus 6r0s0 +3r0

tan5 βminus 3r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D8)

Ch0H+Hminus =m2h0

vo

(2δ213r0tanβ

+2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1minus

2m2Hplusmn

tan4 βm2h0

minus4m2

Hplusmn

tan2 βm2h0

minus2m2

Hplusmn

m2h0

) (D9)

References










ndash 32 ndash























ndash 33 ndash






















ndash 34 ndash








ndash 35 ndash

1 Introduction

2 The Model








42 Direct Detection


5 Summary

A Model Parameters








Acknowledgments


ndash 28 ndash

Appendix

A Model Parameters


12

m211 = minus1

2

[m2H0 cos2 α+m2

h0 sin2 α+


h0)minus 2m2

12

tanβ

](A1)

m222 = minus1

2

[m2h0 cos2 α+m2

H0 sin2 α+


h0)minus 2m2

12

cotβ

](A2)

λ1 =1

v2o cos2 β

[m2H0 cos2 α+m2


](A3)

λ2 =1

v2o sin2 β

[m2h0 cos2 α+m2


](A4)

λ3 =2

v2o sin (2β)

[sinα cosα

(m2H0 minusm2

h0)minusm2

12 + m2H+ sin (2β)

](A5)

λ4 =1

v2o sin (2β)

[2m2

12 +(m2A0 minus 2m2

H+

)sin (2β)

](A6)

λ5 =1

v2o sin (2β)

[2m2


](A7)



Γ(S0 rarr f f) =Nc

8π

(ξSfmf

vo

)2

mS0

(1minus

4m2f

m2S0

)32




0

V )2

16π v2o

m3S0

(1minus

4m2W

m2S0

)12[

12

(mW

mS0

)4

minus 4

(mW

mS0

)2

+ 1





8πmS0

(1minus

4m2χ

m2S0

)32



Γ(S0 rarr gg) =

(mtξ

S0

q

vo

)2α2s

72π3

m3S0

m2t


Iq

∣∣∣∣∣∣2

(B5)

ndash 29 ndash



16πv20

(αemπ

)2∣∣∣∣∣sumq

ξS0

q Q2qIq +

suml

ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn

∣∣∣∣∣2







f(λ) as

f(λ) = minus2

(sinminus1 1

2radicλ

)2

for λ gt1

4

=1

2

(lnη+

ηminus

)2

minus π2

2minus iπ η

+

ηminus for λ lt

1

4(B8)


radic14 minus λ




=

(mfξ

S0

f

vo

)2

g2χS0

1

4π

(1minus

m2l

m2χ

) 32 m2

χ

(4m2χ minusm2

φ)2

(3

xf

)θ (mχ minusmf )


)vrang

=

(ξS

0

V

vo

)2g2χS0

8π

radic1minus

m2Z

m2χ

(16m4χ + 12m4

Z minus 16m2χm

2Z)

(4m2χ minusm2

S0)2

(3

xf


σ(χχrarrW+Wminus

)vrang

=

(ξS

0

V

vo

)2g2χS0

16π

radic1minus

m2W

m2χ

(16m4χ + 12m4

W minus 16m2χm

2W )

(4m2χ minusm2

S0)2

(3

xf



(ξS

0

q αs gχS0

3π32vo

)2m4χ

(4m2χ minusm2

S0)2 +m2S0Γ

(3

2xf


Iq

∣∣∣∣∣∣2

(C4)


2em

2π3v2o

m4χ


q Q2qIq +

suml ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn


S0)2 +m2S0Γ2

times(

3

xf

)(C5)

ndash 30 ndash


rang= c0


C2S0HiHj

g2χS0

16πλ

12

(1m2Hi

4m2χ

m2Hj

4m2χ

)

times 1

(4m2χ minusm2

φ)2

(3

xf

)(C6)




)vrang

=3g4χS0

64πm2χ

(3

xf





m2h0

and s0 =m2

12

m2h0 All


Ch0S0S0 =δ213m

2h0

vo

(minus4δ213r

20

tanβ+

2δ213r0tanβ

minus 8r30tan4 β

+8r20s0tan3 β

+4r20

tan4 βminus 8r0s0

tan3 βminus 8r0s0

tanβ

+2r0

tan4 βminus 2r0

tan2 β+

2s0tan3 β


minus 1

tan4 βminus 2

tan2 βminus 1

)(D1)

CS0h0h0 =δ13m

2h0

vo

(minus4δ213r

20

tan2 β+

2δ213r0tan2 β


tan3 βminus 4r0

tanβ

)(D2)

CS0H0H0 =δ13m

2h0

vo

(minus8δ213r

30

tan2 β+

12δ213r20


tan2 βminus 6r20

tan5 βminus 4r20

tan3 β+

2r20tanβ

+6r0s0tan4 β

+4r0s0tan2 β

minus2r0s0 +3r0

tan5 β+

r0tan3 β


minus 3s0tan4 β


+ 3s0

)(D3)

CS0S0H0 =δ213m

2h0

vo

(minus8δ213r

30

tan2 β+

8δ213r20


tan2 β+

12r30tan5 β

+4r30


tan4 βminus 4r20s0

tan2 βminus 12r20

tan5 β

+8r20

tanβ+

12r0s0tan4 β

+8r0s0tan2 β

minus 4r0s0 +3r0

tan5 βminus r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D4)

CS0H0h0 =δ13m

2h0

vo

(minus4δ213r

30

tan3 β+

4δ213r20


20

tanβminus δ213r0

tan3 β+

3δ213r0tanβ

+4r20

tan4 β+

4r20tan2 β

minus 4r0s0tan3 β

minus4r0s0tanβ

minus 3r0tan2 β

minus r0 +2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1

)(D5)

ndash 31 ndash

CS0H+Hminus =δ13m

2h0

vo

(minus 2r20

tan5 β+

2r20tanβ

+2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0 +r0

tan5 βminus r0


minus 5r0tanβ

minus s0tan4 β


+ s0 minus4m2

Hplusmnr0

tan3 βm2h0

minus4m2

Hplusmnr0

tanβm2h0

)(D6)

CS0A0A0 =δ13m

2h0

vo

(minus

4m2A0r0

tan3 βm2h0

minus4m2

A0r0tanβm2

h0

minus 2r20tan5 β

+2r20

tanβ+

2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0

+r0

tan5 βminus r0


tanβminus s0


tan2 β+ s0

)(D7)

CS0S0S0 =δ313m

2h0

vo

(minus 24r40

tan5 β+

24r30s0tan4 β

+36r30

tan5 βminus 12r30



tan2 βminus 18r20

tan5 β+

12r20tan3 β

+18r20tanβ

+18r0s0tan4 β

+12r0s0tan2 β

minus 6r0s0 +3r0

tan5 βminus 3r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D8)

Ch0H+Hminus =m2h0

vo

(2δ213r0tanβ

+2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1minus

2m2Hplusmn

tan4 βm2h0

minus4m2

Hplusmn

tan2 βm2h0

minus2m2

Hplusmn

m2h0

) (D9)

References










ndash 32 ndash























ndash 33 ndash






















ndash 34 ndash








ndash 35 ndash

1 Introduction

2 The Model








42 Direct Detection


5 Summary

A Model Parameters




Appendix

A Model Parameters


12

m211 = minus1

2

[m2H0 cos2 α+m2

h0 sin2 α+


h0)minus 2m2

12

tanβ

](A1)

m222 = minus1

2

[m2h0 cos2 α+m2

H0 sin2 α+


h0)minus 2m2

12

cotβ

](A2)

λ1 =1

v2o cos2 β

[m2H0 cos2 α+m2


](A3)

λ2 =1

v2o sin2 β

[m2h0 cos2 α+m2


](A4)

λ3 =2

v2o sin (2β)

[sinα cosα

(m2H0 minusm2

h0)minusm2

12 + m2H+ sin (2β)

](A5)

λ4 =1

v2o sin (2β)

[2m2

12 +(m2A0 minus 2m2

H+

)sin (2β)

](A6)

λ5 =1

v2o sin (2β)

[2m2


](A7)



Γ(S0 rarr f f) =Nc

8π

(ξSfmf

vo

)2

mS0

(1minus

4m2f

m2S0

)32




0

V )2

16π v2o

m3S0

(1minus

4m2W

m2S0

)12[

12

(mW

mS0

)4

minus 4

(mW

mS0

)2

+ 1





8πmS0

(1minus

4m2χ

m2S0

)32



Γ(S0 rarr gg) =

(mtξ

S0

q

vo

)2α2s

72π3

m3S0

m2t


Iq

∣∣∣∣∣∣2

(B5)

ndash 29 ndash



16πv20

(αemπ

)2∣∣∣∣∣sumq

ξS0

q Q2qIq +

suml

ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn

∣∣∣∣∣2







f(λ) as

f(λ) = minus2

(sinminus1 1

2radicλ

)2

for λ gt1

4

=1

2

(lnη+

ηminus

)2

minus π2

2minus iπ η

+

ηminus for λ lt

1

4(B8)


radic14 minus λ




=

(mfξ

S0

f

vo

)2

g2χS0

1

4π

(1minus

m2l

m2χ

) 32 m2

χ

(4m2χ minusm2

φ)2

(3

xf

)θ (mχ minusmf )


)vrang

=

(ξS

0

V

vo

)2g2χS0

8π

radic1minus

m2Z

m2χ

(16m4χ + 12m4

Z minus 16m2χm

2Z)

(4m2χ minusm2

S0)2

(3

xf


σ(χχrarrW+Wminus

)vrang

=

(ξS

0

V

vo

)2g2χS0

16π

radic1minus

m2W

m2χ

(16m4χ + 12m4

W minus 16m2χm

2W )

(4m2χ minusm2

S0)2

(3

xf



(ξS

0

q αs gχS0

3π32vo

)2m4χ

(4m2χ minusm2

S0)2 +m2S0Γ

(3

2xf


Iq

∣∣∣∣∣∣2

(C4)


2em

2π3v2o

m4χ


q Q2qIq +

suml ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn


S0)2 +m2S0Γ2

times(

3

xf

)(C5)

ndash 30 ndash


rang= c0


C2S0HiHj

g2χS0

16πλ

12

(1m2Hi

4m2χ

m2Hj

4m2χ

)

times 1

(4m2χ minusm2

φ)2

(3

xf

)(C6)




)vrang

=3g4χS0

64πm2χ

(3

xf





m2h0

and s0 =m2

12

m2h0 All


Ch0S0S0 =δ213m

2h0

vo

(minus4δ213r

20

tanβ+

2δ213r0tanβ

minus 8r30tan4 β

+8r20s0tan3 β

+4r20

tan4 βminus 8r0s0

tan3 βminus 8r0s0

tanβ

+2r0

tan4 βminus 2r0

tan2 β+

2s0tan3 β


minus 1

tan4 βminus 2

tan2 βminus 1

)(D1)

CS0h0h0 =δ13m

2h0

vo

(minus4δ213r

20

tan2 β+

2δ213r0tan2 β


tan3 βminus 4r0

tanβ

)(D2)

CS0H0H0 =δ13m

2h0

vo

(minus8δ213r

30

tan2 β+

12δ213r20


tan2 βminus 6r20

tan5 βminus 4r20

tan3 β+

2r20tanβ

+6r0s0tan4 β

+4r0s0tan2 β

minus2r0s0 +3r0

tan5 β+

r0tan3 β


minus 3s0tan4 β


+ 3s0

)(D3)

CS0S0H0 =δ213m

2h0

vo

(minus8δ213r

30

tan2 β+

8δ213r20


tan2 β+

12r30tan5 β

+4r30


tan4 βminus 4r20s0

tan2 βminus 12r20

tan5 β

+8r20

tanβ+

12r0s0tan4 β

+8r0s0tan2 β

minus 4r0s0 +3r0

tan5 βminus r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D4)

CS0H0h0 =δ13m

2h0

vo

(minus4δ213r

30

tan3 β+

4δ213r20


20

tanβminus δ213r0

tan3 β+

3δ213r0tanβ

+4r20

tan4 β+

4r20tan2 β

minus 4r0s0tan3 β

minus4r0s0tanβ

minus 3r0tan2 β

minus r0 +2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1

)(D5)

ndash 31 ndash

CS0H+Hminus =δ13m

2h0

vo

(minus 2r20

tan5 β+

2r20tanβ

+2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0 +r0

tan5 βminus r0


minus 5r0tanβ

minus s0tan4 β


+ s0 minus4m2

Hplusmnr0

tan3 βm2h0

minus4m2

Hplusmnr0

tanβm2h0

)(D6)

CS0A0A0 =δ13m

2h0

vo

(minus

4m2A0r0

tan3 βm2h0

minus4m2

A0r0tanβm2

h0

minus 2r20tan5 β

+2r20

tanβ+

2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0

+r0

tan5 βminus r0


tanβminus s0


tan2 β+ s0

)(D7)

CS0S0S0 =δ313m

2h0

vo

(minus 24r40

tan5 β+

24r30s0tan4 β

+36r30

tan5 βminus 12r30



tan2 βminus 18r20

tan5 β+

12r20tan3 β

+18r20tanβ

+18r0s0tan4 β

+12r0s0tan2 β

minus 6r0s0 +3r0

tan5 βminus 3r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D8)

Ch0H+Hminus =m2h0

vo

(2δ213r0tanβ

+2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1minus

2m2Hplusmn

tan4 βm2h0

minus4m2

Hplusmn

tan2 βm2h0

minus2m2

Hplusmn

m2h0

) (D9)

References










ndash 32 ndash























ndash 33 ndash






















ndash 34 ndash








ndash 35 ndash

1 Introduction

2 The Model








42 Direct Detection


5 Summary

A Model Parameters






16πv20

(αemπ

)2∣∣∣∣∣sumq

ξS0

q Q2qIq +

suml

ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn

∣∣∣∣∣2







f(λ) as

f(λ) = minus2

(sinminus1 1

2radicλ

)2

for λ gt1

4

=1

2

(lnη+

ηminus

)2

minus π2

2minus iπ η

+

ηminus for λ lt

1

4(B8)


radic14 minus λ




=

(mfξ

S0

f

vo

)2

g2χS0

1

4π

(1minus

m2l

m2χ

) 32 m2

χ

(4m2χ minusm2

φ)2

(3

xf

)θ (mχ minusmf )


)vrang

=

(ξS

0

V

vo

)2g2χS0

8π

radic1minus

m2Z

m2χ

(16m4χ + 12m4

Z minus 16m2χm

2Z)

(4m2χ minusm2

S0)2

(3

xf


σ(χχrarrW+Wminus

)vrang

=

(ξS

0

V

vo

)2g2χS0

16π

radic1minus

m2W

m2χ

(16m4χ + 12m4

W minus 16m2χm

2W )

(4m2χ minusm2

S0)2

(3

xf



(ξS

0

q αs gχS0

3π32vo

)2m4χ

(4m2χ minusm2

S0)2 +m2S0Γ

(3

2xf


Iq

∣∣∣∣∣∣2

(C4)


2em

2π3v2o

m4χ


q Q2qIq +

suml ξS0

l Q2qIq minus ξS

0


2m2Hplusmn

IHplusmn


S0)2 +m2S0Γ2

times(

3

xf

)(C5)

ndash 30 ndash


rang= c0


C2S0HiHj

g2χS0

16πλ

12

(1m2Hi

4m2χ

m2Hj

4m2χ

)

times 1

(4m2χ minusm2

φ)2

(3

xf

)(C6)




)vrang

=3g4χS0

64πm2χ

(3

xf





m2h0

and s0 =m2

12

m2h0 All


Ch0S0S0 =δ213m

2h0

vo

(minus4δ213r

20

tanβ+

2δ213r0tanβ

minus 8r30tan4 β

+8r20s0tan3 β

+4r20

tan4 βminus 8r0s0

tan3 βminus 8r0s0

tanβ

+2r0

tan4 βminus 2r0

tan2 β+

2s0tan3 β


minus 1

tan4 βminus 2

tan2 βminus 1

)(D1)

CS0h0h0 =δ13m

2h0

vo

(minus4δ213r

20

tan2 β+

2δ213r0tan2 β


tan3 βminus 4r0

tanβ

)(D2)

CS0H0H0 =δ13m

2h0

vo

(minus8δ213r

30

tan2 β+

12δ213r20


tan2 βminus 6r20

tan5 βminus 4r20

tan3 β+

2r20tanβ

+6r0s0tan4 β

+4r0s0tan2 β

minus2r0s0 +3r0

tan5 β+

r0tan3 β


minus 3s0tan4 β


+ 3s0

)(D3)

CS0S0H0 =δ213m

2h0

vo

(minus8δ213r

30

tan2 β+

8δ213r20


tan2 β+

12r30tan5 β

+4r30


tan4 βminus 4r20s0

tan2 βminus 12r20

tan5 β

+8r20

tanβ+

12r0s0tan4 β

+8r0s0tan2 β

minus 4r0s0 +3r0

tan5 βminus r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D4)

CS0H0h0 =δ13m

2h0

vo

(minus4δ213r

30

tan3 β+

4δ213r20


20

tanβminus δ213r0

tan3 β+

3δ213r0tanβ

+4r20

tan4 β+

4r20tan2 β

minus 4r0s0tan3 β

minus4r0s0tanβ

minus 3r0tan2 β

minus r0 +2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1

)(D5)

ndash 31 ndash

CS0H+Hminus =δ13m

2h0

vo

(minus 2r20

tan5 β+

2r20tanβ

+2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0 +r0

tan5 βminus r0


minus 5r0tanβ

minus s0tan4 β


+ s0 minus4m2

Hplusmnr0

tan3 βm2h0

minus4m2

Hplusmnr0

tanβm2h0

)(D6)

CS0A0A0 =δ13m

2h0

vo

(minus

4m2A0r0

tan3 βm2h0

minus4m2

A0r0tanβm2

h0

minus 2r20tan5 β

+2r20

tanβ+

2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0

+r0

tan5 βminus r0


tanβminus s0


tan2 β+ s0

)(D7)

CS0S0S0 =δ313m

2h0

vo

(minus 24r40

tan5 β+

24r30s0tan4 β

+36r30

tan5 βminus 12r30



tan2 βminus 18r20

tan5 β+

12r20tan3 β

+18r20tanβ

+18r0s0tan4 β

+12r0s0tan2 β

minus 6r0s0 +3r0

tan5 βminus 3r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D8)

Ch0H+Hminus =m2h0

vo

(2δ213r0tanβ

+2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1minus

2m2Hplusmn

tan4 βm2h0

minus4m2

Hplusmn

tan2 βm2h0

minus2m2

Hplusmn

m2h0

) (D9)

References










ndash 32 ndash























ndash 33 ndash






















ndash 34 ndash








ndash 35 ndash

1 Introduction

2 The Model








42 Direct Detection


5 Summary

A Model Parameters





rang= c0


C2S0HiHj

g2χS0

16πλ

12

(1m2Hi

4m2χ

m2Hj

4m2χ

)

times 1

(4m2χ minusm2

φ)2

(3

xf

)(C6)




)vrang

=3g4χS0

64πm2χ

(3

xf





m2h0

and s0 =m2

12

m2h0 All


Ch0S0S0 =δ213m

2h0

vo

(minus4δ213r

20

tanβ+

2δ213r0tanβ

minus 8r30tan4 β

+8r20s0tan3 β

+4r20

tan4 βminus 8r0s0

tan3 βminus 8r0s0

tanβ

+2r0

tan4 βminus 2r0

tan2 β+

2s0tan3 β


minus 1

tan4 βminus 2

tan2 βminus 1

)(D1)

CS0h0h0 =δ13m

2h0

vo

(minus4δ213r

20

tan2 β+

2δ213r0tan2 β


tan3 βminus 4r0

tanβ

)(D2)

CS0H0H0 =δ13m

2h0

vo

(minus8δ213r

30

tan2 β+

12δ213r20


tan2 βminus 6r20

tan5 βminus 4r20

tan3 β+

2r20tanβ

+6r0s0tan4 β

+4r0s0tan2 β

minus2r0s0 +3r0

tan5 β+

r0tan3 β


minus 3s0tan4 β


+ 3s0

)(D3)

CS0S0H0 =δ213m

2h0

vo

(minus8δ213r

30

tan2 β+

8δ213r20


tan2 β+

12r30tan5 β

+4r30


tan4 βminus 4r20s0

tan2 βminus 12r20

tan5 β

+8r20

tanβ+

12r0s0tan4 β

+8r0s0tan2 β

minus 4r0s0 +3r0

tan5 βminus r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D4)

CS0H0h0 =δ13m

2h0

vo

(minus4δ213r

30

tan3 β+

4δ213r20


20

tanβminus δ213r0

tan3 β+

3δ213r0tanβ

+4r20

tan4 β+

4r20tan2 β

minus 4r0s0tan3 β

minus4r0s0tanβ

minus 3r0tan2 β

minus r0 +2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1

)(D5)

ndash 31 ndash

CS0H+Hminus =δ13m

2h0

vo

(minus 2r20

tan5 β+

2r20tanβ

+2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0 +r0

tan5 βminus r0


minus 5r0tanβ

minus s0tan4 β


+ s0 minus4m2

Hplusmnr0

tan3 βm2h0

minus4m2

Hplusmnr0

tanβm2h0

)(D6)

CS0A0A0 =δ13m

2h0

vo

(minus

4m2A0r0

tan3 βm2h0

minus4m2

A0r0tanβm2

h0

minus 2r20tan5 β

+2r20

tanβ+

2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0

+r0

tan5 βminus r0


tanβminus s0


tan2 β+ s0

)(D7)

CS0S0S0 =δ313m

2h0

vo

(minus 24r40

tan5 β+

24r30s0tan4 β

+36r30

tan5 βminus 12r30



tan2 βminus 18r20

tan5 β+

12r20tan3 β

+18r20tanβ

+18r0s0tan4 β

+12r0s0tan2 β

minus 6r0s0 +3r0

tan5 βminus 3r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D8)

Ch0H+Hminus =m2h0

vo

(2δ213r0tanβ

+2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1minus

2m2Hplusmn

tan4 βm2h0

minus4m2

Hplusmn

tan2 βm2h0

minus2m2

Hplusmn

m2h0

) (D9)

References










ndash 32 ndash























ndash 33 ndash






















ndash 34 ndash








ndash 35 ndash

1 Introduction

2 The Model








42 Direct Detection


5 Summary

A Model Parameters




CS0H+Hminus =δ13m

2h0

vo

(minus 2r20

tan5 β+

2r20tanβ

+2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0 +r0

tan5 βminus r0


minus 5r0tanβ

minus s0tan4 β


+ s0 minus4m2

Hplusmnr0

tan3 βm2h0

minus4m2

Hplusmnr0

tanβm2h0

)(D6)

CS0A0A0 =δ13m

2h0

vo

(minus

4m2A0r0

tan3 βm2h0

minus4m2

A0r0tanβm2

h0

minus 2r20tan5 β

+2r20

tanβ+

2r0s0tan4 β

+4r0s0tan2 β

+ 2r0s0

+r0

tan5 βminus r0


tanβminus s0


tan2 β+ s0

)(D7)

CS0S0S0 =δ313m

2h0

vo

(minus 24r40

tan5 β+

24r30s0tan4 β

+36r30

tan5 βminus 12r30



tan2 βminus 18r20

tan5 β+

12r20tan3 β

+18r20tanβ

+18r0s0tan4 β

+12r0s0tan2 β

minus 6r0s0 +3r0

tan5 βminus 3r0


tanβ

minus 3s0tan4 β


+ 3s0

)(D8)

Ch0H+Hminus =m2h0

vo

(2δ213r0tanβ

+2s0


4s0tanβ

minus 1

tan4 βminus 2

tan2 βminus 1minus

2m2Hplusmn

tan4 βm2h0

minus4m2

Hplusmn

tan2 βm2h0

minus2m2

Hplusmn

m2h0

) (D9)

References










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ndash 35 ndash

1 Introduction

2 The Model








42 Direct Detection


5 Summary

A Model Parameters


























ndash 33 ndash






















ndash 34 ndash








ndash 35 ndash

1 Introduction

2 The Model








42 Direct Detection


5 Summary

A Model Parameters

























ndash 34 ndash








ndash 35 ndash

1 Introduction

2 The Model








42 Direct Detection


5 Summary

A Model Parameters











ndash 35 ndash

1 Introduction

2 The Model








42 Direct Detection


5 Summary

A Model Parameters




lepto-philic 2-hdm + singlet scalar portal induced ...lepto-philic 2-hdm + singlet scalar portal...

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