heavy dark matter through the higgs portal€¦ · heavy dark matter through the higgs portal...

Heavy Dark MatterThrough TheHiggs Portal

IntroductionHidden Sectors, HiddenValleys and Higgs Portals.

DM in Higgs Portal Models

Heavy DM fromSUSY HiggsPortalsThe Model

The SommerfeldEnhancement

DMPhenomenolgyRelic Density Calculation

Direct and IndirectDetection

Summary

Fat HiggsAppendix

Heavy Dark Matter Through The HiggsPortal

Stephen M. West

University of Oxford, Magdalen College

SHEP - 1st February 2008

J. March-Russell, SMW, D. Cumberbatch, D. Hooper:

arXiv:0801.3440 [hep-ph] and more to come...

Summary

Fat HiggsAppendix

Outline

IntroductionHidden Sectors, Hidden Valleys and Higgs Portals.DM in Higgs Portal Models

Heavy DM from SUSY Higgs PortalsThe ModelThe Sommerfeld Enhancement

DM PhenomenolgyRelic Density CalculationDirect and Indirect Detection

Summary

Fat Higgs Appendix

Summary

Fat HiggsAppendix

Outline

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Fat Higgs Appendix

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Fat HiggsAppendix

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Fat Higgs Appendix

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Fat HiggsAppendix

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Fat Higgs Appendix

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Fat HiggsAppendix

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Hidden Sectors.

Hidden sectors common in many extensions of SM,e.g. SUSY, string theory, hidden/secluded RSwarped throats etc...

We consider, extra states not charged under the SM gauge group,

possibly charged under exotic gauge symmetry. SM or MSSM communicates with hidden sector via

Z ′ or Higgs interactions. Nice feature: interactions between hidden sector and

SM involve d ≤ 4 operators. Also consider mass scale of hidden sector close to or

just above weak scale. Attractive alternative to usual desert above weak

scale.

Summary

Fat HiggsAppendix

Hidden Sectors.

Hidden sectors common in many extensions of SM,e.g. SUSY, string theory, hidden/secluded RSwarped throats etc...

We consider, extra states not charged under the SM gauge group,

possibly charged under exotic gauge symmetry. SM or MSSM communicates with hidden sector via

Z ′ or Higgs interactions. Nice feature: interactions between hidden sector and

SM involve d ≤ 4 operators. Also consider mass scale of hidden sector close to or

just above weak scale. Attractive alternative to usual desert above weak

scale.

Summary

Fat HiggsAppendix

SM-hidden sector communication viaZ ′ interactions.

Z ′ interactions occur either by: SM states charged under U(1)′ or Indirectly due to kinetic mixing term εF µν

Y F ′µν

(e.g. Babu, Kolda, March-Ruessll.)

Example Hidden Valley Model: SM gauge group, Gsm, extended by non-abelian

group Gv . SM states only charged under U(1)′ subgroup of Gv . Extra “valley" particles not charged under Gsm. Example Gv = U(1)′×SU(nv ). Interesting collider phenomenology and DM

possibilities.

(e.g. Strassler, Zurek; Han...)

Summary

Fat HiggsAppendix

SM-hidden sector communication viaZ ′ interactions.

Z ′ interactions occur either by: SM states charged under U(1)′ or Indirectly due to kinetic mixing term εF µν

Y F ′µν

(e.g. Babu, Kolda, March-Ruessll.)

Example Hidden Valley Model: SM gauge group, Gsm, extended by non-abelian

group Gv . SM states only charged under U(1)′ subgroup of Gv . Extra “valley" particles not charged under Gsm. Example Gv = U(1)′×SU(nv ). Interesting collider phenomenology and DM

possibilities.

(e.g. Strassler, Zurek; Han...)

Summary

Fat HiggsAppendix

SM-hidden sector communication via“Higgs Portals".

Extra states, not charged under Gsm but can becharged under exotic gauge symmetry.

Communication via interactions involving SM (orMSSM) Higgs

λ |H|2 |φ |2

(Schabinger, Wells; Patt, Wilczek...)

φ is a singlet under Gsm but charged under Ghidden. φ could have many more interactions with hidden

sector states. Changes Higgs phenomenology. Provides opportunities for DM in the hidden sector.

Summary

Fat HiggsAppendix

SM-hidden sector communication via“Higgs Portals".

Extra states, not charged under Gsm but can becharged under exotic gauge symmetry.

Communication via interactions involving SM (orMSSM) Higgs

λ |H|2 |φ |2

(Schabinger, Wells; Patt, Wilczek...)

φ is a singlet under Gsm but charged under Ghidden. φ could have many more interactions with hidden

sector states. Changes Higgs phenomenology. Provides opportunities for DM in the hidden sector.

Summary

Fat HiggsAppendix

Can also have couplings involving fermions:

ψψLH

just neutrino Dirac term or in SUSY

W ⊃ λSHuHd

just the usual term found in models like the NMSSM. Point is ψ or S could have further interactions with

other states from the Hidden sector.

Summary

Fat HiggsAppendix

ψψLH

W ⊃ λSHuHd

Summary

Fat HiggsAppendix

ψψLH

W ⊃ λSHuHd

Summary

Fat HiggsAppendix

DM in Higgs Portal Models.

Assume dominant form of DM comes from hiddensector,

Efficient coannihilation channels for neutralino LSP or Light gravitino LSP in gauge mediated models or Rp violation

Example 1: Direct coupling between hidden andvisible sector

λ |H|2 |φ |2 Coannihilation of hidden sector DM,

(McDonald...)

(Cirelli, Fornengo, Strumia...)

DM with large masses (multi TeV) for large λinteresting parameter range.

Summary

Fat HiggsAppendix

(McDonald...)

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Fat HiggsAppendix

(McDonald...)

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Fat HiggsAppendix

Example 2: Indirect coupling between hidden andvisible sector

λ ′ψψφ + λφψvisψ ′vis

For SUSY modelψvisψ ′

vis ⇒ Higgsino pair, Higgsino Lepton pair. Coannihilation diagram:

ψ ′vis

φλ ′ λ

ψ DM could be heavy requiring large couplings to beviable thermal relic.

For DM above ∼ 1TeV extra non-perturbativeSommerfeld effect important, more later...

Summary

Fat HiggsAppendix

ψ ′vis

φλ ′ λ

Summary

Fat HiggsAppendix

ψ ′vis

φλ ′ λ

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Fat HiggsAppendix

Heavy DM in SUSY Higgs Portal Models

The model defined by the superpotential

W=WMSSM (µ=0)+λNHuHd+t2N+ λ ′2 NS2+

ms2 S2

S has a non-R Z2 symmetry leads to a stable relic. DM particle will be s (fermionic cpt of S). Model is simple extension of MNSSM

(Panagiotakopoulos, Pilaftsis; Dedes et al.)

MNSSM coupling, λ , taken perturbative up to Mp. Our variant, added another singlet, S, with large

(multi TeV) mass. We need large λ and λ ′ to get correct relic

abundance.

Summary

Fat HiggsAppendix

ms2 S2

abundance.

Summary

Fat HiggsAppendix

ms2 S2

abundance.

Summary

Fat HiggsAppendix

ms2 S2

abundance.

Summary

Fat HiggsAppendix

Large coupling and UV completion

Taking cut off for theory Λ0 ≥ MGUT⇒ Couplings, λ ,λ ′, blow up well before Λ0.⇒ S mass term implies large tadpole terms spoilingthe stability of the weak scale. (Panagiotakopoulos, Pilaftsis; Dedes...)

Can take S to be elementary and simultaneouslychoose large values for λ ,λ ′ if theory is an effectivetheory with cutoff Λ0 < 100TeV.

No problem in having a mass for S in this case.But no UV completion

Treat model as effective theory of the “Fat Higgs"model (Harnik et al.)

S ⇒ composite meson field of new susy-preservingstrong-interaction dynamics.

No large tadpole terms. Natural to expect large couplings λ and λ ′.

Summary

Fat HiggsAppendix

Summary

Fat HiggsAppendix

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Fat HiggsAppendix

DM Interactions Lagrangian determining relevant interactions and

masses, L⊃Lfermion+Lscalar, where

Lfermion =(

−λnhu hd−λ nhuhd−λ nhu hd− λ ′2 nss−λ ′nss−ms

2 ss+h.c)

Lscalar= |λ ′ns+mss|2+|λhuhd+t2+(λ ′/2)s2|2+|λnhd |2+|λnhu |2

Aλ λnhuhd+Aλ ′

2 λ ′ns2+ B2 mss2+Ct2n+h.c

+M2hu|hu |2+M2

hd|hd |2

+M2s |s|2+M2

n |n|2,

In the limit ms ≫ msusy, mass differencems −ms ≃ m2

susy/ms < Tf ≃ ms/25.⇒ s and s will freeze out at similar T⇒ must include s annihilations in relic densitycalculation

Relevant scalar interactions:λ ′ms |s|2 n +h.c,

λ ′λhuhds∗2 +h.c

Summary

Fat HiggsAppendix

DM Interactions Lagrangian determining relevant interactions and

masses, L⊃Lfermion+Lscalar, where

Lfermion =(

−λnhu hd−λ nhuhd−λ nhu hd− λ ′2 nss−λ ′nss−ms

2 ss+h.c)

Lscalar= |λ ′ns+mss|2+|λhuhd+t2+(λ ′/2)s2|2+|λnhd |2+|λnhu |2

Aλ λnhuhd+Aλ ′

2 λ ′ns2+ B2 mss2+Ct2n+h.c

+M2hu|hu |2+M2

hd|hd |2

+M2s |s|2+M2

n |n|2,

In the limit ms ≫ msusy, mass differencems −ms ≃ m2

susy/ms < Tf ≃ ms/25.⇒ s and s will freeze out at similar T⇒ must include s annihilations in relic densitycalculation

Relevant scalar interactions:λ ′ms |s|2 n +h.c,

λ ′λhuhds∗2 +h.c

Summary

Fat HiggsAppendix

The Sommerfeld Enhancement

Heavy DM moving at small (relative) velocities, dueto exchange of scalar states⇒ Enhancement ∝ 1/v .

(Sommerfeld, Hisano et al; Strumia et al...)

Sommerfeld enhancement corresponds to thesummation of diagrams

Only significant for s-wave,(AM barrier suppresses effect).

Summary

Fat HiggsAppendix

The Sommerfeld Enhancement

Heavy DM moving at small (relative) velocities, dueto exchange of scalar states⇒ Enhancement ∝ 1/v .

(Sommerfeld, Hisano et al; Strumia et al...)

Sommerfeld enhancement corresponds to thesummation of diagrams

Only significant for s-wave,(AM barrier suppresses effect).

Summary

Fat HiggsAppendix

Sommerfeld Enhancement

Calculation formulated as non-relativistic two-bodyQM problem with a potential.

Equivalent to the distorted Born-wave approximationcommon in nuclear physics.

Can be an enhancement or suppression for vectorstates.

Including the effect (to a good approximation)

σ = Rσ ℓ=0tree

Full calculation of R can be involved. For Yukawa potential, cannot be solved analytically.

Summary

Fat HiggsAppendix

Calculation of the Sommerfeld Enhancement

Our model, only scalar n states are “rungs on theladder"

The Schrödinger equation for the two dark matterparticle state, ψ ,

− 1ms

d2ψdr2 +V .ψ = K ψ , V = − λ ′2

8πr e−mnr , K = msv2

Enhancement factor is

R = |ψ(0)/ψ(∞)|2 .

Outgoing b.c., ψ ′(∞)/ψ(∞) = imsv

Summary

Fat HiggsAppendix

− 1ms

d2ψdr2 +V .ψ = K ψ , V = − λ ′2

R = |ψ(0)/ψ(∞)|2 .

Summary

Fat HiggsAppendix

− 1ms

d2ψdr2 +V .ψ = K ψ , V = − λ ′2

R = |ψ(0)/ψ(∞)|2 .

Summary

Fat HiggsAppendix

Coulomb limit of Sommerfeld Enhancement

Recall approximation ms ≫ msusy

Analytic form for R in limit ε ≡ mn/ms = 0,

1−e−y , y =λ ′2

λ ′2

Small vr limit

R ≈ λ ′2

Next paper, more detailed analysis for Sommerfeldeffect, e.g. non-zero ε .

Summary

Fat HiggsAppendix

Coulomb limit of Sommerfeld Enhancement

Recall approximation ms ≫ msusy

Analytic form for R in limit ε ≡ mn/ms = 0,

1−e−y , y =λ ′2

λ ′2

Small vr limit

R ≈ λ ′2

Next paper, more detailed analysis for Sommerfeldeffect, e.g. non-zero ε .

Summary

Fat HiggsAppendix

Relic Density Calculation

Important points and assumptions:

Take DM masses greater than ∼ 3TeV⇒ Tf ∼ ms

25 > Tc ⇒ EW still good symmetry,⇒ Apart from DM all fermions massless.

Set soft params to zero, Aλ = Aλ ′ . Soft masses negligible compared to ms.

Recall scalar s (ms ∼ ms +m2susy/ms)

⇒ s freezes out at similar T as s⇒ must include s annihilation rates in relic calc.

Summary

Fat HiggsAppendix

Relic Density Calculation

Important points and assumptions:

Take DM masses greater than ∼ 3TeV⇒ Tf ∼ ms

25 > Tc ⇒ EW still good symmetry,⇒ Apart from DM all fermions massless.

Set soft params to zero, Aλ = Aλ ′ . Soft masses negligible compared to ms.

Recall scalar s (ms ∼ ms +m2susy/ms)

⇒ s freezes out at similar T as s⇒ must include s annihilation rates in relic calc.

Summary

Fat HiggsAppendix

Scalar s annihilations. Interactions: λnhuhd + λ ′ms |s|2 n + λ ′λhuhds∗2+h.c.

Scalar states split into CP eigenstates, A= 1√2(φ+ia)

φn2λ′ms λ

λλ′

σ(ss → XX′) =

(λ′λ)2

256πvrm2s

1 − e−y, y =

λ′2

Summary

Fat HiggsAppendix

ss annihilations. Interactions: λ nhuhd + λ nhuhd + λ ′nss+h.c

nλ′ λ

σ(ss → XX′) =

(λ′λ)2

2πvrm2s

1 − e−y, y =

λ′2

Summary

Fat HiggsAppendix

ss annihilations. Interactions: λ ′

2 nss + λnhuhd+h.c

aniλ′γ5 iλγ5

σ(ss → XX′) =

(λ′λ)2

128πvrm2s

1 − e−y, y =

λ′2

Summary

Fat HiggsAppendix

Relic Density Numerics.

Re-label (s,s) as (s1,s2) Define

ri≡gi (1+∆i )

3/2 exp[−x∆i ]geff

, ∆i=(mi−m1)/m1,

geff=∑i gi (1+∆i)3/2 exp[−x∆i ], x=ms/T

For our two species

g1=g2=2, ∆1=0, ∆2=ms−ms≃m2

susyms

Summary

Fat HiggsAppendix

ri≡gi (1+∆i )

, ∆i=(mi−m1)/m1,

For our two species

g1=g2=2, ∆1=0, ∆2=ms−ms≃m2

susyms

Summary

Fat HiggsAppendix

ri≡gi (1+∆i )

, ∆i=(mi−m1)/m1,

For our two species

g1=g2=2, ∆1=0, ∆2=ms−ms≃m2

susyms

Summary

Fat HiggsAppendix

Freeze-out temperature, Tf = ms/xf , found byiteratively solving

xf =ln

0.038geffMpl ms〈σij vr〉√g⋆xf

σeff=∑i,j σij ri rj=∑2i,j σij

gi gjg2

eff(1+∆i )

3/2(1+∆j)3/2 exp(−x(∆i +∆j)).

Final relic density

Ωh2=1.07×109xf√g⋆Mpl (GeV)J , J=

∫ ∞xf

x−2aeffdx

(Griest, Seckel; Gondolo, Gelmini)

Summary

Fat HiggsAppendix

Comparing with and without Sommerfeld.

Plotted for λ = λ ′ = 1.5,2,2.5, with msusy= 100GeV

5 10 15 20 25 30m

Without Sommerfeld

With Sommerfeld

Summary

Fat HiggsAppendix

λ λ ′ parameter space. Plotted for msusy= 100GeV.

0.5 1.0 1.5 2.0 2.5 3.0Λ'

ms~= 23 TeV

ms~= 19 TeV

ms~= 15 TeV

ms~= 11 TeV

ms~= 7 TeV

ms~= 3 TeV

Summary

Fat HiggsAppendix

Direct Detection. Main analyses next paper...

Quick look: Direct detection phenomenology: No restrictive limits

BUT sizeable fraction of future parameter spacecovered by next generation detectors.

Our DM interacts with quarks in nuclei via effectivescalar interaction

L = ∑U=u,c,t

CU ssUU + ∑D=d ,s,b

CDssDD,

CU = ∑i

λUV1iV2iλ ′

, CD = ∑i

λDV1iV3iλ ′

Vij is Higgs mixing matrix. (Griest; Bertone, Hooper, Silk...)

Summary

Fat HiggsAppendix

Direct Detection. Main analyses next paper...

Quick look: Direct detection phenomenology: No restrictive limits

BUT sizeable fraction of future parameter spacecovered by next generation detectors.

Our DM interacts with quarks in nuclei via effectivescalar interaction

L = ∑U=u,c,t

CU ssUU + ∑D=d ,s,b

CDssDD,

CU = ∑i

λUV1iV2iλ ′

, CD = ∑i

λDV1iV3iλ ′

Vij is Higgs mixing matrix. (Griest; Bertone, Hooper, Silk...)

Summary

Fat HiggsAppendix

Direct Detection Cont...

Estimate elastic scattering cross secton per nucleon

σsN ∼ 2×10−7 pb(

λ ′

120GeVmh1

For ms ≥ 3TeV, cross section below currentconstraints from experiments such as XENON andCDMS.

Future measurements could probe parameter region. For smaller values of λ ′,Vij gets harder...

Summary

Fat HiggsAppendix

Indirect Detection.

Indirect signals are modified by potentially largeSommerfeld enhancements.

Depends on astrophysical environment, specificallyvelocity distribution.

Annihilation rates can be enhanced by 103 to 105 ormore.

Could favour objects with low velocity dispersion e.g.dwarf satellite galaxies of the Milky Way.

Full calculation needed: Need to understand resonance structure of the

Sommerfeld enhancement in the non-coulombic andlow vr regime

Need full details of low energy model.

Potential for significant signals in future observations.

Summary

Fat HiggsAppendix

Indirect Detection.

Summary

Fat HiggsAppendix

Indirect Detection.

Summary

Fat HiggsAppendix

Summary Models with very heavy (∼ 3−30TeV ) dark matter. Motivated by Higgs Portal (and Hidden Valley)

models⇒ DM interacts with visible sector only throughHiggs interactions (and Z ′).

Such models have UV completion using a composite“Fat Higgs” model.

DM annihilations are enhanced by non-perturbativeSommerfeld effect.

DM up to ∼30 TeV can be thermal relic with correctrelic abundance.

Our DM potentially detectable by direct and indirectDM experiments.

Sommerfeld corrections can dramatically enhanceDM annihilation rate for low velocities.⇒ Greatly improving detection possibilities.

Summary

Fat HiggsAppendix

Summary

Fat HiggsAppendix

Summary

Fat HiggsAppendix

Summary

Fat HiggsAppendix

The Fat Higgs Model.

The Fat Higgs model is an N = 1 supersymmetricSU(2) gauge theory with six doublets.

Full symmetry is SU(2)L ×SU(2)H gauge andSU(2)R ×SU(2)g ×U(1)R global,U(1)Y subgroup of SU(2)R is also gauged.

SU(2)H becomes strongly coupled at some scale, ΛH

Six doublets charged under SU(2)H form compositeobjects, Mij = TiTj , with (i, j=1...6)

Summary

Fat HiggsAppendix

The Fat Higgs Model.

The Fat Higgs model is an N = 1 supersymmetricSU(2) gauge theory with six doublets.

Full symmetry is SU(2)L ×SU(2)H gauge andSU(2)R ×SU(2)g ×U(1)R global,U(1)Y subgroup of SU(2)R is also gauged.

SU(2)H becomes strongly coupled at some scale, ΛH

Six doublets charged under SU(2)H form compositeobjects, Mij = TiTj , with (i, j=1...6)

Summary

Fat HiggsAppendix

Particle content of the Fat Higgs Model:

Field SU(2)L SU(2)H SU(2)R SU(2)g U(1)R Z2

T1 2 2 1 1 0 +T2 2 2 1 1 0 -T3 1 2 2 1 1 -T4 1 2 2 1 1 +T5 1 2 1 2 1 +T6 1 2 1 2 1 +P11 2 1 1 2 1 +P12 2 1 1 2 1 +P21 2 1 1 2 1 -P22 2 1 1 2 1 -Q11 1 1 2 2 1 -Q12 1 1 2 2 1 -Q21 1 1 2 2 1 +Q22 1 1 2 2 1 +Sa 1 1 1 1 2 -Sb 1 1 1 1 2 -

Summary

Fat HiggsAppendix

More Fat Higgs... Tree Level Superpotential, WFHtot = W1 +W2, where

W1 = y1SaT1T2+y2SbT3T4+y3SaT3T4+y4SbT1T2W2−mT5T6

W2 = y5

After SU(2)H becomes strong, effectivesuperpotential becomes (after canon. norm.)

Wdyn = λ(PfM−v20 M56)+m1SaM12+m2SbM34+m3SaM34+m4SbM12

+ m5(M15P11+M16P12+M25P21+M26P22)

+ m6(M35Q11+M36Q12+M45Q21+M36Q22),

Using NDA , we have (Luty)

v20 ∼ mΛH

(4π)2,

mi ∼ yiΛH4π ,

λ(ΛH ) ∼ 4π.

Summary

Fat HiggsAppendix

More Fat Higgs... Tree Level Superpotential, WFHtot = W1 +W2, where

W1 = y1SaT1T2+y2SbT3T4+y3SaT3T4+y4SbT1T2W2−mT5T6

W2 = y5

After SU(2)H becomes strong, effectivesuperpotential becomes (after canon. norm.)

Wdyn = λ(PfM−v20 M56)+m1SaM12+m2SbM34+m3SaM34+m4SbM12

+ m5(M15P11+M16P12+M25P21+M26P22)

+ m6(M35Q11+M36Q12+M45Q21+M36Q22),

Using NDA , we have (Luty)

v20 ∼ mΛH

(4π)2,

mi ∼ yiΛH4π ,

λ(ΛH ) ∼ 4π.

Summary

Fat HiggsAppendix

Yet More Fat Higgs... Make assumption (m5,m6) ≫ (m1,m2,m3,m4),

integrate out heavy states

W ′dyn = λM56(M14M23−M24M13−v2

0 +M12M34)

+ m1SaM12+m2SbM34+m3SaM34+m4SbM12.

With m1 ∼ m2 ∼ m3 ∼ m4 ∼ m′, fermioniccomponents of Sa,Sb,M12 and M34 mix lightesteigenvalue ∼ m′.

Diagonalization, integrate out all but the lightesteigenvalue, S1,

W=λN(HuHd−v20)+

λ ′2 NS2

2 S21,

where(

,N=M56.

Final assumption: ms1 ≫electroweak scale and softsupersymmetry breaking masses.

Summary

Fat HiggsAppendix

Yet More Fat Higgs... Make assumption (m5,m6) ≫ (m1,m2,m3,m4),

integrate out heavy states

W ′dyn = λM56(M14M23−M24M13−v2

0 +M12M34)

+ m1SaM12+m2SbM34+m3SaM34+m4SbM12.

With m1 ∼ m2 ∼ m3 ∼ m4 ∼ m′, fermioniccomponents of Sa,Sb,M12 and M34 mix lightesteigenvalue ∼ m′.

Diagonalization, integrate out all but the lightesteigenvalue, S1,

W=λN(HuHd−v20)+

λ ′2 NS2

2 S21,

where(

,N=M56.

Final assumption: ms1 ≫electroweak scale and softsupersymmetry breaking masses.

heavy dark matter through the higgs portal€¦ · heavy dark matter through the higgs portal...

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