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2·XII·2011 - Universite de Geneve

Electroweak lights from DM annihilations

Andrea De Simone

Based on:Ciafaloni, Cirelli, Comelli, DS, Riotto, Urbano

JCAP 1106, 018 (2011) [arXiv:1104.2996]JCAP 1110, 034 (2011) [arXiv:1107.4453]

+ work in progress

2·XII·2011 - Universite de Geneve EW lights from DM annihilations

Outline

• Indirect searches for DM

• ElectroWeak Bremsstrahlung in DM annihilations

• Radiation from final state

• Radiation from initial state

• Conclusions

Andrea De Simone 1/30


Dark Matter is real!

Evidences for DM:

• Rotation curves of galaxies

• Energy density budget

• Velocities of galaxiesin clusters

• Weak gravitational lensing

• Structure formation fromprimordial density fluctuations

• etc . . .

1982AJ.....87..945K



Dark Matter Searches

Search strategies:

∗ Collider (in LHC we trust . . . ).Difficult unless correlating /ET with otherhandles (displaced vertex, ISR jets. . . ).

p

p

ET

ET



Dark Matter SearchesSearch strategies:


p

p

ET

ET

∗ Direct detection

• 3 positive hints: DAMA, CoGeNT,CRESST;

• 3 null experiments (so far): Xenon,CDMS, Edelweiss-II;

• puzzling situation: maybe it is tellingus something about the interactionmechanism or the structure of theDM halo. . .

10 100 1000WIMP mass [GeV]

10-9

10-8

10-7

10-6

10-5

10-4

10-3

WIM

P-n

ucle

on c

ross s

ection [pb]

CRESST 1σ

CRESST 2σ

CRESST 2009EDELWEISS-IICDMS-IIXENON100DAMA chan.DAMACoGeNT

M2

M1

[CRESST Coll. 1109.0702]



Dark Matter SearchesSearch strategies:


p

p

ET

ET

∗ Direct detection

• 3 positive hints: DAMA, CoGeNT,CRESST;

• 3 null experiments (so far): Xenon,CDMS, Edelweiss-II;

• puzzling situation: maybe it is tellingus something about the interactionmechanism or the structure of theDM halo. . .

10 100 1000WIMP mass [GeV]

10-9

10-8

10-7

10-6

10-5

10-4

10-3

WIM

P-n

ucle

on c

ross s

ection [pb]

CRESST 1σ

CRESST 2σ

CRESST 2009EDELWEISS-IICDMS-IIXENON100DAMA chan.DAMACoGeNT

M2

M1

[CRESST Coll. 1109.0702]

∗ Indirect detection (Fermi, PAMELA, Hess, AMS/02, IceCube, Antares . . . )



Indirect Detection

Key observable for DM indirect detection: fluxesof stable particles (γ, ν, p, e) from DM annihila-tion/decay in the galactic halo or in the Sun

FIGURE 2. Simulated GLAST allsky map of neutralino DM annihilation in the Galactic halo, for a fiducial observer located 8kpc from the halo center along the intermediate principle axis. We assumedMχ = 46 GeV, !σv" = 5#10$26 cm3 s$1, a pixel sizeof 9 arcmin, and a 2 year exposure time. The flux from the subhalos has been boosted by a factor of 10 (see text for explanation).Backgrounds and known astrophysical gamma-ray sources have not been included.

DM ANNIHILATION ALLSKY MAP

Using the DM distribution in our Via Lactea simulation, we have constructed allsky maps of the gamma-ray flux fromDM annihilation in our Galaxy. As an illustrative example we have elected to pick a specific set of DM particle physicsand realistic GLAST/LAT parameters. This allows us to present maps of expected photon counts.The number of detected DM annihilation gamma-ray photons from a solid angle ΔΩ along a given line of sight (θ ,

φ ) over an integration time of τexp is given by

Nγ (θ ,φ) = ΔΩ τexp!σv"M2χ

!" Mχ

Eth

#dNγdE

$Aeff(E)dE

%"

losρ(l)2dl, (2)

where Mχ and !σv" are the DM particle mass and velocity-weighted cross section, Eth and Aeff(E) are the detectorthreshold and energy-dependent effective area, and dNγ/dE is the annihilation spectrum.We assume that the DM particle is a neutralino and have chosen standard values for the particle mass and annihilation

cross section:Mχ = 46 GeV and !σv" = 5#10$26 cm3 s$1. These values are somewhat favorable, but well within therange of theoretically and observationally allowed models. As a caveat we note that the allowed Mχ -!σv" parameterspace is enormous (see e.g. [7]), and it is quite possible that the true values lie orders of magnitude away from thechosen ones, or indeed that the DM particle is not a neutralino, or not even weakly interacting at all. We include onlythe continuum emission due to the hadronization and decay of the annihilation products (bb and uu only, for our lowMχ ) and use the spectrum dNγ/dE given in [8].For the detector parameters we chose an exposure time of τexp = 2 years and a pixel angular size of Δθ = 9 arcmin,

corresponding to the 68% containment GLAST/LAT angular resolution. For the effective area we used the curvepublished on the GLAST/LAT performance website [9] and adopted a threshold energy of Eth = 0.45 GeV (chosen to

[Kuhlen et al. 2007]

[Fermi Coll. 1110.2591]

Rise in e+ fraction.Possible signal of DM?also OK with astrophysics. . .



Indirect Detection

In the other channels: from absence of signal, limits are placed on the (mχ, vσann) plane.

Photon and neutrino data

101 102 103

WIMP mass [GeV]

10-26

10-25

10-24

10-23

10-22

10-21

WIM

P c

ross

sect

ion [

cm3

/s]

Upper limits, Joint Likelihood of 10 dSphs

3 ·10−26

bb Channel

τ+ τ− Channel

µ+ µ− Channel

W+W− Channel

[Fermi-LAT Coll. – 1108.3546]

10 26

10 24

10 22

10 20

10 18

103 104<

Av>

[cm3s

1 ]

m [GeV]

Natural scale

Unitaritybb

WW

!!,

Einasto ProfileHalo Uncertainy

[IceCube Coll. – 1101.3349]



Indirect Detection

kinetic energy [GeV]-110 1 10 210

-1 s

sr]

2an

tipro

ton

flux

[GeV

m

-610

-510

-410

-310

-210

-110

AMS (M. Aguilar et al.)

BESS-polar04 (K. Abe et al.)

BESS1999 (Y. Asaoka et al.)

BESS2000 (Y. Asaoka et al.)

CAPRICE1998 (M. Boezio et al.)

CAPRICE1994 (M. Boezio et al.)

PAMELA

[PAMELA Coll. – 1007.0821]

⇓

[Evoli et al. – 1108.0664]

p data and d expectations.

[Donato, Fornengo, Maurin – 0803.2640]



Indirect DetectionStatement of the problem:

if the microscopic physics is known (L ),what is the spectrum of stable particles at the detection point?

γ

χ

e

ν

p

SM ev

olut

ion

prop

agat

ion

dete

ctio

n

χ

DM annihilationparticle physics−−−−−−−−−→ primary fluxes

astrophysics−−−−−−−→ observed fluxes

The particle physics evolution proceeds in 2 steps:

DM annihilation model−−−−→ primary channelsradiation/hadronization/decay−−−−−−−−−−−−−−−−−→ primary fluxes

QCD, QED (only `→ `γ, γ → ff ), NO EW



ElectroWeak Bremsstrahlung

p

χ

χ

π0

π+

e+

µ+

Ze+

e- νµνeνµ

γ

γ

∗ The final state of the DM annihilation process can radiate γ, Z,W±.

∗ It is a SM effect and can affect the final fluxes of stable particles importantly.[Bergstrom (1989); Bringmann, Bergstrom, Edsjo (2008); Ciafaloni, Comelli, Riotto, Sala, Strumia, Urbano (2010)]



ElectroWeak Bremsstrahlung

p

χ

χ

π0

π+

e+

µ+

Ze+

e- νµνeνµ

γ

γ

∗ The final state of the DM annihilation process can radiate γ, Z,W±.

∗ It is a SM effect and can affect the final fluxes of stable particles importantly.[Bergstrom (1989); Bringmann, Bergstrom, Edsjo (2008); Ciafaloni, Comelli, Riotto, Sala, Strumia, Urbano (2010)]

Why can EW Bremsstrahlung have a big effect on the final spectra?

I Log-enhanced terms: ∆σ/σ ∼ αW log2(M 2DM/M

2W ) ∼ 0.3, for MDM ∼ TeV.

I SU(2)L ⊗ U(1)Y quantum numbers:EW interactions connect all SM particles ; all species will be present in the final spectrum.

I Fragmentation of energy:a few very energetic particles are converted into many soft particles.



IR-logs in DM annihilations

Bloch-Nordsieck theorem: observables which are inclusive over soft final states are IR safe.

BN theorem can be violated in inclusive cross sections if the initial state is prepared with a fixed non-abelian charge. [Ciafaloni, Ciafaloni, Comelli (2000-2001)]

DM DM→ X (inclusive)bremsstrahlung−−−−−−−−→

no logs (BN theorem) (if DM gauge-singlet)αW log2(s/M 2

W )? (BN violation?) (if DM EW-charged)

DM DM→ e+ + X (not incl.)bremsstrahlung−−−−−−−−→ αW log2(s/M 2

W )

• Double-logs come from soft-collinear singularities:∫ dkT

kT

∫dxx ,

where x = fraction of EW , kT transverse momentum;

• If the emitting particle is non-relativistic, there is no phase-space region for kT singularity;



IR-logs in DM annihilations

Bloch-Nordsieck theorem: observables which are inclusive over soft final states are IR safe.

BN theorem can be violated in inclusive cross sections if the initial state is prepared with a fixed non-abelian charge. [Ciafaloni, Ciafaloni, Comelli (2000-2001)]

DM DM→ X (inclusive)bremsstrahlung−−−−−−−−→

no logs (BN theorem) (if DM gauge-singlet)

((((((((((((

αW log2(s/M 2W ) (if DM EW-charged)

DM DM→ e+ + X (not incl.)bremsstrahlung−−−−−−−−→ αW log2(s/M 2

W )

• Double-logs come from soft-collinear singularities:∫ dkT

kT

∫dxx ,

where x = fraction of EW , kT transverse momentum;

• If the emitting particle is non-relativistic, there is no phase-space region for kT singularity;

• if DM is EW-charged, one may have BN violation in inclusive DM annihilations, which would producedouble-logs; but the non-rel regime closes this possibility.

• IR cutoff is physical for a broken gauge theory.



Spectra with EW BremsstrahlungDM DM→ e+

Le−L , γγ,W

+LW

−L

101 1 10 102 103103

102

101

1

10

E in GeV

dNdlnE

eL at M 3000 GeV

10-1 1 10 102 10310-3

10-2

10-1

1

10

E in GeV

dNd

lnE

Γ at M = 3000 GeV

10-1 1 10 102 10310-2

10-1

1

10

102

E in GeV

dNd

lnE

WT at M = 3000 GeV

—— γ

—— e+

—— ν

—— p

[Ciafaloni, Comelli, Riotto, Sala, Strumia, Urbano (2010)]



Importance of EW corrections

EW corrections are particularly relevant in 3 situations:

1. when the low-energy regions of the spectra, which are largely populated by thedecay products of the emitted gauge bosons, are the ones contributing the most tothe observed fluxes of stable particles;

2. when some species are absent without EW corrections (e.g. p from χχ→ `+`−);

3. when σ(2→ 3), with soft gauge boson emission, is comparable or even dom-inant with respect to σ(2→ 2):

3a. the main 2→ 2 annihilation channels is helicity suppressed andEW Bremsstrahlung lifts the suppression (for gauge-singlet Majorana DM);

3b. EW Bremsstrahlung lifts the suppression of a 2 → 2 annihilation channel andmakes it comparable with the main one (for gauge-charged Majorana DM);



Annihilations of Majorana fermions

vσann = a + b v2 +O(v4)

↑ ↑s-wave p-wave (today v ∼ 10−3)

For a Majorana fermion and SM singlet (e.g. Bino in SUSY)

χ

f

f

χ

only p-wave(mf Mχ)

Radiation−−−−−−→χ

f

f

χ

χ

f

f

χ

there is an s-wave!



The ModelThe DM couples to the SM via a heavy scalar doublet: S =

(η+

η0

)

L = LSM + Lχ + LS + Lint

Lχ =1

2χ(i/∂ −Mχ)χ ,

LS = (DµS)†(DµS)−M 2SS†S ,

Lint = yLχ(Liσ2S) + h.c.

= yL(χPLf2η+ − χPLf1η

0) + h.c.

Mass parameters: Mχ,MS ;Mχ, r ≡ (MS/Mχ)2 ≥ 1

χ0(k1)χ0(k2)→ fi(p1) fi(p2)

fχ

χ f

η+,η0

Mff ∼1

rM 2χ

[uf(p1) γαPL vf(p2)][vχ(k2) γαγ5 uχ(k1)]

vχ(k2)γαγ5uχ(k1) = −

=(p1+p2)α︷︸︸︷(k1 + k2)α

2Mχvχ(k2)γ5uχ(k1)

− i2Mχ

vχ(k2)σαβ (k1 − k2)β︸︷︷︸∼O(v)

γ5uχ(k1) =⇒ vσ ∼ 1M2χ

v2

r2



The Model

Now add radiation of EW gauge bosons ;

fχ

χ f

η+,η0

fχ

χ f

η+,η0

FSR VIBSchematically, the amplitude is

M∼ O(v)

Mχ

[O(

1

r

)∣∣∣∣FSR

+ O(

1

r2

)∣∣∣∣FSR

]+O(v0)

Mχ

[O(

1

r2

)∣∣∣∣VIB

+ O(

1

r2

)∣∣∣∣FSR

]

and the cross section

vσ(χχ→ ffZ) ∼ αWM 2

χ

[O(v2

r2

)+O

(v2

r3

)+O

(1

r4

)]

Important lesson:

I limiting the expansion to O(1/r) in the amplitude keeps the annihilation in p-wave.

I at O(1/r2), with VIB diagrams, the s-wave is opened.



When does the 3-body process dominate over the 2-body one?

Estimate:

vσ(2→ 2) ∼ 1

M 2χ

v2

r2

vσ(2→ 3) ∼ 1

M 2χ

αW4π

1

r4

σ(2 → 3) & σ(2 → 2)

when

r .

√αW4π

1

v∼ 50

(r ≡M 2S/M

2χ)

10!2

10!1

100

101

102

103

104

!v(2

!3)

/!v(2

!2)

m!±/mDM

mDM = 300 ,m!0 = m!±

!v("" ! #ee)/!v("" ! ee)

!v("" ! Zee)/!v("" ! ee)

!v("" ! Z$$)/!v("" ! ee)

!v("" ! We$)/!v("" ! ee)

[Garny, Ibarra, Vogl – 1105.5367]



Effective Field Theory

Integrate out the heavy scalar S:

Leff = LSM + Lχ +1

r

O6

M 2χ

+1

r2

O8

M 4χ

+ ...

The lowest-dimensional operator gives a p-wave annihilation:

O6 =1

2|yL|2

[χγ5γµχ

] [LγµPLL

]=⇒ vσ(χχ→ ffZ)

∣∣O6∝ |yL|

4

M 2χ

v2

r2

• O8 ; s-wave. O8 can be more important than O6 despite larger dimensionality.

• Warning: in this case, naive dimensional analysis fails to assess the relative impor-tance of operators in the expansion.

• Need to carry out a general operator expansion in v and 1/Λ.

(in progress with Monin, Thamm, Urbano)



Effective Field TheorySuppose χ interacts only with left-handed SM fermions.

Leff = LSM + χ(i/∂ −Mχ)χ +1

Λ2O6 +

1

Λ3O7 +

1

Λ4O8 + · · ·

Non-relativistic bilinears which are not velocity-suppressed:

〈0|χγ5, γ5γ0, γ5∂0, γ5γ

0∂0

χ|(p0, ~p); (p0,−~p)〉 ∼ v0

There are only a few operators contributing to χχ→ LLA in s-wave:

• Dim-6: O6|v0 = ∅

• Dim-7: O7|v0 = [χγ5χ][L←→/D PLL]→ 0 on the e.o.m. /DL = 0

• Dim-8:O8|v0 ⊃ [χγ5γµχ]

[L←−/D−→DµPLL + L

←−Dµ

−→/DPLL

]→ 0 on the e.o.m. /DL = 0

=⇒ ONLY ONE dim-8 operator contributing to s-wave:

O8|v0 = [χγ5γµχ][L←−D ργµ

−→D ρPLL

]

This is useful to place model-independent limits from ID data.

(in progress with Monin, Thamm, Urbano)



Numerics

χχ→ e+e− , νν , e+e−γ , e+e−Z , ννZ , e±νW∓

• our MC generates primary annihilation events (2 → 3) according to the |M|2 distri-bution;

• PYTHIA 8 simulates showering + hadronization + decay to final stable SM particles;extract primary energy spectra at interaction point for each species;(Technical remark: PYTHIA 6 does not include γ → ff branchings in the showering)

• diffusion equations for the cosmic-ray propagation in the galactic halo.!

e

"

p

PYT

HIA

8

prop

agat

ion

final

flux

es

e+ e-

Z

our MC



Energy spectra at the interaction point

10-4 10-3 10-2 10-1 110-3

10-2

10-1

1

10

x = Ekinetic MΧ

dNd

lnx

full Hthis workL

LO

Γ e

Ν

p

MS = 4 TeV

Mχ = 1 TeV

dNf

d lnx=

1

σ(2→ 2)

dσ(χχ→ f + X)

d lnx

“LO” means adding EW radiation atthe lowest order, keeping only theO(1/r) in the amplitude (p-wave).

∗ Bump of primary hard photons due to s-wave annihilation χχ→ e+e−γ.

∗ Large low-energy tails due to showering and hadronization of W,Z.



Ratios

10-4 10-3 10-2 10-1 1

1

10

102

x = Ee MΧ

dNd

lnx

@dN

dln

xDL

O

Positrons

MS= 4 TeV

MS= 6 TeV

MS= 8 TeV

10-4 10-3 10-2 10-1 1

1

10

102

x = EΝ MΧ

dNd

lnx

@dN

dln

xDL

O

Neutrinos

MS= 4 TeV

MS= 6 TeV

MS= 8 TeV

10-4 10-3 10-2 10-1 1

1

10

102

x = EΓ MΧ

dNd

lnx

@dN

dln

xDL

O

Photons

MS= 4 TeV

MS= 6 TeV

MS= 8 TeV

10-4 10-3 10-2 10-1 1

1

10

102

x = IEp - mpM MΧ

dNd

lnx

@dN

dln

xDL

O

Antiprotons

MS= 4 TeV

MS= 6 TeV

MS= 8 TeV

∗ dN/dE/[dN/dE]LO ∼ O(10− 100).Of course, much larger enhancement wrt not including EW corrections.



Propagated fluxes

Flux of cosmic rays received at Earth: dΦf/dE ≡ vfnf/(4π), where the number density nf(E, ~x) is thesolution of the diffusion-loss equation

dnfdt−K0(E/GeV)δ · ∇2nf︸︷︷︸

diffusion

− ∂

∂E(b(E, ~x)nf)

︸︷︷︸energy losses

+∂

∂z(sign(z)Vconv nf)

︸︷︷︸convection

= Q(E, ~x)︸︷︷︸source

− 2h δ(z) Γnf︸︷︷︸decay, annihilations

Q(E, ~x) ∝ [ρDM(~x)]2〈σv〉∑

f

BfdNf

dE

DM profiles and propagation parameters are variated simultaneously.ρ(r) rs [kpc] ρs [GeV/cm3]

NFW ρsrsr

(1 +

r

rs

)−2

24.42 0.184

Einasto ρs exp

[− 2

0.17

[(r

rs

)0.17

− 1

]]28.44 0.033

Burkertρs

(1 + r/rs)(1 + (r/rs)2)12.7 0.712

• Burkert/Isothermal: better fit to rotation curves

• Einasto/NFW: better fit to N-body simulations10-3 10-2 10-1 1 10 102

10-2

10-1

1

10

102

103

104

10¢¢ 30¢¢ 1¢ 5¢ 10¢ 30¢ 1o 2o 5o 10o20o45o

r @kpcD

Ρ DM

@GeV

cm3

D

Angle from the GC @degreesD

NFW

Moore

Iso

Einasto EinastoB

Burkert

r

Ρ

[From Cirelli et al. 1012.4515]



Propagated fluxes

Electrons or positrons AntiprotonsModel δ K0 [kpc2/Myr] δ K0 [kpc2/Myr] Vconv [km/s] L [kpc]MIN 0.55 0.00595 0.85 0.0016 13.5 1MED 0.70 0.0112 0.70 0.0112 12 4MAX 0.46 0.0765 0.46 0.0765 5 15

dΦe±

dE(E, ~x) =

ve±

4π b(E, ~x)

1

2

(ρMχ

)2

〈σv〉∫ Mχ

E

dEsdNe±

dE(Es) I(E,Es, ~x),

dΦp

dE(E, ~x) =

vp4π

(ρMχ

)2

R(E)1

2〈σv〉dNp

dE

dΦγ,ν

dE(E) =

r4π

1

2

(ρMχ

)2

J ∆Ω 〈σv〉dNγ,ν

dE, with J =

1

∆Ω

∫

∆Ω

∫

l.o.s.

ds

r

(ρ(r(s, θ))

ρ

)2

,

R(E), I(E,Es, ~x), J encapsulate all the astrophysics and depend on the propagation parameters andthe halo profiles, but not on the particle physics model.



Propagated fluxes

10-3 10-2 10-1 1

x = Ekinetic MΧ

x3dF

dx

Apar

ticle

scm

2s

srEH

arbi

trar

yno

rmal

izat

ionL

Electrons or Positrons

full Hthis workL

LO

propagation uncertainty

MΧ = 1 TeV

MS = 4 TeV

10-4 10-3 10-2 10-1 1

x = Ekinetic MΧ

dFd

xAp

artic

les

m2

ssr

EHar

bitr

ary

norm

aliz

atio

nL

Antiprotons

full Hthis workLLO

propagation uncertainty

MΧ = 1 TeV

MS = 4 TeV

10-3 10-2 10-1 1

x = Ekinetic MΧ

E2

dFd

EAG

eV2

cm

2s

srEH

arbi

trar

yno

rmal

izat

ionL

Gamma Rays

full Hthis workL

LO

DM profile uncertainty

MΧ = 1 TeV

MS = 4 TeV

b = 5o 30o window

• Spectra of charged particles (e±, p) get distorted by propagation.

• Neutral particles (γ, ν) just go straight, no spectrum distortion

• Propagation does not spoil the effect of s-wave opening.



Initial State RadiationLet’s abandon the hypothesis that DM is a gauge singlet...Consider DM is the neutral Majorana component of a multiplet charged under SU(2)L × U(1)Y , e.g.

SU(2)-triplet with Y = 0 (wino-like):

χ+

χ0

χ−

←− DM particle

Gauge interactions: Lkin ⊃ χ i /D χ ⊃ εabc χa /W

bχc

? Dominant annihilation channel (if kinematically al-lowed): χ0χ0 → W+W−, in s-wave.

? ISR lifts the helicity suppression and makes the fermionchannel also in s-wave;χ0χ0 → ff can be competitive with χ0χ0 → W+W−.

χ0

χ0

W-

W+

f

f

χ0

χ0

χ+

W-



Initial State Radiation with EFT

EFT analysis. Most general dimension-6 operators (Majorana nature forbids some operators):

Leff =CD

Λ2δab(L γµPLL

) (χaγµγ5χ

b)

+ iCND

Λ2εabc(L γµPLσ

cL) (χaγµχb

)




EFT analysis. Most general dimension-6 operators (Majorana nature forbids some operators):

Leff =CD

Λ2δab(L γµPLL

) (χaγµγ5χ

b)

+ iCND

Λ2εabc(L γµPLσ

cL) (χaγµχb

)

The amplitude for the process: χ0(k1)χ0(k2)→ f1(p1) f2(p2) W−(k) is

MISR ∼ CNDg

Λ2[uf γµPL vf ]

[vχ

(/ε∗(/k − /k2 + Mχ)γµ

m2W − 2k · k2

+γµ (/k1 − /k + Mχ)/ε∗

m2W − 2k · k1

)uχ

]

v→0−→ CNDg

Λ2[uf γµPL vf ]

[vχ/ε∗/k, γµ

m2W − 2k0Mχ

uχ

]6= 0

f

f

χ0

χ0

χ+

W-



Initial State Radiation with EFTEFT analysis. Most general dimension-6 operators (Majorana nature forbids some operators):

Leff =CD

Λ2δab(L γµPLL

) (χaγµγ5χ

b)

+ iCND

Λ2εabc(L γµPLσ

cL) (χaγµχb

)

The amplitude for the process: χ0(k1)χ0(k2)→ f1(p1) f2(p2) W−(k) is

MISR ∼ CNDg

Λ2[uf γµPL vf ]

[vχ

(/ε∗(/k − /k2 + Mχ)γµ

m2W − 2k · k2

+γµ (/k1 − /k + Mχ)/ε∗

m2W − 2k · k1

)uχ

]

v→0−→ CNDg

Λ2[uf γµPL vf ]

[vχ/ε∗/k, γµ

m2W − 2k0Mχ

uχ

]6= 0

f

f

χ0

χ0

χ+

W-

The relevant cross-section behaviours are

vσ(χ0χ0 → W+W−) =g4

8πM 2χ

vσff(χχ→ fifi) ∼ C2D

1

M 2χ

O(M 4

χ

Λ4

)O(v2) ,

vσFSR(χ0χ0 → f1f2W−) ∼ C2

D

g2

M 2χ

O(M 4

χ

Λ4

)O(v2) ,

vσISR(χ0χ0 → f1f2W−) ∼ C2

ND

g2

M 2χ

O(M 4

χ

Λ4

)O(v0) .

ISR lifts the helicity suppression already at the level of dim-6 operators.

For CND ∼ (g/√

8π)(Λ/Mχ)2, the 3-body ISR cross section is comparable with the one for WW.




Comparison of e+, p spectra from W+W− (dashed) and from ISR (solid).Each contribution is normalized to 1 (proper channel-weighing is model-dependent).

10-4 10-3 10-2 10-1 110-2

10-1

1

10

x = Ee+ M Χ

dNd

lnx

udW

eΝW

10-4 10-3 10-2 10-1 110-3

10-2

10-1

1

10

x = IEp - mpM M Χ

dNd

lnx

udW

eΝW

Distinguishing features with respect to W+W−:

I abundant hard e+ in the eνW channel, due to primary positrons;

I abundant soft p in the udW channel, due to low-energy emitted W .



Initial State Radiation in a toy modelToy model (as before): Lint = −yχL (σaχ

a)S + h.c.

Integrating out S would match to the EFT lagrangian with: CND/Λ2 = −CD/Λ2 = |yχ|2/(4M 2S)

FSRV

V

VIB

ISRV=W

V

s channelV=W

"A"

"D"

"F"

"C"

V

"B"

"E"

"F, exc."

Schematically, the amplitude is

M ∼ g|yχ|2O(v)

Mχ

[O(

1

r

)∣∣∣∣FSR

+ O(

1

r2

)∣∣∣∣FSR

]+ g|yχ|2

O(v0)

Mχ

[O(

1

r

)∣∣∣∣ISR

+ O(

1

r2

)∣∣∣∣VIB+FSR

]

+g3O(v0)

Mχ

∣∣∣∣s−channel

and the s-wave part of the cross section is

vσ(χ0χ0 → νLW−e+

L) =g2|yχ|4

144π3M 2χr

2

︸︷︷︸ISR

+g4|yχ|2

96π3M 2χr︸︷︷︸

ISR/s-channel

+g6 [1 + 24 ln(2Mχ/mW )]

4608π3M 2χ︸︷︷︸

s-channel

+O(

1

r3

)



Initial State Radiation in a toy model

0.5 1.0 1.5 2.0 2.5 3.00

1

2

3

4

5

6

7

y!

!!3"bo

dy"#!!W

W"

!u d W" #!u dW#

!WWM!$ 3000 GeV, r $ 1.07M!$ 1000 GeV, r $ 1.2M!$ 500 GeV, r $ 1.44M!$ 500 GeV, r $ 4

0.5 1.0 1.5 2.0 2.5 3.00

2

4

6

8

y!

!!3"bo

dy"#!!W

W",M !

#3TeV

!u d W" $!u dW$

!WWr # 1r # 1.06r # 1.36r # 2.8

Mχ = 3 TeV, r ≡ (MS/Mχ)2

For large – but still perturbative – values of yχ ISR starts to dominate over the 2-bodyannihilation into gauge bosons.



Collider-DD connection ?N

N

W+

χ0

χ0

χ+

χ

N

χ

N

Mono-W + /ET Direct Detection

mono-jet analyses atTeVatron and LHC

∗ Data from mono-W+ /ET searches at collid-ers can be used to constrain DM – quarksinteractions.

∗ In practice: add signal events to the SMBG and require agreement with observa-tion within e.g. 90% CL; then, translate thebounds into DD scattering rates.

∗ Results are complementary to and compet-itive with those from Direct Detection(in progress).

0.5 1.0 5.0 10.0 50.0 100.010!44

10!42

10!40

10!38

10!36

m" !GeV"

#SI!n!cm2 "

u$% u "$%

"d$% d "$%

"uu""dd""

CDMS

CoGeNTDAMA

DAMA!w. channeling"cc""bb""

[Bai et al. 1005.3797]

90 C.L.

101 100 101 102 1031046104510441043104210411040103910381037

WIMP mass mΧ GeVWIMPnucleoncrosssectionΣNcm2

ATLAS 7TeV, 1fb1 VeryHighPt

Spinindependent

Solid : ObservedDashed : Expected

ΧΓΜΧqΓΜq

Αs ΧΧ GΜΝGΜΝ

CDMSXEN

ON10

XENON10

0

DAMA q 33CoGeNT CRESST

[Fox et al. 1109.4398]



Conclusions

EW corrections are an important SM effect (no exotics!) and have animpact on energy spectra when MDM MW .

Main effects: all final stable particles are present; the low-energy spectracan be greatly enhanced.

EW Bremsstrahlung can take place either when DM is a gauge singlet orwhen it belongs to a multiplet charged under EW interactions.

Particularly relevant when there is a suppression mechanism for the 2-body cross section (e.g. Majorana DM annihilates through s-wave onceEW radiation is included).

The resulting spectra get substantially enhanced by factors O(10 − 100)

(with respect to p-wave only).Even more drastic effect with respect to the case without EW corrections.

⇒ Reliable calculations of fluxes for DM Indirect Detection should in-clude EW radiation.


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