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
2·XII·2011 - Universite de Geneve EW lights from DM annihilations
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
Andrea De Simone 2/30
2·XII·2011 - Universite de Geneve EW lights from DM annihilations
Dark Matter Searches
Search strategies:
∗ Collider (in LHC we trust . . . ).Difficult unless correlating /ET with otherhandles (displaced vertex, ISR jets. . . ).
p
p
ET
ET
Andrea De Simone 3/30
2·XII·2011 - Universite de Geneve EW lights from DM annihilations
Dark Matter SearchesSearch strategies:
∗ Collider (in LHC we trust . . . ).Difficult unless correlating /ET with otherhandles (displaced vertex, ISR jets. . . ).
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]
Andrea De Simone 3/30
2·XII·2011 - Universite de Geneve EW lights from DM annihilations
Dark Matter SearchesSearch strategies:
∗ Collider (in LHC we trust . . . ).Difficult unless correlating /ET with otherhandles (displaced vertex, ISR jets. . . ).
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 . . . )
Andrea De Simone 3/30
2·XII·2011 - Universite de Geneve EW lights from DM annihilations
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. . .
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2·XII·2011 - Universite de Geneve EW lights from DM annihilations
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]
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2·XII·2011 - Universite de Geneve EW lights from DM annihilations
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]
Andrea De Simone 6/30
2·XII·2011 - Universite de Geneve EW lights from DM annihilations
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
Andrea De Simone 7/30
2·XII·2011 - Universite de Geneve EW lights from DM annihilations
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)]
Andrea De Simone 8/30
2·XII·2011 - Universite de Geneve EW lights from DM annihilations
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.
Andrea De Simone 8/30
2·XII·2011 - Universite de Geneve EW lights from DM annihilations
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;
Andrea De Simone 9/30
2·XII·2011 - Universite de Geneve EW lights from DM annihilations
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.
Andrea De Simone 9/30
2·XII·2011 - Universite de Geneve EW lights from DM annihilations
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)]
Andrea De Simone 10/30
2·XII·2011 - Universite de Geneve EW lights from DM annihilations
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);
Andrea De Simone 11/30
2·XII·2011 - Universite de Geneve EW lights from DM annihilations
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!
Andrea De Simone 12/30
2·XII·2011 - Universite de Geneve EW lights from DM annihilations
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
Andrea De Simone 13/30
2·XII·2011 - Universite de Geneve EW lights from DM annihilations
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.
Andrea De Simone 14/30
2·XII·2011 - Universite de Geneve EW lights from DM annihilations
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]
Andrea De Simone 15/30
2·XII·2011 - Universite de Geneve EW lights from DM annihilations
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)
Andrea De Simone 16/30
2·XII·2011 - Universite de Geneve EW lights from DM annihilations
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)
Andrea De Simone 17/30
2·XII·2011 - Universite de Geneve EW lights from DM annihilations
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
Andrea De Simone 18/30
2·XII·2011 - Universite de Geneve EW lights from DM annihilations
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.
Andrea De Simone 19/30
2·XII·2011 - Universite de Geneve EW lights from DM annihilations
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.
Andrea De Simone 20/30
2·XII·2011 - Universite de Geneve EW lights from DM annihilations
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]
Andrea De Simone 21/30
2·XII·2011 - Universite de Geneve EW lights from DM annihilations
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.
Andrea De Simone 22/30
2·XII·2011 - Universite de Geneve EW lights from DM annihilations
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.
Andrea De Simone 23/30
2·XII·2011 - Universite de Geneve EW lights from DM annihilations
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-
Andrea De Simone 24/30
2·XII·2011 - Universite de Geneve EW lights from DM annihilations
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
)
Andrea De Simone 25/30
2·XII·2011 - Universite de Geneve EW lights from DM annihilations
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
)
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-
Andrea De Simone 25/30
2·XII·2011 - Universite de Geneve EW lights from DM annihilations
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.
Andrea De Simone 25/30
2·XII·2011 - Universite de Geneve EW lights from DM annihilations
Initial State Radiation with EFT
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 .
Andrea De Simone 26/30
2·XII·2011 - Universite de Geneve EW lights from DM annihilations
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
)
Andrea De Simone 27/30
2·XII·2011 - Universite de Geneve EW lights from DM annihilations
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.
Andrea De Simone 28/30
2·XII·2011 - Universite de Geneve EW lights from DM annihilations
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]
Andrea De Simone 29/30
2·XII·2011 - Universite de Geneve EW lights from DM annihilations
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.
Andrea De Simone 30/30
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