Alessandro Strumia, talk at Planck 2008 about the univocal predictions of Minimal Dark Matter: DM is an automatically stable weak 5plet with M = 9.6 TeV that gives a detectable cosmic ray positron excess thanks to Sommerfeld-enhanced annihilations into W +W −...:
page 35 of http://www.ifae.es/planck2008/21-05_beta/Strumia.pdf
Later seen by PAMELA, excluded by ATIC, which is now excluded by FERMI... Implications of the positron/electron excesses on Dark Matter properties
1) The data 2) DM annihilations? 3) γ and ν constraints 4) DM decays?
Alessandro Strumia, talk at Planck 2009 From arXiv:0809.2409, 0811.3744, 0811.4153, 0905.0480 with M. Cirelli, G. Bertone, M. Kadastik, P. Meade, M. Papucci, M. Raidal, M. Taoso E. Nardi, F. Sannino, T. Volansky, www.cern.ch/astrumia/PAMELA.pdf Indirect signals of Dark Matter
DM DM annihilations in our galaxy might give detectable γ, e+, p,¯ d.¯ The galactic DM density profile
DM velocity: β ≈ 10−3. DM is spherically distributed with uncertain profile:
γ " α#(β−γ)/α r 1 + (r /rs) ρ(r) = ρ α r 1 + (r/rs) 3 r = 8.5 kpc is our distance from the Galactic Center, ρ ≡ ρ(r ) ≈ 0.3 GeV/cm ,
DM halo model α β γ rs in kpc Isothermal ‘isoT’ 2 2 0 5 Navarro, Frenk, White ‘NFW’ 1 3 1 20 ρ(r) is uncertain because DM is like capitalism according to Marx: a gravitational system (slowly) collapses to the ground state ρ(r) = δ(r). Maybe our galaxy is communist: ρ(r) ≈ low constant, as in isoT.
Moore 3 1000 cm
NFW
GeV Einasto, Α = 0.17 Earth
in 10 Ρ isoT ®
density 0.1 DM
0.001 0.01 0.1 1 10 100 Galacto-centric radius r in kpc DM DM signal boosted by sub-halos?
N-body simulations suggest that DM might clump in subhalos:
Annihilation rate ∝ R dV ρ2 increased by a boost factor B = 1 ↔ 100 ∼ a few Simulations neglect normal matter, that locally is comparable to DM. Propagation of e± in the galaxy
2 ∂ Φ + = v +f/4π where f = dN/dV dE obeys: −K(E) · ∇ f − (E˙f ) = Q. e e ∂E 1 ρ 2 dN + • Injection: Q = hσvi e from DM annihilations. 2 M dE δ • Diffusion coefficient: K(E) = K0(E/ GeV) ∼ RLarmor = E/eB. ˙ 2 2 • Energy loss from IC + syn: E = E · (4σT /3me )(uγ + uB). • Boundary: f vanishes on a cylinder with radius R = 20 kpc and height 2L. 2 Propagation model δ K0 in kpc /Myr L in kpc Vconv in km/s min 0.85 0.0016 1 13.5 med 0.70 0.01124 12 max 0.46 0.0765 15 5
min med max
Result: e± reach us from the Galactic Center only in the max case 1
The data ABC of charged cosmic rays e±, p±, He, B, C... Their directions are randomized by galactic magnetic fields B ∼ µG. The info is in their energy spectra.
We hope to see DM annihilation products as excesses in the rarer e+ andp ¯.
Experimentalists need to bring above the atmosphere (with balloons or satel- lites) a spectrometer and/or calorimeter, able of rejecting e− and p.
This is difficult above 100 GeV, also because CR fluxes decrease as ∼ E−3.
Energy spectra below a few GeV are ∼useless, because affected by solar activity. p/p¯ : PAMELA
Consistent with background
10-1 ç BESS 95+97 ó ÷óæó÷æóó BESS 98 ó óçòóóòóóò÷óæóóæ óóóóôó ôôó òæ BESS 99 10-2 ó óòôóòô ôò÷ ô ó ò ó í BESS 00 ÷ò æ - ô í Wizard MASS 91 ó ô æò CAPRICE 94
GeV ò í æ CAPRICE 98 sr -3 æò 10 ò AMS-01 98
sec PAMELA 08 2 æ m 1 -4 æ in 10 æ flux p
10-5
10-6 10-1 100 101 102 103 p kinetic energy T in GeV
Future: PAMELA, AMS e+/(e+ + e−): PAMELA
30% PAMELA 09 PAMELA is a spectrometer + ò à HEAT 94+95 CAPRICE 94 ò calorimeter sent to space. It ò AMS-01 ò MASS 91 + − à ò can discriminate e , e , p, p,¯ . . . ìì à æ à æ 10% ò and measure their energies up ò ì æ ò à ì æ æ to (now) 100 GeV. Astrophys- æ ò ìæà æ à ì fraction æ æ ò æ æ ì ical backgrounds should give a ææ ìàæ ææ ì æ ææ à positron fraction that decreases Positron with energy. This happens below 3% 10 GeV, where the flux is reduced by the present solar polarity. Growing excess above 10 GeV 1% 10-1 1 10 102 103 Energy in GeV
The PAMELA excess suggest that it might manifest in other experiments: if e+/e− continues to grow, it reaches e+ ∼ e− around 1 TeV... e+ + e−: FERMI and HESS
These experiments cannot discriminate e+/e−, but probe higher energy.
0.03 ò ò
ò ò
ò ò ò ò ò ò ì ò ò ò ì ì ææææææ ò ò ì ì òì æææ ò à sec æò æ æ æ æ æ æ æ æ æ æ æ æ 2 æ à æ cm
æ æ ì 2 à ì 0.01 FERMI ò GeV
L ì
+ ò e HESS08 à + - e
H à
3 HESS09 E ATIC08 à
à
0.003 ò 10 102 103 104 à Energy in GeV
Hardening at 100 GeV + softening at 1 TeV Are these real features? Likely yes.
Systematic errors, not yet defined, are here (conservatively?) incoherently added bin-to-bin to the smaller statistical error, allowing for a power-law fit. (ATIC)
Peak at 800 GeV?
In arXiv:0809.2409 we proposed that
+ -1 the large e excess could be seen also 10 HESS08 in e+ +e− and found the ATIC anomaly ATIC08 PPB-BETS08 HEAT on web sites of past minor conferences. EC ì ííííí í à çíç AMS ì ìà sec ç ç ç ô í à ATIC was later published on Nature, 2 ç íò òçCAPRICE94ç à ò òà à à cm ò Tangçàòet al. ààà í àà àìô à æà
2 à and the topic attracted attention. ççááááá ç ç àô í ô æ ò á á ô -2 áá ç í ô ô æ GeV 10 çá á á à L ò ìô
FERMI now finds that ATIC is wrong. + ô à e ò á æ + çá æ -
e ô H The FERMI paper was accepted in 3 3 á ô æ E çò æ days by PRL: a unpaid referee cannot á à æ validate an expensive experiment. áçá á
Why do pay (attention to) journals? - 10 á3ç 1 10 102 103 104 ò á Energy in GeV
á ... Just a pulsar?
A pulsar is a neutron star with a rotating intense magnetic field. The resulting electric field ionizes and accelerates e− (and maybe iron) → γ → e+e−, that are presumably further accelerated by the pulsar wind nebula (Fermi mechanism).
2 ˙ 2 2 4 3 • Epulsar = Iω /2, Epulsar = −BsurfaceR ω /6c = magnetic dipole radiation.
−E/M p • The guess isΦ e− ≈ Φe+ ∝ · e /E where p ≈ 2 and M are constants.
Known nearby pulsars (B0656+14, Geminga, ?) would need an unplausibly (?) large fraction of energy that goes into e±: ∼ 0.3.
Tests: • γ (but beamed? still alive?); • angular anisotropies (but local B?); 2
Model-independent theory of DM indirect detection Model-independent DM annihilations
Indirect signals depend on the DM mass M, non-relativistic σv, primary BR: W +W −, ZZ, Zh, hh Gauge/higgs sector DM DM → e+e−, µ+µ−, τ +τ − Leptons b¯b, t¯t, qq¯ quarks, q = {u, d, s, c} No γ because DM is neutral. Direct detection bounds suggest no Z.
The energy spectra of the stable final-state particles
± ∓ ( ) e , p , ν e,µ,τ , γ depend on the polarization of primaries.
The higher-order γ spectrum is model-dependent:
γ = (Brehmstalung/fragmentation) + (one-loop) + (3-body) The DM spin
Non-relativistic s-wave DM annihilations can be computed in a model-independent way because they are like decays of the two-body D = DM DM state.
If DM is a fundamental weakly-interacting particle, its spin can be 0, 1/2 or 1, so the spin of D can only be 0, 1 or 2
1 ⊗ 1 = 1, 2 ⊗ 2 = 1asymm ⊕ 3symm, 3 ⊗ 3 = 1symm ⊕ 3asymm ⊕ 5symm So:
2 • D can have spin 0 for any DM spin. It couples to vectors DFµν and to 2 higgs Dh , not to light fermions: D`L`R is m`/M suppressed.
• D can have spin 1 only if DM is a Dirac fermion or a vector. + − PAMELA motivates a large σ(DM DM → ` ` ): only possible for Dµ[`γ¯ µ`]. DM annihilations into fermions f
• D can only couple as ¯ DfLfR + h.c. = DΨf Ψf 2.0 ¯ Μ+ with negative helicity with Ψf = (fL, fR) in Dirac notation. It means zero helicity on average, and 1.5 is typically suppressed by mf /M. • Dµ can couple as Μ+ with positive helicity N L
¯ ¯ x [f γ f ] = [Ψ γ P Ψ] d Dµ L µ L Dµ f µ L 1.0 N d or H ¯ ¯ Dµ[fRγµfR] = Dµ[Ψf γµPRΨ] 0.5 i.e. fermions with Left or Right helicity. + + + Decays like µ → ν¯µe νe give e with 0.0 2 dN/dx|L = 2(1 − x) (1 + 2x) 0.0 0.2 0.4 0.6 0.8 1.0 Positron energy fraction x 3 dN/dx|R = 4(1 − x )/3 DM annihilations into W, Z
• The effective interactions 2 DFµνµνρσFρσ and DFµν 1.4
give vectors with T ranverse polarization 1.2 (with different unobservable helicity corre- lations), that decay in ff¯ with E = x M as: 1.0 N
2 L dN/d cos θ = 3(1 + cos θ)/8 x 0.8 d N d H dN/dx = 3(1 − 2x + 3x2)/2, 0.6 Transverse vector
0.4 2 • DAµ gives Longitudinal vectors (accon- 0.2 ting for DM annihilations into Higgs Gold- Longitudinal vector stones), that decay as 0.0 0.0 0.2 0.4 0.6 0.8 1.0 2 dN/d cos θ = 3(1 − cos θ)/4 Fermion energy fraction x
dN/dx = 6x(1 − x). DM annihilations into the higgs h
We can again focus on D, so that the effective interaction Dh2 gives DM annihilations into hH Since they have no spin, there are no polarization issues.
¯ We assume mh = 115 GeV, so h decays mostly into bb.
DM annihilations into Zh will not be considered, as they are are essentially given by the average of the ZLZL and hh channels. Final state spectra for M = 1 TeV
We consider the allowed s-wave primary annihilation channels:
{e, µL, µR, τL, τR,WL,WT ,ZL,ZT , h, q, b, t}, computed with our Mathematica MonteCarlo + Phytia8 + (Tauola+Phytia6)
e+ p Γ 10-5 10 e q 10-3 WL Μ ZL Μ L WT R -6 ZT 10 t E 1 -4 Τ fraction 10 WL dlog
fraction W L T ZL Γ ZΤRT b
t proton h - -7 -1 - 10 dlogN 10 Positron 10 5 h b Anti q
10-6 10-8 10-2 10 102 103 10 102 103 10 102 103 Energy in GeV Energy in GeV Energy in GeV
Annihilations into leptons give qualitatively different energy spectra.
ΤR 3
Implications of the data Fitting procedure
• PAMELA and FERMI systematic uncertainties?
+ − + − p • multiply each expected e , e , p /p backgrounds times AiE i with free Ai and pi = 0 ± 0.05, and marginalize over Ai, pi.
• solar modulation as uncorrelated uncertainty below 20 GeV: ±6% at 10 GeV, ±30% at 1 GeV.
• DM halo: marginalize over isoT/NFW/Moore with flat prior.
• Propagation: marginalize over MIN/MED/MAX with flat prior. (MED is favored?).
• Statistical techniques: as reviewed in appendix B of hep-ph/0606054. Fittingt PAMELA positron data b
20 h e q Μ Z L 15 L ΜR Τ WT L ZT ΤR 2
Χ 10 q b WL t
5 ΜR WT ΜL WL e ΤL,R ZT
0 ZL 100 300 1000 3000 10000 30000 h DM mass in GeV
If M > TeV everything fits. At smaller M only annihilations into leptons or W . The σv needed for PAMELA
e 106 10-20 ΜL 105 ΜR -21 10 ΤL e 4 sec B 10 ΤR
-22 3 10 q
3 cm factor 10
in b -23 10 v
Σ t 2 e
Boost 10 B W 10-24 T W 10 L 10-25 ZT 1 ZL 100 300 1000 3000 10000 30000 h DM mass in GeV
σv larger than what suggested by cosmology by a factor Be The cosmological σv
2 Thermal DM reproduces the cosmological DM abundance ΩDMh ≈ 0.11 for σv ≈ 3 × 10−26 cm3/sec around freeze-out, i.e. v ∼ 0.2. up to co-annihilations and resonances. Possible extrapolations to v ∼ 10−3:
-23 10 103
1.3 2 3 5 10 30 100 1000 10-24 Sommerfeld s- wave 102
-25 out
10 - s-wave L Α sec V 3 M freeze - H
26 cm 10 10 - M
in Sommerfeld p wave = Ε v Σ 10-27 Α galaxy 1 our -28 -wave cosmological
10 in p at v v ¬ ¬ -29 10 10-1 0.0003 0.001 0.003 0.01 0.03 0.1 0.3 10-1 1 10 102 103 DM velocity v Α v
The Sommerfeld effect is the quantum analogous of this classical effect: the 2 2 2 sun attracts slower bodies, enhancing its cross section: σ = πR (1+vescape/v )
If DM is thermal PAMELA needs s-wave + Sommerfeld and/or a boost factor (DM in sub-halos has small velocity dispersion: Sommerfeld boosts the boost) Non thermal DM
+ − E.g. a wino that with M ≈ 100 GeV annihilates into WT WT with the correct g4(1 − M2 /M2)3/2 = 2 W σv 2 2 2 2 2πM (2 − MW /M ) But it contradicts PAMELAp ¯ data (unless Bp Be or low L or etc...):
DM with M = 150 GeV that annihilates into W+W-
-1 10 10-2 30% HESS08 ò àPAMELA 08 ATIC08 ò PPB-BETS08 ò ò ìà ò à æ EC òìà æ æ ì 10% òì ííííí í í à ò à æ sec ç ç ì ìà æ 2 ç æ ìò ìæà æ à çí ç ô í à à 10-3 ææ ìææ ç òò òçç à ææìàæ òæ ì cm ò à à æ æ ì ò ç àòà à àà ææ ç2 íá àààôà ìô à æà à çòáá áá á ç ç í ô æ fraction á ô p PAMELA 08 áá -2 ç í ô ô æ
GeV 10 3% çá á á ò à p L ìô
+ ô à æ æ æ çáò e á æææ + æ æææææ - ô
Positron -4
e æ á H ô æ 10 ææ ç 3 æ ò E æ æ 1% background? á æ à æ áçá æ background? á -5 0.3% áç 10-3 10 1 10 102 103 104 10 102 103 104 1 10 102 103 104 á ò Positron energy in GeV Energy in GeV p kinetic energy in GeV
á
background? ZL q ZT h
WT
b Fitting PAMELA e+ anti p¯ data
Assuming equal boost & propagation for e+ andp ¯ (otherwise everything goes):
40 e ΤR ΜL
35 ΜR t ΤL ΤL ΤR 30 q 2 Χ ΜL b WL 25 e ΜR t
WT
WL 20 ZT
ZL 15 h 100 300 1000 3000 10000 30000 DM mass in GeV > DM must annihilate into leptons or into W, Z with M∼ 10 TeV
Indeed a W at rest givesp ¯ with Ep > mp. So a W with energy E = M gives Ep > Mmp/MW , above the PAMELA threshold for M > 10 TeV. Fitting PAMELA e+ and FERMI e+ + e−
DM annihilation hh
50
45 4Μ-sh bb
40 4e
2 Μ Μ
Χ 35
30 4Μ pulsar with 4Τ 25 F = E-pe-EM Τ+Τ-
20 300 1000 3000 10000 30000 DM mass in GeV
Compatible if DM has TeV mass and annihilates into some leptons.
FERMI excludes that PAMELA is due to a DM lighter than about 1 TeV. Dark Matter identified?
DM with M = 3. TeV that annihilates into Τ+Τ- with Σv = 1.9 ´ 10-22 cm3s
30% 0.03 ò 10-5 FERMI ò FERMI09 PAMELA 09 HESS08 ò sr ò HESS09ò ò ò ò ì sec sec ò æ ò ò 2 2 ò ì ì -6 ææææææ ò ò ò ì ì òì æææòò à 10 æææææææææææ æ æ 10% æ æ cm brehm
cm à æ
2 æ ì æ æ æ æ à ì fraction æ æ æ æ 0.01 ò GeV IC æ æ æ æ æ æ æ GeV ì L in -7 ò 10 + à E e d + à CMB - Γ
Positron 3% e F H d 3 E à 2 10-8 E dust à background? star 1% 0.003 ò 2 3 4 10 102 103 104 10 10 10 à 10 0.01 0.1 1 10 100 1000 Positron energy in GeV Energy in GeV Photon energy in GeV
(The CDF µ anomaly motivates a hidden-sector that decays into τ +τ −) New Dark Matter models
DM with M = 3. TeV that annihilates into 4Μ with Σv = 8.4 ´ 10-23 cm3s
30% 0.03 ò 10-5 FERMI ò FERMI09 PAMELA 09 HESS08 ò sr ò HESS09ò ò ò ò ì sec sec ò æ ò ò 2 2 ò ì ì -6 ææææææ ò ò ò ì ì òì æææòò à 10 æææææææææææ æ æ 10% æ æ cm
cm à æ
2 æ ì æ æ æ æ à ì fraction æ æ æ æ 0.01 ò GeV IC æ æ æ æ æ æ æ GeV ì in L -7 ò 10 + à E e
d CMB + à - Γ
Positron 3% e F H 3 d dust brehm E à 2 10-8 E
à background? star 1% 0.003 ò 2 3 4 10 102 103 104 10 10 10 à 10 0.01 0.1 1 10 100 1000 Positron energy in GeV Energy in GeV Photon energy in GeV PAMELA vs SUSY & co
• Fit PAMELA with a neutralino at M ∼ 100 GeV that annihilates into e+e−γ 6 thanks to a fine-tuned slepton mass, invoking a huuge boost Be ∼ 10 ;
• Unnatural SUSY at many TeV with σv enhanced by Sommerfeld;
• SUSY + ad hoc stable new particles. E.g. aν ˜R lighter than MW and with a large Yukawa νRLH annihilates into L;
• DM vectors or fermions suggested by wUED (would be Universal Extra Di- mensions) or by LHT (Little Higgs with non-anomalous T -parity) annihilate ∼ 30% into leptons, but ∼ 70% into q, W . DM models for PAMELA and FERMI
DM is charged under a dark gauge group, to get the Sommerfeld enhancement.
For PAMELA. [Cirelli, Kadastik, Raidal, Strumia] proposed that DM as a Dirac fermion with M ≈ 2 TeV and charge q ≈ 2 under Lµ − Lτ (suggested by θ23 ≈ π/4), gauged with αV ≈ 1/50 (giving the correct thermal abundance) and mass MV ≈ MZ, giving the gµ − 2 anomaly + Sommerfeld.
2 At 1 loop Lµ − Lτ mixes with the photon: θ ∼ egV ln(mτ /mµ)/6π ∼ 0.005. 2 2 2 4 −42 2 Direct cross section: σSI = 4πq αV αmN θ /MV ≈ 10 cm
For PAMELA, ATIC (×), DAMA (?), INTEGRAL (×?) and EGRET (×?). < [Arkani-Hamed, Weiner et al.] proposed that the new vector is light MV ∼ mN and couples to SM particles only via a mixing with the photon,
2 −2÷3 θ ∼ egV ln(MPl/M?)/6π ∼ 10 so that: • V automatically decays into light leptons e, µ, π±; • V gives a small 2 2 −9 ∼6 δaµ ∼ αθ (mµ/MV ) /π ∼ 10 ; V gives a 10 too large elastic σSI. If the DM gauge group is non abelian, DM has multiple components with 100 ? keV (∼ αV MV ) mass splittings, one can instead get an inelastic σdir that can explain DAMA (but M = 1 TeV is too heavy?) 3
Bounds from γ, ν indirect detection Photons from DM
DM DM → `+`− is unavoidably accompanied by photons:
• Brehmstralung from `± (if ` = τ also τ → π0 → γγ). Largest Eγ ∼ MDM, probed by HESS.
± ± 0 • Inverse Compton: e γ → e γ scatterings on CMB and star-light: E˙ ∝ uγ. 2 Intermediate Eγ0 ∼ Eγ(Ee/me) ∼ 10 GeV probed by FERMI.
± 2 • Synchrotron: e in the galactic magnetic fit: E˙ ∝ uB = B /2. −6 Small Eγ ∼ 10 eV, probed by radio-observations: Davies, VLT, WMAP.
Problem: γ point to their source, and it is unclear which one is better for DM. Solution: astrophysicists anyhow like to observe astrophysical backgrounds. γ from brehmstralung
2 !2 dΦγ 1 r ρ dNγ Z ds ρ(r) = 2 Jhσvi ,J = dΩ dE 24π MDM dE line−of−sight r ρ NFW Einasto isoT/cored region ∆Ω 14700 7600 14 Galactic Center 1 · 10−5 hJi∆Ω = −4 2400 3000 14 Galactic Ridge 3 · 10 1000 − 140 Sagittarius dSph 2 · 10−5
106 Moore 104 NFW 3 2
cm 10
GeV 1 Einasto, Α = 0.17 Center Ridge pc
in -2
r 10 GC Ρ - GC ® Galactic Galactic FERMI -4 - 10 isoT - - - IR radio Γ Γ Γ & & & & & Earth 10-6 10-6 10-4 10-2 1 102 104 r in pc The HESS observations
a M = 10 TeV into W+W-, Galactic Center b M = 1 TeV into Μ-Μ+, Galactic Ridge
10-11 10-6
æ L æ sr -7 L sec æ æ 10 æ 2 æ æ æ æ æ TeV cm æ æ -8 æ æ æ sec 10 æ 2 TeV æ -12 æ æ 10 cm in æ æ 1 E -9 æ
d 10 æ in Γ
E æ N d d Γ
2 -10 æ N
E 10
æ d æ 10-13 10-11 10-1 1 10 10-1 1 10 Γ energy in TeV Γ energy in TeV
DM signals computed for NFW and σv = 10−23 cm3/sec. We conservatively impose that no point is exceeded at 3σ: so the 1st example above is allowed.
Another bound from the DM-dominated Sagittarius dwarf spheroidal galaxy at 24 kpc from us, that was observed by HESS for 11h finding no γ excess. Radio observations
104 Around the GC magnetic fields equipartition B B contain more energy than 102 light, diffusion and advection 1
± Gauss constant B seem negligible, so all the e in 10-2 B energy goes into synchrotron E 10-4 radiation. The unknown B only 10-6 determines the maximal νsyn: 10-6 10-4 10-2 1 102 104 r in pc 3 2 dWsyn 2e B ν eBE B p 2 ( 1) where = = 1 4 MHz ≈ δ − νsyn 3 . . dν 3me νsyn 4πme G me Davies 1976 oservations at the lower ν = 0.408 GHz give the robust and dom- inant bound as the observed GC radio-spectrum is harder than synchrotron: Z dWsyn σv 2 2 −16 erg ν = dV ρ E(ν) Ne(E(ν)) < 4πr × 2 · 10 dν 2M2 400 cone cm2 s
BIG uncertainty in the DM density ρ at 1pc from the GC: NFW or ...? Inverse Compton and FERMI
± 0 0 A fraction uγ/uB ∼ 1 of the e energy goes into eγ → e γ . Initial γ: Eγ ∼ eV from star-light and Eγ ∼ meV from CMB. 2 Final γ: Eγ0 ∼ Eγ(Ee/me) ∼ 10 GeV. IC dominates of brehms at lower E.
EGRET excess not confirmed by FERMI, that agrees with astro background. FERMI data shown only below 10 GeV, away from GC (10◦ < latitude < 20◦).
1 ! 10"5 % 5 ! 10"6 FERMI09 I 1 approx Full res. sr
sec "6 2 1 ! 10 cm ! 5 ! 10"7 GeV in dE ! Γ
# 1 ! 10"7 d 2 E 5 ! 10"8
1 ! 10"8 0.01 0.1 1 10 100 1000 Photon energy in GeV ν observations
( ) ± ν µ scattering in the rock below the detector produce trough-going µ
r hσvi ρ2 3G2 M2p Z 1 dN Φ F ∆Ω 2 ν µ ≈ 2 · J · · dx x 8π M παµ 0 dx where p ∼ 0.125 is the momentum fraction carried by each quark in the nucleon ± and αµ = 0.24 TeV/kmwe = −dE/d` is the µ energy loss.
The total µ± rate negligibly depends on the DM mass M.
SuperKamiokande got the dominant bounds in cones up to 30◦ around the GC
2 Φµ < 0.02/cm s The photon bounds
Assuming NFW, conservative bounds from HESS γ observations of the Galac- tic Center, Galactic Ridge, Sagittarius Dwarf and from and radio observations of the GC exclude the green (allowed by PAMELA) and red region (+FERMI):
DM DM ® e+e-, NFW profile DM DM ® Μ+Μ-, NFW profile DM DM ® Τ+Τ-, NFW profile
-20 -20 -20 GC-VLT 10 10 GC-VLT 10 GC-VLT dS-Γ dS-Γ
dS-Γ IC IC GR-Γ GCGR-Γ 10-22 GC-Γ 10-22 Ν 10-22 Ν sec sec sec -Γ 3 IC 3 3 GC GR-Γ cm cm cm in in in v v v Σ 10-24 PAMELA and FERMI Σ 10-24 PAMELA and FERMI Σ 10-24 PAMELA and FERMI
GC-radio GC-radio GC-radio 10-26 10-26 10-26 102 103 104 102 103 104 102 103 104 DM mass in GeV DM mass in GeV DM mass in GeV
(Way out: Sommerfeld × boosts can enhance GC γ less than e±?)
FERMI IC measurements can test if DM generates the e± excesses An isotheramal profile is ok
dS-Γ dS-Γ DM DM ® e+e-, Einasto profile DM DM ® Μ+Μ-, Einasto profile DM DM ® Τ+Τ-, Einasto profile dS-Γ 10-20 10-20 10-20
GC-Γ GC-Γ IC IC -Γ 10-22 GR-Γ 10-22 GR 10-22 GC-Γ sec sec Ν sec Ν 3 IC 3 3
cm cm cm GR-Γ in in in v v v Σ 10-24 PAMELA and FERMI Σ 10-24 PAMELA and FERMI Σ 10-24 PAMELA and FERMI GC-radio GC-radio GC-radio
10-26 10-26 10-26 102 103 104 102 103 104 102 103 104 DM mass in GeV DM mass in GeV DM mass in GeV DM DM → VV → `+`−`+`− is better
γ yield reduced from ln M/m to ln m /m . And smoother e± dS-Γ ` V ` DM DM ® 4e, Einasto profile DM DM ® 4Μ, Einasto profile DM DM ® 4Τ, Einasto profile dS-Γ 10-20 10-20 10-20 GC-Γ GR-Γ GC-Γ IC IC -22 GR-Γ -22 -22 10 IC 10 Ν 10 Ν GC-Γ sec sec sec 3 3 3 GR-Γ cm cm cm in in in v v v Σ 10-24 PAMELA and FERMI Σ 10-24 PAMELA and FERMI Σ 10-24 PAMELA and FERMI GC-radio GC-radio GC-radio
10-26 10-26 10-26 102 103 104 102 103 104 102 103 104 DM mass in GeV DM mass in GeV DM mass in GeV DM DM → 4e, 4µ, 4τ
Best fits for Einasto MED. Charge is the coupling to electric charge:
Positron Fraction e++e- Flux 1 ´ 10-5 0.300 0.0200 Charge 5 ´ 10-6 FERMI09 0.200 e± 0.0150 ± ± 0.150 Μ Τ
± sr D Τ 1
- -6 sec ´ 0.100 ± Charge 2 1 10 sec ± Τ 2 0.0100 cm Μ - ± 5 ´ 10-7 0.070 e cm 2 GeV Fraction
0.050 in GeV
@ 0.0070
dE ± E e Γ
d Charge F Positron -7 ± d 1 ´ 10 2 0.030 Μ dN 3 PAMELA08 E E 0.0050 5 ´ 10-8 0.020 FERMI HESS08 0.015 HESS09 ´ -8 0.010 0.0030 1 10 10 50 100 500 1000 50 100 500 1000 5000 0.01 0.1 1 10 100 1000 Energy @GeVD Energy @GeVD Photon energy in GeV
Galactic Ridge ÈbÈ<0.3, ÈlÈ<0.8 Galactic Center Up-going Muons from ΝΜ 4 - 10 7 SuperK
10-4 Τ±
-8 D 10 ± 1 ± D Τ - 3 Τ 1 sr - 1 D - 1 sec - 2 s sec - 2 2
-9 -
cm 10 -5 cm @
cm 10 ± ± Μ 2 GeV e @ ± Flux GeV @ E e ± ´ d -10 E 10 Μ 14 Γ d N Γ 10 d N 2 d
E -6 ± 2 10 Μ
E 1 10-11 HESS2006 3Σ HESS2003 3Σ Charge HESS 3Σ Charge Charge -12 10 -7 0 10 0 5 10 15 20 25 30 200 500 1000 2000 5000 200 500 1000 2000 5000 1 ´ 104 Cone Half Angle @degD Energy @GeVD Energy @GeVD 4
DM decays DM decays are compatible with NFW
If instead DM decays with life-time τ, replace ρ2σv/2M2 → ρ1/Mτ:
DM ® 4Μ, NFW profile DM ® Μ+Μ-, NFW profile DM ® Τ+Τ-, NFW profile
1027 1027 1027 PAMELA and FERMI PAMELA and FERMI PAMELA and FERMI
1026 1026 1026 sec sec sec IC GR-Γ in in in Τ IC Τ IC Τ Ν Ν 25 Ν 25 GR-Γ 25
time 10 GC-Γ
time 10 time 10 - - - dS-Γ life life life GC GC-Γ 24 - GR-Γ 24 24
DM GC 10 radio DM 10 DM 10 -radio dS-Γ GC -radio GCdS--ΓΓ 1023 1023 1023 102 103 104 102 103 104 102 103 104 DM mass in GeV DM mass in GeV DM mass in GeV
With DM decay PAMELA/FERMI are allowed for all DM density profiles DM decay not constrained by BBN, CMB e± excesses suggest SU(2) technicolor!?
DM decays suggests M ∼ few TeV, which naturally implies the observed 3 2 ρ M M ! / 5 ∼ DM ∼ e−M/Tdec ρb mp Tdec if the DM density is due to a baryon-like asymmetry kept in thermal equilibrium by weak sphalerons down to Tdec ∼ 200 GeV.
Possible if DM is a chiral fermion or is made of chiral fermions. The DM mass is M ∼ λv ∼ 2 TeV for λ ∼ 4π: strong dynamics a-la technicolor. 4 5 26 GUT-suppressed dimension 6 4-fermion operators give τ ∼ MGUT/M ∼ 10 s. If the technicolor group is SU(2) with techni-q Q = (2, 0) under SU(2)L⊗U(1)Y
• DM is a QQ bound state, scalar and SU(2)-singlet as suggested by data.
+ − • A 4-fermion QQLL¯ operator allows a slowDM → ` ` : no Π ' WL involved.
• Usual problems of technicolor: minimal correction to the S parameter... Conclusions
The PAMELA/FERMI/HESS excesses might be due to pulsars or to DM:
• 3 TeV DM that annihilates in τ +τ − if the DM density ρ(r) is quasi-constant.
• 3 TeV DM that annihilates in 4µ, better if ρeff is quasi-constant.
• DM that decays mostly into µ or τ, whatever ρ(r) is.
• sub-TeV DM and a lot of the DM possibilities cannot fit the e± excesses.
This can soon be tested by new experimental results:
• The e+ fraction must continue to grow at higher energies? PAMELA up to 270GeV, maybe on 15 May 09. Later AMS.
• Is an excess present in p¯ at higher energies? One more data-point from PAMELA09? Later AMS up to 1 TeV?
• IC (and maybe FSR) must give a γ excess: FERMI on 12 August 09.