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 IPMU, kaizen-ed to December 10, 2009 From arXiv:0809.2409, 0811.3744, 0811.4153, 0905.0480, 0908.1578, 0912.0742 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: ≈ − " α#(β γ)/α r γ 1 + (r =rs) − ρ(r) = ρ α r 1 + (r=rs) r = 8:5 kpc is our distance from the Galactic Center, ρ ρ(r ) 0:38 GeV=cm3, ≡ ≈ 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, or spirals, is communist: ρ(r) low constant, as in isoT. ≈ Moore 3 1000 cm NFW Einasto, a = 0.17 Earth GeV 10 in Burkert r ® isoT 0.1 density DM 0.001 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 − · r − @E 2 1 ρ dN + Injection: Q = σv e from DM annihilations. • 2 M h i dE δ Diffusion coefficient: K(E) = K0(E= GeV) RLarmor = E=eB. • 2 ∼ 2 Energy loss from IC + syn: E_ = E (4σ =3m )(uγ + u ). • · T e B 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 Small diffusion in a small volume, or large diffusion in a large volume? Main 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, ATICs, HESS, BETS + These experiments cannot discriminate e =e−, but probe higher energy. 0.03 ò ò ò ò ò ææ ò æ ò æ æ ò ò ì æ æ æ æ ò æ ò æ æ ò ò ì ì æ ææ æ ææ ò ò òì æ æ æææ ò ì ì à sec æ ò æ æ 2 æ æ æ æ æ æ æ æ æ æ æ æ 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. Hardening also in ATICs. Systematic errors, not yet defined, are here incoherently added bin-to-bin to the smaller statistical error, allowing for a power-law fit. ... 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 = I! =2, E_pulsar = B R ! =6c = magnetic dipole radiation. • − surface E=M p The guess isΦ Φ + e− =E where p 2 and M are constants. • e− ≈ e / · ≈ Known nearby pulsars (B0656+14, Geminga, ?) would need an unplausibly (?) large fraction of energy that goes into e : 0:3. ± ∼ Test: angular anisotropies (but can be faked by local B(~x), pulsar motion). 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: 8 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 f g 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 ; d;¯ γ depend on the polarization of primaries: WL or T and µL or R. The γ spectrum is generated by various higher-order effects: γ = (Final State Radiation) + (one-loop) + (3-body) We include FSR and ignore the other comparable but model dependent effects 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)L=0 state. If DM is a fundamental weakly-interacting particle, its spin J 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 Scalar D can only couple as • 2.0 ¯ DfLfR + h.c. = DΨf Ψf m+ 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. Huge m+ with positive helicity N weak corrections if . M MW L x d Vector can couple as 1.0 Dµ N d • H ¯ ¯ Dµ[fLγµfL] or Dµ[fRγµfR] i.e. fermions with Left or Right helicity. 0.5 + + + Decays like µ ν¯µe νe give e with ! dN=dx = 2(1 x)2(1 + 2x) jL − 0.0 0.0 0.2 0.4 0.6 0.8 1.0 dN=dx = 4(1 x3)=3 jR − Positron energy fraction x 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 cos = 3(1 + cos ) 8 x 0.8 dN=d θ θ = 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 dN=d cos θ = 3(1 cos2 θ)=4 − Fermion energy fraction x dN=dx = 6x(1 x): − Final state spectra for M = 1 TeV Two-body primary channels: e;µ L; µR;τ L; τR;W L;WT ;Z L;ZT ;h; q;b;t . e+ p 10-5 e 10-3 WT m ZT q b 10-4 WtL fraction fraction L W tR T -6 h Z 10 WL T ZL t ZL proton h - -5 Positron 10 b Anti t 10-6 10-7 10 102 103 10 102 103 q Energy in GeV Energy in GeV g d 10 -8 10 t sr h q sec 2 b E 1 m W 1 dlog Z in g -9 T 10 d -1 d dlogN 10 F d ´ T 10-2 10-10 10 102 103 1 10 102 103 Energy in GeV Energy in GeVnucleon Annihilations into leptons give qualitatively different energy spectra.