Implications of the positron/electron excesses on Dark Matter - PowerPoint PPT Presentation

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, GGI, March 23, 2010

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: � ( β − γ ) /α 1 + ( r ⊙ /r s ) α � γ � � r ⊙ ρ ( r ) = ρ ⊙ 1 + ( r/r s ) α r r ⊙ = 8 . 5 kpc is our distance from the Galactic Center, ρ ⊙ ≡ ρ ( r ⊙ ) ≈ 0 . 38 GeV / cm 3 , DM halo model r s in kpc α β γ 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 DM density Ρ in GeV � cm 3 1000 NFW Einasto, Α � 0.17 Earth � 10 Burkert isoT 0.1 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: � dV ρ 2 increased by a boost factor B = 1 ↔ 100 ∼ a few Annihilation rate ∝ Simulations neglect normal matter, that locally is comparable to DM.

Propagation of e ± in the galaxy Φ e + = v e + f/ 4 π where f = dN/dV dE obeys: − K ( E ) · ∇ 2 f − ∂ ∂E ( ˙ Ef ) = Q . � ρ � 2 � σv � dN e + Injection : Q = 1 • from DM annihilations. 2 M dE Diffusion coefficient: K ( E ) = K 0 ( E/ GeV) δ ∼ R Larmor = E/eB . • E = E 2 · (4 σ T / 3 m 2 ˙ Energy loss from IC + syn: e )( u γ + u B ). • • Boundary : f vanishes on a cylinder with radius R = 20 kpc and height 2 L . K 0 in kpc 2 /Myr Propagation model δ L in kpc V conv in km/s min 0.85 0.0016 1 13.5 med 0.70 0.0112 4 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 ∼ µ G. The info is in their energy spectra. We hope to see DM annihilation products as excesses in the rarer e + and ¯ p . 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 BESS 95 � 97 � � BESS 98 ����� � �� � � � � � � � � � � � ����� � � � � � BESS 99 � � � ���� ������� �� � � 10 � 2 BESS 00 � � � � � � � Wizard � MASS 91 p flux in 1 � m 2 sec sr GeV � �� � � � CAPRICE 94 � � CAPRICE 98 �� 10 � 3 � � AMS � 01 98 PAMELA 08 � � 10 � 4 � 10 � 5 10 � 6 10 � 1 10 0 10 1 10 2 10 3 p kinetic energy T in GeV Future: PAMELA, AMS

e + / ( e + + e − ) : PAMELA 30 � PAMELA 09 � HEAT 94 � 95 � PAMELA is a spectrometer + CAPRICE 94 � AMS � 01 � calorimeter sent to space. It can � MASS 91 � � � � � � e + , e − , p, ¯ � discriminate p, . . . and � � � 10 � � � � measure E up to ∼ 200 GeV. Positron fraction � � � � � � e − are primaries and e + secon- � � � � � � � � � � � � � � � � � � � daries, so e + /e − decreases as the � � � � � � containment time τ ∼ E − δ . 3 � Spectra below 10 GeV distorted by the present solar polarity. Growing excess above 10 GeV 1 � 10 � 1 10 2 10 3 1 10 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 � � � � � � � � � ����� � � � E 3 � e � � e � � GeV 2 � cm 2 sec � ������� � � � � �������� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 0.01 FERMI � � � HESS08 � � HESS09 � ATIC08 � � 0.003 � 10 2 10 3 10 4 10 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 astrophysics? 1) Maybe secondaries are produced in the acceleration region: then e + /e − can grow with E , but also ¯ p/p , B/C, Ti/Fe... 2) A pulsar is a neutron star with a rotating intense magnetic field. The result- ing electric field ionizes and accelerates e − → γ → e + e − , that are presumably further accelerated by the pulsar wind nebula (Fermi mechanism). surface R 2 ω 4 / 6 c 3 = magnetic dipole radiation. • E pulsar = Iω 2 / 2, ˙ E pulsar = − B 2 • The guess is Φ e − ≈ Φ e + ∝ ǫ · e − E/M /E p where p ≈ 2 and M are constants. Known nearby pulsars (B0656+14, Geminga, ?) would need an unplausibly (?) large fraction ǫ of energy that goes into e ± : ǫ ∼ 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: W + W − ,  ZZ, Zh, hh Gauge/higgs sector   e + e − , µ + µ − , τ + τ − DM DM → Leptons b ¯ t ¯  q ¯ quarks, q = { u, d, s, c } b, t, q  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: W L or T and µ L 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 = 1 asymm ⊕ 3 symm , 3 ⊗ 3 = 1 symm ⊕ 3 asymm ⊕ 5 symm So: • D can have spin 0 for any DM spin . It couples to vectors D F 2 µν and to higgs D h 2 , not to light fermions: D ℓ L ℓ R is m ℓ /M suppressed. • D can have spin 1 only if DM is a Dirac fermion or a vector . PAMELA motivates a large σ (DM DM → ℓ + ℓ − ): only possible for D µ [¯ ℓγ µ ℓ ].

DM annihilations into fermions f • Scalar D can only couple as 2.0 D f L f R + h.c. = D ¯ Ψ f Ψ f Μ � with negative helicity with Ψ f = ( f L , ¯ f R ) in Dirac notation. 1.5 It means zero helicity on average, and is typically suppressed by m f /M . Huge Μ � with positive helicity weak corrections if M ≫ M W . � d N � d x �� N 1.0 • Vector D µ can couple as D µ [ ¯ D µ [ ¯ f L γ µ f L ] or f R γ µ f R ] 0.5 i.e. fermions with L eft or R ight helicity. Decays like µ + → ¯ ν µ e + ν e give e + with dN/dx | L = 2(1 − x ) 2 (1 + 2 x ) 0.0 0.0 0.2 0.4 0.6 0.8 1.0 dN/dx | R = 4(1 − x 3 ) / 3 Positron energy fraction x

DM annihilations into W, Z • The effective interactions D F 2 and D F µν ǫ µνρσ F ρσ 1.4 µν give vectors with T ranverse polarization 1.2 (with different unobservable helicity corre- lations), that decay in f ¯ 1.0 f with E = x M as: � d N � d x �� N dN/d cos θ = 3(1 + cos 2 θ ) / 8 0.8 dN/dx = 3(1 − 2 x + 3 x 2 ) / 2 , 0.6 Transverse vector 0.4 • D A 2 gives L ongitudinal vectors (accon- µ 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 − cos 2 θ ) / 4 Fermion energy fraction x dN/dx = 6 x (1 − x ) .

Final state spectra for M = 1 TeV Two-body primary channels: e, µ L , µ R , τ L , τ R , W L , W T , Z L , Z T , h, q, b, t . e � p 10 � 5 e 10 � 3 Anti � proton fraction W T Z T Positron fraction Μ q b Τ L Τ R 10 � 4 W L Z T Z L W T h 10 � 6 W L t Z L h 10 � 5 b t 10 � 6 10 � 7 10 10 2 10 3 10 10 2 10 3 q Energy in GeV Energy in GeV Γ d 10 10 � 8 t T � d � d � d T in 1 � m 2 sec sr q h b dlogN Γ � dlog E 1 W Z 10 � 9 10 � 1 10 � 2 10 � 10 10 10 2 10 3 1 10 10 2 10 3 Energy in GeV Energy in GeV � nucleon Annihilations into leptons give qualitatively different energy spectra.