Can multistate dark matter annihilation explain the high-energy cosmic ray lepton anomalies?

Abstract

Multistate dark matter (DM) models with small mass splittings and couplings to light hidden sector bosons have been proposed as an explanation for the PAMELA/Fermi/H.E.S.S. high-energy lepton excesses. We investigate this proposal over a wide range of DM density profiles, in the framework of concrete models with doublet or triplet dark matter and a hidden SU(2) gauge sector that mixes with standard model hypercharge. The gauge coupling is bounded from below by the DM relic density, and the Sommerfeld enhancement factor is explicitly computable for given values of the DM and gauge boson masses $M$, $\ensuremath{\mu}$ and the (largest) dark matter mass splitting $\ensuremath{\delta}{M}_{12}$. Sommerfeld enhancement is stronger at the galactic center than near the Sun because of the radial dependence of the DM velocity profile, which strengthens the inverse Compton (IC) gamma ray constraints relative to usual assumptions. We find that the PAMELA/Fermi/H.E.S.S. lepton excesses are marginally compatible with the model predictions, and with CMB and Fermi gamma ray constraints, for $M\ensuremath{\cong}800\text{ }\text{ }\mathrm{GeV}$, $\ensuremath{\mu}\ensuremath{\lesssim}200\text{ }\text{ }\mathrm{MeV}$, and a dark matter profile with noncuspy Einasto parameters $\ensuremath{\alpha}\ensuremath{\gtrsim}0.20$, ${r}_{s}\ensuremath{\sim}30\text{ }\text{ }\mathrm{kpc}$. We also find that the annihilating DM must provide only a subdominant ($\ensuremath{\lesssim}0.4$) component of the total DM mass density, since otherwise the boost factor due to Sommerfeld enhancement is too large.