Sommerfeld enhancements for thermal relic dark matter

Abstract

The annihilation cross section of thermal relic dark matter determines both its relic density and indirect detection signals. We determine how large indirect signals may be in scenarios with Sommerfeld-enhanced annihilation, subject to the constraint that the dark matter has the correct relic density. This work refines our previous analysis through detailed treatments of resonant Sommerfeld enhancement and the effect of Sommerfeld enhancement on freeze out. Sommerfeld enhancements raise many interesting issues in the freeze out calculation, and we find that the cutoff of resonant enhancement, the equilibration of force carriers, the temperature of kinetic decoupling, and the efficiency of self-interactions for preserving thermal velocity distributions all play a role. These effects may have striking consequences; for example, for resonantly-enhanced Sommerfeld annihilation, dark matter freezes out but may then chemically recouple, implying highly suppressed indirect signals, in contrast to naive expectations. In the minimal scenario with standard astrophysical assumptions, and tuning all parameters to maximize the signal, we find that, for force-carrier mass ${m}_{\ensuremath{\phi}}=250\text{ }\text{ }\mathrm{MeV}$ and dark matter masses ${m}_{X}=0.1$, 0.3, and 1 TeV, the maximal Sommerfeld enhancement factors are ${S}_{\mathrm{eff}}=7$, 30, and 90, respectively. Such boosts are too small to explain both the PAMELA and Fermi excesses. Nonminimal models may require smaller boosts, but the bounds on ${S}_{\mathrm{eff}}$ could also be more stringent, and dedicated freeze out analyses are required. For concreteness, we focus on $4\ensuremath{\mu}$ final states, but we also discuss $4e$ and other modes, deviations from standard astrophysical assumptions and nonminimal particle physics models, and we outline the steps required to determine if such considerations may lead to a self-consistent explanation of the PAMELA or Fermi excesses.