Precise relic WIMP abundance and its impact on searches for dark matter annihilation

Abstract

If dark matter (DM) is a weakly interacting massive particle (WIMP) that is a thermal relic of the early Universe, then its total self-annihilation cross section is revealed by its present-day mass density. This result for a generic WIMP is usually stated as $⟨\ensuremath{\sigma}v⟩\ensuremath{\approx}3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}26}\text{ }\text{ }{\mathrm{cm}}^{3}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$, with unspecified uncertainty, and taken to be independent of WIMP mass. Recent searches for annihilation products of DM annihilation have just reached the sensitivity to exclude this canonical cross section for 100% branching ratio to certain final states and small WIMP masses. The ultimate goal is to probe all kinematically allowed final states as a function of mass and, if all states are adequately excluded, set a lower limit to the WIMP mass. Probing the low-mass region is further motivated due to recent hints for a light WIMP in direct and indirect searches. We revisit the thermal relic abundance calculation for a generic WIMP and show that the required cross section can be calculated precisely. It varies significantly with mass at masses below 10 GeV, reaching a maximum of $5.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}26}\text{ }\text{ }{\mathrm{cm}}^{3}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ at $m\ensuremath{\approx}0.3\text{ }\text{ }\mathrm{GeV}$, and is $2.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}26}\text{ }\text{ }{\mathrm{cm}}^{3}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ with feeble mass dependence for masses above 10 GeV. These results, which differ significantly from the canonical value and have not been taken into account in searches for annihilation products from generic WIMPs, have a noticeable impact on the interpretation of present limits from Fermi-LAT and $\mathrm{WMAP}+\mathrm{ACT}$.