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Potentially Large One-loop Corrections to WIMP Annihilation

We compute one-loop corrections to the annihilation of non--relativistic particles $χ$ due to the exchange of a (gauge or Higgs) boson $ϕ$ with mass $μ$ in the initial state. In the limit $m_χ\gg μ$ this leads to the "Sommerfeld enhancement" of the annihilation cross section. However, here we are interested in the case $μ\lsim m_χ$, where the one--loop corrections are well--behaved, but can still be sizable. We find simple and accurate expressions for annihilation from both $S-$ and $P-$wave initial states; they differ from each other if $μ\neq 0$. In order to apply our results to the calculation of the relic density of Weakly Interacting Massive Particles (WIMPs), we describe how to compute the thermal average of the corrected cross sections. We apply this formalism to scalar and Dirac fermion singlet WIMPs, and show that the corrections are always very small in the former case, but can be very large in the latter. Moreover, in the context of the Minimal Supersymmetric Standard Model, these corrections can decrease the relic density of neutralinos by more than 1%, if the lightest neutralino is a strongly mixed state.