Potentially Large One-loop Corrections to WIMP Annihilation

Understand

We compute one-loop corrections to the annihilation of non--relativistic particles $\chi$ due to the exchange of a (gauge or Higgs) boson $\phi$ with mass $\mu$ in the initial state.

• In the limit $m_\chi \gg \mu$ this leads to the "Sommerfeld enhancement" of the annihilation cross section.
• However, here we are interested in the case $\mu \lsim m_\chi$, 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 $\mu \neq 0$.