Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2009-11-19
Phys.Rev.D81:105004,2010
Physics
High Energy Physics
High Energy Physics - Phenomenology
25 pages, 8 figures. Added an appendix showing that the approximation works well in a scalar toy model. To be published in PRD
Scientific paper
10.1103/PhysRevD.81.105004
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 $\mu \neq 0$. 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.
Drees Manuel
Kim Marina J.
Nagao Keiko I.
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