Calculating the Annihilation Rate of Weakly Interacting Massive Particles

We develop a formalism that allows one to systematically calculate the weakly interacting massive particle (WIMP) annihilation rate into gamma rays whose energy far exceeds the weak scale. A factorization theorem is presented which separates the radiative corrections stemming from initial-state potential interactions from loops involving the final state. This separation allows us to go beyond the fixed order calculation, which is polluted by large infrared logarithms. For the case of Majorana WIMPs transforming in the adjoint representation of SU(2), we present the result for the resummed rate at leading double-log accuracy in terms of two initial-state partial-wave matrix elements and one hard matching coefficient. For a given model, one may calculate the cross section by finding the tree level matching coefficient and determining the value of a local four-fermion operator. The effects of resummation can be as large as 100% for a 20 TeV WIMP. However, for lighter WIMP masses relevant for the thermal relic scenario, leading-log resummation modifies the Sudakov factors only at the 10% level. Furthermore, given comparably sized Sommerfeld factors, the total effect of radiative corrections on the semi-inclusive photon annihilation rate is found to be percent level. The generalization of the formalism to other types of WIMPs is discussed.