Gamma rays from muons from WIMPs: Implementation of radiative muon decays for dark matter analyses

Dark matter searches in gamma ray final states often make use of the fact that photons can be produced from final state muons. Modern Monte Carlo generators and DM codes include the effects of final state radiation from muons produced in the dark matter annihilation process itself, but neglect the O(1%) radiative correction that arises from the subsequent muon decay. After implementing this correction we demonstrate the effect that it can have on dark matter phenomenology by considering the case of dark matter annihilation to four muons via scalar mediator production. We first show that the AMS-02 positron excess can no longer easily be made consistent with this final state once the Fermi-LAT dwarf limits are calculated with the inclusion of radiative muon decays, and we next show that the Fermi-LAT galactic centre gamma excess can be improved with this final state after inclusion of the same effect. We provide code and tables for the implementation of this effect in the popular dark matter code micrOMEGAs, providing a solution for any model producing final state muons.