  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.
