A conservative upper bound on the total dark matter (DM) annihilation rate can be obtained by constraining the appearance rate of the annihilation products which are hardest to detect. The production of neutrinos, via the process $chi chi to bar u u $, has thus been used to set a strong general bound on the dark matter annihilation rate. However, Standard Model radiative corrections to this process will inevitably produce photons which may be easier to detect. We present an explicit calculation of the branching ratios for the electroweak bremsstrahlung processes $chi chi to bar u u Z$ and $chi chi to bar u e W$. These modes inevitably lead to electromagnetic showers and further constraints on the DM annihilation cross-section. In addition to annihilation, our calculations are also applicable to the case of dark matter decay.
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