Bremsstrahlung in dark matter annihilation

We show that the energy spectra from dark matter (DM) annihilation into $f^{+}{f}^{-}\gamma$ (where $f$ is a light fermion) via chirality preserving interactions are identical in 3 scenarios: (a) DM is a Majorana fermion and the particle exchanged is a scalar, (b) DM is a Majorana fermion and the particle exchanged is a vector and © DM is a scalar and the particle exchanged is a fermion. For cases (a) and ©, we also calculate the differential cross section to ${\mathrm{\ell }}^{+}{f}^{-}V$, where $V=W,Z,\gamma$, and $\mathrm{\ell }$ is a light fermion that may or not be the same as $f$. The form of the cross section depends on whether the DM is a Majorana fermion or a scalar but in both cases its form is independent of $V$.