GeV-scale dark matter with $p$-wave Breit-Wigner enhanced annihilation

We consider a light scalar dark matter candidate with mass in the GeV range whose $p$-wave annihilation is enhanced through a Breit-Wigner resonance. The annihilation actually proceeds in the $s$-channel via a dark photon mediator whose mass is nearly equal to the masses of the incoming particles. We compute the temperature at which kinetic decoupling between dark matter and the primordial plasma occurs and show that including the effect of kinetic decoupling can reduce the dark matter relic density by orders of magnitude. For typical scalar masses ranging from 200 MeV to 5 GeV, we determine the range of values allowed for the dark photon couplings to the scalar and to the standard model particles after requiring the relic density to be in agreement with the value extracted from cosmological observations. We then show that $\mu$ and $y$-distortions of the CMB spectrum and X-ray data from XMM-Newton strongly constrain the model and rule out the region where the dark matter annihilation cross-section is strongly enhanced at small dispersion velocities. Constraints from direct detection searches and from accelerator searches for dark photons offer complementary probes of the model.