Unitarity Bound on Dark Matter in Low-temperature Reheating Scenarios

Abstract

Model-independent theoretical upper bound on the thermal dark matter (DM) mass can be derived from the maximum inelastic DM cross-section featuring the whole observed DM abundance. We deploy partial-wave unitarity of the scattering matrix to derive the maximal thermally-averaged cross section for general number-changing processes $r\to 2$ (with $r\ge 2$), which may involve standard model particles or occur solely within the dark sector. The usual upper limit on the DM mass for $s$-wave annihilation is around 130 TeV (1 GeV) for $r=2$ (3), only applies in the case of a freeze-out occurring in the standard cosmological scenario. We consider the effects of two nonstandard cosmological evolutions, characterized by low-temperature reheating: $i)$ a kination-like scenario and $ii)$ an early matter-dominated scenario. In the first case, early freeze-out strengthens the unitarity bound to a few TeVs for WIMPs; while in the second case, the WIMP DM can be as heavy as $\sim 10^{10}$ GeV due to a large entropy dilution.