Scattering versus forbidden decay in dark matter freeze-in

It is generically believed that the two-body scattering is suppressed by higher-order weak couplings with respect to the two-body decay. We show that this does not always hold when a heavy particle is produced by a forbidden decay in a thermal plasma, where the scattering shares the same order of couplings with the decay. We find that there is a simple and close relation between the forbidden decay and the same-order scattering. To illustrate this point, we consider the freeze-in production of heavy dark matter via a light scalar mediator. We point out that when the Boltzmann (quantum) statistics is used, the forbidden decay can contribute to the dark matter relic density at 5%-24% (10%-39%) with a weak thermal coupling, while the contribution from the scattering channel can be several orders of magnitude larger than from the forbidden decay if the thermal coupling is much smaller. Such a relative effect between the scattering and the forbidden decay could also exist in other plasma-induced processes, such as the purely thermal generation of the right-handed neutrino dark matter, or of the lepton asymmetry in leptogenesis.

Automated summary

We find that in thermal plasma, scattering and decay can have the same order of couplings. This is contrary to the common belief that scattering is suppressed compared to decay. We provide an example of freeze-in production of heavy dark matter to illustrate this point. The relative contributions of scattering and decay depend on the thermal coupling strength.