Scattering versus Forbidden Decay in Dark Matter Freeze-in

TL;DR

This paper demonstrates that in a thermal plasma, forbidden decay processes can significantly contribute to dark matter production, and their relation to scattering processes depends on the coupling strength, challenging common assumptions.

Contribution

It reveals the close relation between forbidden decay and same-order scattering in plasma, showing forbidden decay can be a substantial dark matter source under certain conditions.

Findings

Forbidden decay contributes 5-24% to relic density with weak coupling.

Scattering can dominate over forbidden decay when coupling is very small.

The effect applies to other plasma-induced processes like leptogenesis.

Abstract

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 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 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.