Multiple Soft Scatterings in Scalar Dark Matter Freeze-In

TL;DR

This paper improves the calculation of scalar dark matter production during freeze-in by including the Landau-Pomeranchuk-Migdal effect, providing more accurate relic density estimates and comparing different computational approaches.

Contribution

It introduces a novel equation for the LPM rate of scalar particles and combines it with existing 1PI results, advancing the precision of dark matter relic density calculations.

Findings

LPM effect contributes 1% to 27% to relic density depending on parameters.

The new method shows deviations of -30% to +20% compared to semi-classical approaches.

The impact of LPM increases with larger gauge couplings and smaller mass splittings.

Abstract

We present an improved calculation of the freeze-in production rate for scalar dark matter (DM) from a gauge-charged parent particle via a renormalizable interaction. Building on the previously developed 1PI-resummed framework to accurately capture the relevant regime $T \sim M$, we expand the analysis to include the Landau-Pomeranchuk-Migdal (LPM) effect, which contributes at leading order $g^2 T$ to the interaction rate in the ultra-relativistic limit. To this end, we derive an equation for the LPM rate of a scalar particle for the first time and combine it with the previous 1PI results, providing a new state-of-the art calculation. In contrast to the 1PI results, the LPM treatment neglects vacuum mass scales such that a phenomenological switch-off function between the ultra-relativistic and non-relativistic regime is required. We propose a new function motivated by a thermal loop contribution and compare it to other approaches in the literature, quantifying the resulting uncertainty of this method. Depending on the gauge coupling and mass splitting between DM and mediator particles, the LPM effect contributes between 1% and 27% to the relic density, with the impact increasing for larger gauge couplings and smaller mass splittings. Additionally, we compare our results to commonly used semi-classical Boltzmann approaches. For instance, when these include decays and scatterings regulated with thermal masses, we find deviations ranging from -30% to +20% depending on the mass splitting. Finally, we compare to results based on hard-thermal-loop (HTL) approximations.