Dark matter freeze-in from non-equilibrium QFT: towards a consistent treatment of thermal effects

TL;DR

This paper develops a comprehensive quantum field theory approach to calculate dark matter relic abundance, including thermal effects and comparing various approximation schemes, revealing significant deviations from traditional methods.

Contribution

It introduces a full quantum field theoretical calculation of dark matter production with thermal corrections, surpassing previous approximations like HTL and Boltzmann equations.

Findings

Thermal masses in Boltzmann equations cause 10-30% deviation from the quantum result.

HTL approximation is accurate at small gauge couplings, deviating only a few percent.

Tree-level propagators underestimate dark matter abundance by up to 100%.

Abstract

We study thermal corrections to a model of real scalar dark matter (DM) interacting feebly with a SM fermion and a gauge-charged vector-like fermion mediator. We employ the Closed-Time-Path (CTP) formalism for our calculation and go beyond previous works by including the full dependence on the relevant mass scales as opposed to using (non)relativistic approximations. In particular, we calculate the DM production rate by employing 1PI-resummed propagators constructed from the leading order term in the loop expansion of the 2PI effective action, beyond the Hard-Thermal-Loop (HTL) approximation. We compare our findings to commonly used approximation schemes, including solving the Boltzmann equation using momentum-independent thermal masses in decay processes and as regulators for $t$-channel divergences. We also compare with the result when employing HTL propagators and their tree-level limit. We find that the DM relic abundance when using thermal masses in the Boltzmann approach deviates between $-10\%$ and $+30\%$ from our calculation, where the size and sign strongly depend on the mass splitting between the DM candidate and the gauge-charged mediator. The HTL-approximated result is more accurate at small gauge couplings, only deviating by a few percent at large mass splittings, whereas it overestimates the relic density up to $25\%$ for small mass splittings. Calculations using tree-level propagators in the CTP formalism or semiclassical Boltzmann equations without scatterings underestimate the dark matter abundance and can lead to deviations of up to $-100\%$ from the 1PI-resummed result.