Smooth interpolation between thermal Born and LPM rates

TL;DR

This paper introduces a method to smoothly interpolate between LPM-resummed and Born-level rates in plasma interactions, broadening applicability in cosmological and high-energy physics contexts.

Contribution

It proposes a new interpolation procedure that bridges LPM and Born approximations, improving rate calculations across diverse plasma conditions.

Findings

The interpolation method is demonstrated for right-handed neutrino production.

The method is also applied to dilepton production in QCD plasma.

Results show improved accuracy over a wide range of momenta and masses.

Abstract

In a weakly coupled ultrarelativistic plasma, $1 + n \leftrightarrow 2 + n$ scatterings, with $n \ge 0$, need sometimes to be summed to all orders, in order to determine a leading-order interaction rate. To implement this "LPM resummation", kinematic approximations are invoked. However, in cosmological settings, where the temperature changes by many orders of magnitude and both small and large momenta may play a role, such approximations are not always justified. We suggest a procedure to smoothly interpolate between LPM-resummed $1 + n \leftrightarrow 2 + n$ and Born-level $1 \leftrightarrow 2$ results, rendering the outcome applicable to a broader range of masses and momenta. The procedure is illustrated for right-handed neutrino production from a Standard Model plasma, and dilepton production from a QCD plasma.