The LPM effect in sequential bremsstrahlung: analytic results for sub-leading (single) logarithms

TL;DR

This paper derives analytic formulas for sub-leading single logarithmic corrections to the in-medium gluon splitting rate, enhancing understanding of radiative corrections in high-energy QCD media.

Contribution

It provides the first analytic expressions for sub-leading single logarithms in the LPM effect for gluon splitting in a QCD medium.

Findings

Analytic formulas for single logarithmic corrections derived.

Clarifications on the applicability of the formulas provided.

Enhances precision in modeling in-medium parton splittings.

Abstract

Consider the in-medium splitting $g \to gg$ of a very high-energy gluon traversing a QCD medium, accounting for the Landau-Pomeranchuk-Migdal (LPM) effect. It has been known for some time that soft radiative corrections to that splitting generate a double-log correction to the splitting rate, whose effects can be absorbed into running of the medium parameter $\hat q$ describing the rate of transverse momentum kicks to high-energy particles due to small-angle scattering from the medium. Less has been known about sub-leading, single logarithms in this context. In this paper, we find analytic formulas for those single logs (with various caveats and clarifications).