The LPM effect in sequential bremsstrahlung: 4-gluon vertices

TL;DR

This paper advances the understanding of the LPM effect in QCD by calculating double gluon bremsstrahlung rates with overlapping coherence lengths, including complex 4-gluon interactions beyond previous approximations.

Contribution

It completes the calculation of double gluon bremsstrahlung rates by incorporating 4-gluon vertices and overlapping coherence effects without soft-gluon approximations.

Findings

Calculated double gluon bremsstrahlung rates with 4-gluon vertices.

Included overlapping coherence length effects in the LPM regime.

Extended previous models beyond soft-gluon approximations.

Abstract

The splitting processes of bremsstrahlung and pair production in a medium are coherent over large distances in the very high energy limit, which leads to a suppression known as the Landau-Pomeranchuk-Migdal (LPM) effect. In this paper, we continue study of the case when the coherence lengths of two consecutive splitting processes overlap (which is important for understanding corrections to standard treatments of the LPM effect in QCD), avoiding soft-gluon approximations. In particular, this paper completes the calculation of the rate for real double gluon bremsstrahlung from an initial gluon with various simplifying assumptions (thick media; $\hat q$ approximation; and large $N_c$) by now including processes involving 4-gluon vertices.