The LPM effect in sequential bremsstrahlung 2: factorization

TL;DR

This paper investigates the Landau-Pomeranchuk-Migdal (LPM) effect in sequential bremsstrahlung, focusing on overlapping formation times and their impact on double gluon emission rates in high-energy QCD media.

Contribution

It provides a detailed analysis of overlapping double splitting processes, offering a method to distinguish them from independent emissions without soft-gluon approximations.

Findings

Derived correction term for overlapping double gluon bremsstrahlung

Explicit calculation of the correction in a simplified QCD medium

Clarified the separation between overlapping and independent splittings

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 analysis 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 analyzes the subtle problem of how to precisely separate overlapping double splitting (e.g.\ overlapping double bremsstrahlung) from the case of consecutive, independent bremsstrahlung (which is the case that would be implemented in a Monte Carlo simulation based solely on single splitting rates). As an example of the method, we consider the rate of real double gluon bremsstrahlung from an initial gluon with various simplifying assumptions (thick media; $\hat q$ approximation; large $N_c$; and neglect for the moment of processes involving 4-gluon vertices) and explicitly compute the correction $\Delta\,d\Gamma/dx\,dy$ due to overlapping formation times.