The LPM effect in sequential bremsstrahlung: incorporation of "instantaneous'' interactions for QCD

TL;DR

This paper advances the understanding of the Landau-Pomeranchuk-Migdal effect in QCD by incorporating instantaneous longitudinal gluon exchanges into the calculation of overlapping formation time effects in gluonic splittings.

Contribution

It extends previous nearly-complete calculations to fully include instantaneous longitudinal gluon exchanges in overlapping formation time effects within QCD.

Findings

Complete rate calculations including longitudinal gluon exchanges.

Improved modeling of gluonic splittings with overlapping formation lengths.

Enhanced theoretical framework for high-energy QCD bremsstrahlung.

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. We continue study of the case when the coherence lengths (formation lengths) of two consecutive splitting processes overlap, avoiding soft-emission approximations. Previous work made a ``nearly-complete'' calculation of the effect of overlapping formation times on gluonic splittings such as $g \to gg \to ggg$ (with simplifying assumptions such as an infinite QCD medium and the large-$N_c$ limit). In this paper, we extend those previous rate calculations from nearly-complete to complete by including processes involving the exchange of longitudinally-polarized gluons. In the context of Lightcone Pertubation Theory, used earlier for the ``nearly-complete'' calculation, such exchanges are instantaneous in lightcone time and have their own diagrammatic representation.