The LPM Effect in sequential bremsstrahlung: $1/N_c^2$ corrections

TL;DR

This paper investigates the accuracy of the large-$N_c$ approximation in modeling overlapping formation times in sequential gluon splittings within a quark-gluon plasma, calculating the first non-trivial correction beyond the leading order.

Contribution

It provides the first calculation of the $1/N_c^2$ correction to large-$N_c$ results for overlapping gluon splittings, revealing complex color dynamics.

Findings

Calculated the $1/N_c^2$ correction to overlap effects in gluon splittings.

Identified non-trivial color dynamics at order $1/N_c^2$.

Enhanced understanding of quantum interference effects in in-medium parton showers.

Abstract

An important question concerning in-medium high-energy parton showers in a quark-gluon plasma or other QCD medium is whether consecutive splittings of the partons in a given shower can be treated as quantum mechanically independent, or whether the formation times for two consecutive splittings instead have significant overlap. Various previous calculations of the effect of overlapping formation times have either (i) restricted attention to a soft bremsstrahlung limit, or else (ii) used the large-$N_c$ limit (where $N_c{=}3$ is the number of quark colors). In this paper, we make a first study of the accuracy of the large-$N_c$ limit used by those calculations of overlap effects that avoid a soft bremsstrahlung approximation. Specifically, we calculate the $1/N_c^2$ correction to previous $N_c{=}\infty$ results for overlap $g \to gg \to ggg$ of two consecutive gluon splittings $g \to gg$. At order $1/N_c^2$, there is interesting and non-trivial color dynamics that must be accounted for during the overlap of the formation times.