Strongly vs. weakly coupled in-medium showers: energy stopping in large-$N_f$ QED

TL;DR

This paper compares energy deposition in large-$N_f$ QED showers to gluonic showers, developing a framework to understand overlapping splittings and their impact on medium-induced energy loss.

Contribution

It introduces a framework for analyzing energy deposition in large-$N_f$ QED showers, enabling better comparisons with gluonic shower effects and exploring quark contributions.

Findings

Overlapping splittings have a larger impact in large-$N_f$ QED than in gluonic showers.

Adjusting the medium parameter $$ can absorb some effects of overlapping splittings.

The developed framework facilitates future studies on quark effects in medium-induced showers.

Abstract

Inside a medium, showers originating from a very high-energy particle may develop via medium-induced splitting processes such as hard bremsstrahlung or pair production. During shower development, two consecutive splittings sometimes overlap quantum mechanically, so that they cannot be treated independently. Some of these effects can be absorbed into an effective value of a medium parameter known as $\hat q$. Previous calculations (with certain simplifying assumptions) have found that, after adjusting the value of $\hat q$, the leftover effect of overlapping splittings is quite small for purely gluonic large-$N_c$ showers but is very much larger for large-$N_f$ QED showers, at comparable values of $N\alpha$. Those works did not quite make for apples-to-apples comparisons: the gluon shower work investigated energy deposition from a gluon-initiated shower, whereas the QED work investigated charge-deposition from an electron-initiated shower. As a first step to tighten up the comparison, this paper investigates energy deposition in the QED case. Along the way, we develop a framework that should be useful in the future to explore whether the very small effect of overlapping splitting in purely gluonic showers is an artifact of having ignored quarks.