In-medium gluon radiation spectrum with all-order resummation of multiple scatterings in longitudinally evolving media

TL;DR

This paper extends the calculation of the in-medium gluon radiation spectrum to include longitudinal expansion of the medium, improving the modeling of jet quenching phenomena in evolving quark-gluon plasma.

Contribution

It introduces a numerical implementation for the fully-resummed gluon spectrum in expanding media, validating and improving scaling laws for realistic medium evolution.

Findings

Scaling laws are validated for expanding media with power-law temperature decay.

The new implementation enables more accurate phenomenological studies of jet quenching.

Static medium calculations are significantly improved by incorporating medium expansion effects.

Abstract

Over the past years, there has been a sustained effort to systematically enhance our understanding of medium-induced emissions occurring in the quark-gluon plasma, driven by the ultimate goal of advancing our comprehension of jet quenching phenomena. To ensure meaningful comparisons between these new calculations and experimental data, it becomes crucial to model the interplay between the radiation process and the evolution of the medium parameters, typically described by a hydrodynamical simulation. This step presents particular challenges when dealing with calculations involving the resummation of multiple scatterings, which have been shown to be necessary for achieving an accurate description of the in-medium emission process. In this paper, we extend our numerical calculations of the fully-resummed gluon spectrum to account for longitudinally expanding media. This new implementation allows us to quantitatively assess the accuracy of previously proposed scaling laws that establish a correspondence between an expanding medium and a ``static equivalent''. Additionally, we show that such scaling laws yield significantly improved results when the static reference case is replaced by an expanding medium with the temperature following a simple power-law decay. Such correspondence will enable the application of numerical calculations of medium-induced energy loss in realistic evolving media for a broader range of phenomenological studies.