# Dynamical quenching weights in an expanding medium

## TL;DR

This paper extends the theoretical framework for calculating parton energy loss in expanding media, providing a more accurate description of jet quenching in dynamic environments like quark-gluon plasma.

## Contribution

It introduces a rate equation approach for quenching weights in expanding media within the BDMPSZ formalism, incorporating medium expansion effects into the calculations.

## Key findings

- Derived a dynamical scaling law for expanding media
- Validated the scaling law for gluon splitting rates
- Enhanced the understanding of jet quenching in evolving environments

## Abstract

In this work, we extend the resummation of multiple medium-induced emissions to apply to dynamically expanding media. This is done by recasting the quenching weight as the solution of a rate equation with medium-induced partonic splitting functions that are sensitive to the expansion. We perform the calculations in the framework of Baier-Dokshitzer- Mueller-Peigne-Schiff-Zakharov (BDMPSZ) formalism for multiple soft scatterings with a time-dependent transport coefficient. Furthermore, we discuss the validity of a dynamical scaling law that relates the spectrum in an expanding medium to the equivalent static case with re-scaled medium parameters and test the scaling law for the gluon splitting rates.