From soft to hard radiation: the role of multiple scatterings in medium-induced gluon emissions

TL;DR

This paper compares analytical approximations and numerical methods to understand medium-induced gluon emissions, revealing three regimes characterized by different scattering dynamics and coherence effects in strongly interacting matter.

Contribution

It provides a detailed analysis of the validity of various approximations by comparing them with a comprehensive all-order resummation numerical approach, identifying distinct physical regimes.

Findings

Three regimes identified: high-energy dominated by single hard scattering.

Intermediate-energy regime where multiple scatterings exhibit coherence effects.

Low-energy regime with single scattering and suppression due to virtual corrections.

Abstract

A proper understanding of the physics of medium-induced gluon emissions is known to be of critical importance to describe the properties of strongly interacting matter under extreme conditions. In this regard, many theoretical efforts have been directed towards obtaining analytical calculations which might help us discerning the underlying physical picture and the dominant dynamics for different regimes. These analytical approaches rely on approximations whose validity is analyzed here by comparing their results with a recently developed numerical evaluation which includes all-order resummation of multiple scatterings. More specifically, by quantitatively comparing the energy spectrum and rates, we observe that three different regimes -- each with its corresponding physical picture -- emerge naturally from the equations: the high-energy regime where the emission process is dominated by a single hard scattering, the intermediate-energy regime where coherence effects among multiple scatterings become fundamental, and the low-energy regime where the dynamics is again dominated by a single scattering but where one must include the suppression factor due to the probability of not having any further scatterings (which is obtained through the resummation of virtual terms).