Universality aspects of quantum corrections to transverse momentum broadening in QCD media

TL;DR

This paper investigates non-linear quantum corrections to transverse momentum broadening in dense QCD media, revealing universal scaling behavior and super-diffusive dynamics through analytic and numerical methods.

Contribution

It introduces a novel analytic framework for understanding quantum corrections to TMB, demonstrating universal scaling and super-diffusive behavior in QCD media.

Findings

Identification of super-diffusive, heavy-tailed distribution in TMB

Analytic solutions showing universal scaling regime

Good agreement between analytic and numerical results

Abstract

We study non-linear quantum corrections to transverse momentum broadening (TMB) of a fast parton propagating in dense QCD matter in the leading logarithmic approximation. These non-local corrections yield an anomalous super-diffusive behavior characterized by a heavy tailed distribution which is associated with L\'{e}vy random walks. Using a formal analogy with the physics of traveling waves, we show that at late times the transverse momentum distribution tends to a universal scaling regime. We derive analytic solutions in terms of an asymptotic expansion around the scaling limit for both fixed and running coupling. We note that our analytic approach yields a good agreement with the exact numerical solutions down to realistic values of medium length. Finally, we discuss the interplay between system size and energy dependence of the diffusion coefficient $\hat q$ and its connection with the gluon distribution function that is manifest at large transverse momentum transfer.