Letter
Open Access

Anomalous diffusion in QCD matter

Paul Caucal ^1,* and Yacine Mehtar-Tani ^1,2,†

¹Physics Department, Brookhaven National Laboratory, Upton, New York 11973, USA
²RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973, USA

^*pcaucal@bnl.gov
^†mehtartani@bnl.gov

Phys. Rev. D 106, L051501 – Published 12 September, 2022

DOI: https://doi.org/10.1103/PhysRevD.106.L051501

Abstract

We study the effects of quantum corrections on transverse momentum broadening of a fast parton passing through dense QCD matter. We show that, at leading logarithmic accuracy the broadening distribution tends at late times or equivalently for large system sizes $L$ to a universal distribution that only depends on a single scaling variable $k_{T}^{2} / Q_{s}^{2}$ where the typical transverse momentum scale increases with time as $\ln Q_{s}^{2} ≃ (1 + 2 β) \ln L - \frac{3}{2} (1 + β) \ln \ln L$ up to nonuniversal terms, with an anomalous dimension $β \sim \sqrt{α_{s}}$ . This property is analogous to geometric scaling of gluon distributions in the saturation regime and traveling-wave solutions to reaction-diffusion processes. We note that since $β > 0$ the process is super-diffusive, which is also reflected at large transverse momentum where the scaling distribution exhibits a heavy tail $k_{T}^{- 4 + 2 β}$ akin to Lévy random walks.

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Phys. Rev. D 106, L051501– Published 12 September, 2022

Vol. 106, Iss. 5 — 1 September 2022

Received 12 October 2021
Accepted 18 August 2022

DOI: https://doi.org/10.1103/PhysRevD.106.L051501

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Anomalous diffusion in QCD matter

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