Anomalous diffusion in QCD matter

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 $k_{\perp }^2/Q_s^2$ where the typical transverse momentum scale increases with time as $\ln Q_s^2\simeq (1+2\beta )\ln L-\frac{3}{2}(1+\beta )\ln \ln L$ up to non-universal terms, with an anomalous dimension $\beta \sim \sqrt{{\alpha }_s}$. This property is analogous to geometric scaling of gluon distributions in the saturation regime and traveling waves solutions to reaction-diffusion processes. We note that since $\beta >0$ the process is super-diffusive, which is also reflected at large transverse momentum where the scaling distribution exhibits a heavy tail $k_{\perp }^{4-2\beta }$ akin to Lévy random walks.

Comments: 10 pages, 3 figures, 3 supplemental materials