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 kT2/Qs2 where the typical transverse momentum scale increases with time as ln Qs2≃(1+2β)ln L-32(1+β)ln ln L up to nonuniversal terms, with an anomalous dimension β∼αs. 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 kT-4+2β akin to Lévy random walks.