Anomalous diffusion in QCD matter

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 beta) ln L -3/2(1 + beta) ln ln L up to nonuniversal terms, with an anomalous dimension beta similar to root alpha(s). This property is analogous to geometric scaling of gluon distributions in the saturation regime and as traveling-wave 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(T)(-4+2 beta) akin to Levy random walks.

Automated summary

This study investigates the quantum corrections on the transverse momentum broadening of a fast parton passing through dense QCD matter. It is shown that, at leading logarithmic accuracy, the broadening distribution tends to a universal distribution that only depends on a single scaling variable at late times or for large system sizes. The typical transverse momentum scale increases with time, and the process exhibits super-diffusion. The scaling distribution also shows a heavy tail similar to Levy random walks at large transverse momentum.