Anomalous diffusion in QCD matter

We study the effects of quantum corrections on transverse momentum broadening a fast parton passing through dense QCD matter. show that, at leading logarithmic accuracy distribution tends late times or equivalently for large system sizes $L$ to universal that only depends single scaling variable ${k}_{T}^{2}/{Q}_{s}^{2}$ where typical scale increases with time as $\mathrm{ln}\text{ }{Q}_{s}^{2}\ensuremath{\simeq}(1+2\ensuremath{\beta})\mathrm{ln}\text{ }L\ensuremath{-}\frac{3}{2}(1+\ensuremath{\beta})\mathrm{ln}\text{ }\mathrm{ln}\text{ }L$ up nonuniversal terms, an anomalous dimension $\ensuremath{\beta}\ensuremath{\sim}\sqrt{{\ensuremath{\alpha}}_{s}}$. This property is analogous geometric gluon distributions in saturation regime and traveling-wave solutions reaction-diffusion processes. note since $\ensuremath{\beta}>0$ process super-diffusive, which also reflected exhibits heavy tail ${k}_{T}^{\ensuremath{-}4+2\ensuremath{\beta}}$ akin L\'evy random walks.