Extended Geometric Scaling from Generalized Traveling Waves

TL;DR

This paper extends the geometric scaling in QCD by mapping the BK equation with noise and generalized coupling to a stochastic wave equation, deriving new analytic solutions and scaling variables that broaden the applicability of geometric scaling predictions.

Contribution

It introduces a novel mapping of the BK equation to a stochastic wave equation with generalized coupling, leading to new analytic traveling wave solutions and scaling variables.

Findings

Derived new analytic traveling wave solutions.

Extended the validity range of geometric scaling in QCD.

Introduced a new scaling variable for running coupling.

Abstract

We define a mapping of the QCD Balitsky-Kovchegov equation in the diffusive approximation with noise and a generalized coupling allowing a common treatment of the fixed and running QCD couplings. It corresponds to the extension of the stochastic Fisher and Kolmogorov-Petrovsky-Piscounov equation to the radial wave propagation in a medium with negative-gradient absorption responsible for anomalous diffusion,non-integer dimension and damped noise fluctuations. We obtain its analytic traveling wave solutions with a new scaling curve and in particular for running coupling a new scaling variable allowing to extend the range and validity of the geometric-scaling QCD prediction beyond the previously known domain.