Saturation momentum: From fixed to running coupling

Abstract

Of late, it has been possible to establish and exploit connections between the evolution of parton distribution functions in quantum chromodynamics (QCD) and reaction diffusion systems in statistical physics. On that side stands the well studied Fischer-Kolmogorov-Petrovsky-Piscounov (FKPP) equation in its deterministic and stochastic (sFKPP) variants, respectively. On the side of QCD stand the JIMWLK equation, its recent extensions, and the Balitsky-Kovchegov (BK) equation. The key to extracting information on the solutions of the equation of motion in both fields is primarily the fact that both groups of equations describe the propagation into an unstable state. Unfortunately, the translation works mostly for the case of a fixed coupling constant only. Here, it is shown that, because the system is evolving away from an unstable fix point, it is possible to translate information from the fixed to the running coupling case. This is demonstrated for the saturation momentum in the regime of asymptotically high rapidities [1].