Quantum chromodynamics at high energy and statistical physics

TL;DR

This paper reviews how statistical physics models, especially reaction-diffusion processes and stochastic equations, enhance understanding of high-energy QCD phenomena like color glass condensates and parton saturation.

Contribution

It establishes a novel connection between QCD scattering amplitudes and reaction-diffusion systems governed by stochastic nonlinear equations, enriching theoretical and phenomenological insights.

Findings

QCD scattering amplitudes resemble noisy traveling waves.

Universal properties of reaction-diffusion systems apply to QCD.

Statistical physics methods improve understanding of parton saturation.

Abstract

When hadrons scatter at high energies, strong color fields, whose dynamics is described by quantum chromodynamics (QCD), are generated at the interaction point. If one represents these fields in terms of partons (quarks and gluons), the average number densities of the latter saturate at ultrahigh energies. At that point, nonlinear effects become predominant in the dynamical equations. The hadronic states that one gets in this regime of QCD are generically called ``color glass condensates''. Our understanding of scattering in QCD has benefited from recent progress in statistical and mathematical physics. The evolution of hadronic scattering amplitudes at fixed impact parameter in the regime where nonlinear parton saturation effects become sizable was shown to be similar to the time evolution of a system of classical particles undergoing reaction-diffusion processes. The dynamics of such a system is essentially governed by equations in the universality class of the stochastic Fisher-Kolmogorov-Petrovsky-Piscounov equation, which is a stochastic nonlinear partial differential equation. Realizations of that kind of equations (that is, ``events'' in a particle physics language) have the form of noisy traveling waves. Universal properties of the latter can be taken over to scattering amplitudes in QCD. This review provides an introduction to the basic methods of statistical physics useful in QCD, and summarizes the correspondence between these two fields and its theoretical and phenomenological implications.