Quantum chromodynamics at high energy and statistical physics

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.Comment: 92 pages, review paper. v2: a few mistakes corrected at various places, some parts clarified. To be published in Phys. Re

On parton number fluctuations at various stages of the rapidity evolution

“…Detailed theoretical studies have been carried out in the dipoledipole case at ultra-asymptotic energies, and predictions for the rapidity dependence of the saturation scale and for the scaling of the scattering amplitudes have been argued, based on an analogy between what QCD evolution is expected to look like in the saturation regime and reaction-diffusion processes [13,14]. One peculiar feature of the evolution is that when the rapidity is large enough, no memory is kept of the initial condition and of the early stages.…”

Statistical physics in QCD evolution towards high energies

“…Since our presentation here is rather concise, we refer the reader to those papers for details and to the review paper of Ref. [Mun09].…”

KLWMIJ Reggeon field theory beyond the large N c limit

“…1 Our aim in the present paper is to understand which type of Reggeon interactions are contained in the KLWMIJ Hamiltonian beyond leading order. This is important in order to understand whether the theory can be eventually cast into a form of reaction-diffusion process [23,24]. Another reason for the study is to further clarify the evolution of higher order operators which are relevant for correlation-type observables, such as the ridge [25][26][27].…”