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.

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

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• The Color Glass Condensate
• A Large Hadron Electron Collider at CERN: Report on the Physics and Design Concepts for Machine and Detector
• Statistics at the tip of a branching random walk and the delay of traveling waves
• High Gluon Densities in Heavy Ions Collisions
• Semi-inclusive Deep Inelastic Scattering at small x
• Investigating entanglement entropy at small-x in DIS off protons and nuclei
• Phenomenological picture of fluctuations in branching random walks
• A new approach to computing the asymptotics of the position of Fisher-KPP fronts
• KLWMIJ Reggeon Field Theory beyond the large $N_c$ limit
• On parton number fluctuations at various stages of the rapidity evolution
• Analytical asymptotics for hard diffraction
• Investigating the QCD dynamical entropy in high-energy hadronic collisions
• Correlations in impact-parameter space in a hierarchical saturation model for QCD at high energy
• On the genealogy of branching random walks and of directed polymers
• Page Entropy of Proton System in Deep-Inelastic-Scattering at Small-$x$
• Lecture notes on "Quantum chromodynamics and statistical physics"
• Two Langevin equations in the Doi-Peliti formalism
• Fluctuations of the multiplicity of produced particles in onium-nucleus collisions
• Gluon density fluctuations in dilute hadrons
• QCD traveling waves phenomenology revisited
• Nuclear scattering configurations of onia in different frames
• The Status of Parton Saturation and the CGC
• Probabilistic picture for particle number densities in stretched tips of the branching Brownian motion
• Monte Carlo study of the tip region of branching random walks evolved to large times
• Anomalous dimension of transverse momentum broadening in planar $\mathcal{N}=4$ SYM
• Evaluating the ratio of the exclusive vector meson photoproduction to inclusive hadron/jet production cross section in ultraperipheral heavy ion collisions