Lecture notes on "Quantum chromodynamics and statistical physics"

Abstract

The concepts and methods used for the study of disordered systems have proven useful in the analysis of the evolution equations of quantum chromodynamics in the high-energy regime: Indeed, parton branching in the semi-classical approximation relevant at high energies is a peculiar branching-diffusion process, and parton branching supplemented by saturation effects (such as gluon recombination) is a reaction-diffusion process. In these lectures, we first introduce the basic concepts in the context of simple toy models, we study the properties of the latter, and show how the results obtained for the simple models may be taken over to quantum chromodynamics.

58 pages, 32 figures. Lectures given at the Huada school on QCD, Central China Normal University, Wuhan, China, June 2-13, 2014

References in corpus (36)

• Computing Quark and Gluon Distribution Functions for Very Large Nuclei
• Operator expansion for high-energy scattering
• Gluon Distribution Functions for Very Large Nuclei at Small Transverse Momentum
• Small-x F_2 Structure Function of a Nucleus Including Multiple Pomeron Exchanges
• Nonlinear Gluon Evolution in the Color Glass Condensate: I
• Saturation Effects in Deep Inelastic Scattering at low $Q^2$ and its Implications on Diffraction
• Front propagation into unstable states
• Nonlinear Gluon Evolution in the Color Glass Condensate: II
• Unitarization of the BFKL Pomeron on a Nucleus
• Saturation in Diffractive Deep Inelastic Scattering
• Geometric scaling for the total gamma^* p cross section in the low x region
• Shift in the velocity of a front due to a cut-off
• Saturation and BFKL dynamics in the HERA data at small x
• The Energy Dependence of the Saturation Momentum
• Geometric Scaling above the Saturation Scale
• Front propagation into unstable states: Universal algebraic convergence towards uniformly translating pulled fronts
• Geometric scaling as traveling waves
• Solution to the evolution equation for high parton density QCD
• Traveling wave fronts and the transition to saturation
• Universal features of JIMWLK and BK evolution at small x
• Universal behavior of QCD amplitudes at high energy from general tools of statistical physics
• Small-x physics beyond the Kovchegov equation
• A phenomenological theory giving the full statistics of the position of fluctuating pulled fronts
• Diffusion into infra-red and unitarization of the BFKL pomeron
• Numerical analysis of the Balitsky-Kovchegov equation with running coupling: dependence of the saturation scale on nuclear size and rapidity
• Noisy traveling waves: effect of selection on genealogies
• Geometric scaling in diffractive deep inelastic scattering
• The high energy asymptotics of scattering processes in QCD
• Quantum chromodynamics at high energy and statistical physics
• Phenomenological picture of fluctuations in branching random walks
• Dipole model analysis of high precision HERA data
• On parton number fluctuations at various stages of the rapidity evolution
• Non linear evolution: revisiting the solution in the saturation region
• On Certain Two Dimensional Integrals that Appear In Conformal Field Theory
• On the anomalous dimensions of the multiple pomeron exchanges
• Hamiltonian solutions of the 3-body problem in (2+1)-gravity

Cited by in corpus (10)

• High Gluon Densities in Heavy Ions Collisions
• An Analytical Solution of the Balitsky-Kovchegov Equation with the Homogeneous Balance Method
• Rapidity gap distribution in diffractive deep-inelastic scattering and parton genealogy
• Fluctuations of the multiplicity of produced particles in onium-nucleus collisions
• Gluon density fluctuations in dilute hadrons
• Particle-number distribution in large fluctuations at the tip of branching random walks
• Scattering from an external field in quantum chromodynamics at high energies: from foundations to interdisciplinary connections
• The BMS Equation and c\bar{c} Production; A Comparison of the BMS and BK Equations
• Diffractive patterns in deep-inelastic scattering and parton genealogy
• Low-$x$ Physics in $pA$ Collisions and at the EIC