Universal behavior of QCD amplitudes at high energy from general tools of statistical physics

Abstract

We show that high energy scattering is a statistical process essentially similar to reaction-diffusion in a system made of a finite number of particles. The Balitsky-JIMWLK equations correspond to the time evolution law for the particle density. The squared strong coupling constant plays the role of the minimum particle density. Discreteness is related to the finite number of partons one may observe in a given event and has a sizeable effect on physical observables. Using general tools developed recently in statistical physics, we derive the universal terms in the rapidity dependence of the saturation scale and the scaling form of the amplitude, which come as the leading terms in a large rapidity and small coupling expansion.

arXiv comment14 pages, 2 figures; v2: Secs. 2 and 3 substantially rewritten and Sec. 4 expanded in order to make more explicit the connection with statistical physics. Acknowledgment and reference added. Results and conclusions unchanged. To appear in Phys. Lett. B

References in corpus (33)

• Operator expansion for high-energy scattering
• Small-x F_2 Structure Function of a Nucleus Including Multiple Pomeron Exchanges
• Nonlinear Gluon Evolution in the Color Glass Condensate: I
• The Wilson renormalization group for low x physics: towards the high density regime
• Front propagation into unstable states
• The BFKL Equation from the Wilson Renormalization Group
• Unitarization of the BFKL Pomeron on a Nucleus
• The Renormalization Group Equation for the Color Glass Condensate
• Unitarity at small Bjorken x
• 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
• Unitarization of Gluon Distribution in the Doubly Logarithmic Regime at High Density
• The Energy Dependence of the Saturation Momentum
• Geometric Scaling above the Saturation Scale
• Geometric scaling as traveling waves
• Traveling wave fronts and the transition to saturation
• Factorization for high-energy scattering
• The Energy Dependence of the Saturation Momentum from RG Improved BFKL Evolution
• Universal features of JIMWLK and BK evolution at small x
• Effects of Fluctuations on Propagating Fronts
• Effective field theory for the small-x evolution
• Small-x physics beyond the Kovchegov equation
• Diffusion into infra-red and unitarization of the BFKL pomeron
• Studies of Unitarity at Small~$x$ Using the Dipole Formulation
• Large multiplicity fluctuations and saturation effects in onium collisions
• From Color Glass to Color Dipoles in high-energy onium--onium scattering
• Rare fluctuations and the high-energy limit of the S-matrix in QCD
• Non linear gluon evolution in path-integral form
• Multiplicity distribution of colour dipoles at small~$x$
• Microscopic models of traveling wave equations
• Hybrid method for simulating front propagation in reaction-diffusion systems
• Numerical schemes for continuum models of reaction-diffusion systems subject to internal noise
• OEDIPUS: Onium Evolution, Dipole Interaction and Perturbative Unitarisation Simulation

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