Travelling waves and impact-parameter correlations

Abstract

It is usually assumed that the high-energy evolution of partons in QCD remains local in coordinate space. In particular, fixed impact-parameter scattering is thought to be in the universality class of one-dimensional reaction-diffusion processes as if the evolutions at different points in the transverse plane became uncorrelated through rapidity evolution. We check this assumption by numerically comparing a toy model with QCD-like impact-parameter dependence to its exact counterpart with uniform evolution in impact-parameter space. We find quantitative differences, but which seem to amount to a mere rescaling of the strong coupling constant. Since the rescaling factor does not show any strong alpha_s-dependence, we conclude that locality is well verified, up to subleading terms at small alpha_s.

13 pages, 11 figures; corrected typos

References in corpus (38)

• 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
• Evolution at small x_bj: The Color Glass Condensate
• The Energy Dependence of the Saturation Momentum
• Geometric scaling as traveling waves
• Traveling wave fronts and the transition to saturation
• Effects of Fluctuations on Propagating Fronts
• 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
• A Langevin equation for high energy evolution with pomeron loops
• 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
• Universality and tree structure of high energy QCD
• Extension of the JIMWLK Equation in the Low Gluon Density Region
• Effective Hamiltonian for QCD evolution at high energy
• Non-linear QCD evolution with improved triple-pomeron vertices
• From target to projectile and back again: selfduality of high energy evolution
• A collinear model for small-x physics
• Energy Conservation and Saturation in Small-x Evolution
• The high energy asymptotics of scattering processes in QCD
• Microscopic models of traveling wave equations
• Small-x Dipole Evolution Beyond the Large-N_c Limit
• Fluctuations effects in high-energy evolution of QCD
• On the Probabilistic Interpretation of the Evolution Equations with Pomeron Loops in QCD
• OEDIPUS: Onium Evolution, Dipole Interaction and Perturbative Unitarisation Simulation
• One-dimensional model for QCD at high energy
• The BFKL Pomeron in 2+1 Dimensional QCD

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• Running coupling and pomeron loop effects on inclusive and diffractive DIS cross sections
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