Longitudinal Rescaling and High-Energy Effective Actions

Abstract

Under a rescaling of longitudinal coordinates $x^{0,3}$ by a factor $\lambda$ which is taken to zero, the classical QCD action simplifies dramatically. This is the high-energy limit, as $\lambda$ is of order $s^{-1/2}$, where $s$ is the center-of-mass energy squared of a hadronic collision. We find the quantum corrections to the rescaled action at one loop, in particular finding the anomalous powers of $\lambda$ in this action, for $\lambda$ close to unity. The method is an integration over high-momentum components of the gauge field. This is a Wilsonian renormalization procedure, and counterterms are needed to make the sharp-momentum cut-off gauge invariant. Our result for the quantum action is found, assuming that the logarithm of $\lambda$ is small, which is essential for the validity of perturbation theory. If $\lambda$ is sufficiently small (so that its logarithm is large), then the perturbative renormalization group breaks down. This is due to uncontrollable fluctuations of the longitudinal chromomagnetic field.

Version to appear in Physical Review D

References in corpus (34)

• 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
• The Wilson renormalization group for low x physics: towards the high density regime
• Green's Functions in the Color Field of a Large Nucleus
• The BFKL Equation from the Wilson Renormalization Group
• The Renormalization Group Equation for the Color Glass Condensate
• The Intrinsic Glue Distribution at Very Small x
• The Wilson renormalization group for low x physics: Gluon evolution at finite parton density
• Non-Abelian Weizsacker-Williams field and a two-dimensional effective color charge density for a very large nucleus
• Factorization and high-energy effective action
• Unitarization of Gluon Distribution in the Doubly Logarithmic Regime at High Density
• Gauge invariant effective action for high-energy processes in QCD
• Fock Space Distributions, Structure Functions, Higher Twists and Small x
• Factorization for high-energy scattering
• Quantum structure of the non-Abelian Weizsacker-Williams field for a very large nucleus
• Effective field theory for the small-x evolution
• Vector potential versus colour charge density in low-x evolution
• On solutions of the Balitsky-Kovchegov equation with impact parameter
• Diffusion into infra-red and unitarization of the BFKL pomeron
• Effective Hamiltonian for QCD evolution at high energy
• High-enegy effective action from scattering of QCD shock waves
• Symmetry Properties of the Effective Action for High-Energy Scattering in QCD
• Wong's equations and the small x effective action in QCD
• Integrable Models and Confinement in (2+1)-Dimensional Weakly-Coupled Yang-Mills Theory
• Small x Gluons in Nuclei and Hadrons
• String Tensions and Representations in Anisotropic 2+1-Dimensional Weakly-Coupled Yang-Mills Theory
• Lattice QCD-2+1
• Glueball Masses in (2+1)-Dimensional Anisotropic Weakly-Coupled Yang-Mills Theory
• Composite Strings in (2+1)-Dimensional Anisotropic Weakly-Coupled Yang-Mills Theory
• Near-integrability and confinement for high-energy hadron-hadron collisions
• Anisotropy beta functions

Cited by in corpus (5)

• A nonperturbative foundation of the Euclidean-Minkowskian duality of Wilson-loop correlation functions
• Renormalisation of gauge theories on general anisotropic lattices and high-energy scattering in QCD
• Longitudinal Rescaling of Quantum Electrodynamics
• Scaling Transformation for Nonlocal Interactions
• Renormalization of QCD under longitudinal rescaling