Longitudinal Rescaling and High-Energy Effective Actions

TL;DR

This paper investigates the classical and quantum behavior of QCD under longitudinal rescaling, deriving the effective high-energy action and analyzing quantum corrections using a Wilsonian renormalization approach.

Contribution

It provides the first calculation of quantum corrections to the high-energy limit of QCD with longitudinal rescaling, including anomalous powers of the scale parameter.

Findings

Quantum corrections introduce anomalous powers of the rescaling parameter.

Perturbation theory is valid only when the logarithm of the scale factor is small.

Breakdown of perturbation theory occurs at very small scales due to chromomagnetic fluctuations.

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.