Wong's equations and the small x effective action in QCD

TL;DR

The paper addresses small-x QCD by contrasting a standard gauge-invariant small-x action with an alternative formulation based on Wong's equations, using the logarithm of the Wilson line ($\ln W$) to couple color charges. It shows that the $\ln W$ action, motivated by the worldline approach, reproduces the BFKL evolution and yields a Hermitian, traceless Lie-algebra current, matching the conventional action up to cubic order. The authors demonstrate that differences between the two formalisms vanish at leading nonlinear order, while the $\ln W$ form avoids a potentially troublesome $d_{abcd}$ term and may streamline next-to-leading-order small-x computations. Overall, the $\ln W$ action provides a symmetry-favorable framework for exploring high-density, small-$x$ QCD dynamics and beyond-LO corrections.

Abstract

We propose a new form for the small x effective action in QCD. This form of the effective action is motivated by Wong's equations for classical, colored particles in non-Abelian background fields. We show that the BFKL equation, which sums leading logarithms in x, is efficiently reproduced with this form of the action. We argue that this form of the action may be particularly useful in computing next-to- leading-order results in QCD at small x.