Invariant color calculus and generalized Balitsky-Kovchegov hierarchy

TL;DR

This paper generalizes the Balitsky-Kovchegov equation to include dipoles with arbitrary color charges, introduces a new color expression transformation method, and explores implications for gluon Reggeization and higher color exchanges.

Contribution

It presents a novel generalization of the BK equation for arbitrary color charges and introduces an indexless transformation method for color expressions.

Findings

Derived the generalized BK equation for arbitrary color charges.

Proved gluon Reggeization in any color channel.

Identified a color duplication of Regge poles.

Abstract

We derive generalization of the Balitsky-Kovchegov (BK) equation for a dipole, which consists of a parton and an antiparton of arbitrary charge. At first, we develop one method of indexless transformation of color expressions. The method is based on an evaluation of the Casimir operator on a tensor product. From the JIMWLK equation we derive the evolution equation for a single parton and prove gluon Reggeization in an arbitrary color channel. We show that there is a color duplication of such Regge poles. Higher t-channel color exchange has its own Regge pole, which residue is proportional to the quadratic Casimir. Taking a fundamental representation, we derive the usual BK equation and shed new light on the meaning of linear and nonlinear terms. Finally, we discuss a linearized version of the generalized BK equation.