Resummation of non-global logarithms and the BFKL equation

TL;DR

This paper develops a systematic resummation method for non-global logarithms in gauge theories using a color density matrix, deriving the BFKL and JIMWLK equations at next-to-leading order and discussing higher-order extensions.

Contribution

It introduces a novel approach to resum non-global logarithms via a color density matrix, connecting it to shockwave scattering and deriving key evolution equations at NLO.

Findings

Derived the NLO BFKL and JIMWLK equations using the color density matrix approach.

Demonstrated exponentiation of divergences to all logarithmic orders.

Discussed the potential extension to three-loop accuracy for the evolution equations.

Abstract

We consider a `color density matrix' in gauge theory. We argue that it systematically resums large logarithms originating from wide-angle soft radiation, sometimes referred to as non-global logarithms, to all logarithmic orders. We calculate its anomalous dimension at leading- and next-to-leading order. Combined with a conformal transformation known to relate this problem to shockwave scattering in the Regge limit, this is used to rederive the next-to-leading order Balitsky-Fadin-Kuraev-Lipatov equation (including its nonlinear generalization, the so-called Balitsky-JIMWLK equation), finding perfect agreement with the literature. Exponentiation of divergences to all logarithmic orders is demonstrated. The possibility of obtaining the evolution equation (and BFKL) to three-loop is discussed.