Small-$x$ QCD evolution of $2 n$ Wilson line correlator: the weak field limit

TL;DR

This paper derives the energy evolution equations for multiple Wilson line correlators in small-$x$ QCD, demonstrating their reduction to the BJKP equation in the weak field limit, and provides a computational tool for analysis.

Contribution

It explicitly formulates the $x$-evolution of $2 n$ Wilson line correlators using the JIMWLK equation and connects it to the BJKP equation in the linear regime, including a downloadable Mathematica program.

Findings

Derived explicit expressions for $2 n$ Wilson line evolution.

Showed reduction to BJKP equation in weak field limit.

Provided a Mathematica tool for calculations.

Abstract

We write down explicit expressions for the $x$-evolution (equivalent to energy or rapidity evolution) of $2 n$ ($n = 1, 2, ...$) Wilson lines using the JIMWLK equation and the Color Glass Condensate formalism. We investigate the equation in the weak gluon field limit (linear regime) by expanding the Wilson lines in powers of the gluon field and show that it reduces to the BJKP equation describing the evolution of a state of $2 n$ Reggeized gluons with energy. We also make available for download a {\it Mathematica} program which provides this expression for any value of $n$.