Order-by-order Analytic Solution to the BFKL Equation

TL;DR

This paper introduces a regularization method for solving the BFKL equation order-by-order in perturbation theory, providing a simple formula for the Fourier transform of the gluon Green function and validating it against previous results.

Contribution

It presents a novel regularization approach enabling order-by-order solutions of the BFKL equation using sums over multiple poles, applicable to complex kernels.

Findings

Agreement with previous results at tested orders

Simple formula for Fourier transform of gluon Green function

Method applicable to more complex kernels

Abstract

We propose a regularization of the BFKL equation which allows for its solution in each order of perturbation theory by means of a sum over multiple poles. This sum can be presented in a rather simple formula for the Fourier transform in the azimuthal angle of the gluon Green function. In order to test our method, we have compared a few orders in the expansion to previous results by Del Duca, Dixon, Duhr and Pennington, finding agreement. Our formalism is general and can be applied to other, more complicated, kernels.