Solution of the BFKL Equation at Next-to-leading Order

TL;DR

This paper tackles the forward-scattering BFKL equation in next-to-leading logarithmic accuracy by developing an iterative solution in the omega plane that retains full angular (conformal-spin) dependence. A dimensional-regularization treatment with a phase-space cutoff isolates a finite kernel, yielding a compact forward equation with a running coupling scale. It introduces a finite omega0 and an angular kernel to capture NLLA corrections, and converts the omega-space solution back to energy space via an inverse Mellin transform for numerical use. The framework enables numerically tractable, spin-resolved predictions at NLLA and sets the stage for computing cross-sections and studying final-state multiplicities in high-energy QCD.

Abstract

We solve the Balitsky-Fadin-Kuraev-Lipatov equation in the next-to-leading logarithmic approximation for forward scattering with all conformal spins using an iterative method.