Solving the BFKL Equation in the Next-to-Leading Approximation

TL;DR

The paper tackles solving the BFKL equation in the next-to-leading logarithmic approximation for forward scattering while preserving all conformal spins. It develops an energy-space iterative solution using dimensional regularization with a real-emission cutoff to render the kernel finite. The authors derive a compact forward solution with an explicit ω0 structure and demonstrate weak dependence on the infrared cutoff, enabling numerical implementation that retains the full angular information. This work enables direct NLLA phenomenology with transverse-momentum-space impact factors and lays the groundwork for non-forward extensions and supersymmetric variants.

Abstract

The Balitsky-Fadin-Kuraev-Lipatov equation in the next-to-leading logarithmic approximation is solved using an iterative method. We derive the solution for forward scattering with all conformal spins. A discussion of the infrared finiteness of the results is included.