NLO corrections to the BFKL equation in QCD and in supersymmetric gauge theories

TL;DR

The paper computes next-to-leading order corrections to the BFKL kernel in QCD and in extended supersymmetric gauge theories, expressing the t-channel eigenvalues as functions of the anomalous dimension $\gamma$ and conformal spin $n$. It develops a detailed calculation framework using angular integrals and Gegenbauer expansions to obtain the NLO eigenvalues $\chi(n,\gamma)$ and $\delta(n,\gamma)$, and analyzes the resulting cross-section asymptotics, including the role of the running coupling. A striking result is that in $N=4$ SUSY the non-analytic in $n$ terms cancel, signaling a simplification and possible integrability of the reggeon dynamics and a deeper connection between BFKL and DGLAP in this theory. The work also provides explicit expressions for SUSY contributions from gluinos and scalars, the SUSY Regge trajectory, and the corresponding anomalous-dimension expansions, with implications for small-$x$ phenomenology and the structure of high-energy scattering in conformal theories.

Abstract

We study next-to-leading corrections to the integral kernel of the BFKL equation for high energy cross-sections in QCD and in supersymmetric gauge theories. The eigenvalue of the BFKL kernel is calculated in an analytic form as a function of the anomalous dimension γof the local gauge-invariant operators and their conformal spin n. For the case of an extended N=4 SUSY the kernel is significantly simplified. In particular, the terms non-analytic in n are canceled. We discuss the relation between the DGLAP and BFKL equations in the N=4 model.