Non-forward NLO BFKL Kernel

TL;DR

This work completes the non-forward NLO BFKL kernel by calculating the previously missing two-gluon production contribution. It develops a comprehensive framework separating virtual and real parts, and derives the symmetric and octet-related pieces of the two-gluon contribution, including detailed evaluations of the J1, J2, and J3 integrals and the handling of divergences. The resulting expressions enable the full kernel for all t-channel color representations, with explicit singlet (Pomeron) and octet channels, and provide a path to coupling renormalization. The findings enhance predictive power for high-energy QCD processes in non-forward kinematics, including the Pomeron kernel recently discussed.

Abstract

Details of the calculation of the non-forward BFKL kernel at next-to-leading order (NLO) are offered. Specifically we show the calculation of the two-gluon production contribution. This contribution was the last missing part of the kernel. Together with the NLO gluon Regge trajectory, the NLO contribution of one-gluon production and the contribution of quark-antiquark production which were found before it defines the kernel completely for any colour state in the $t$-channel, in particular the Pomeron kernel presented recently.