The quark part of the non-forward BFKL kernel and the ``bootstrap'' for the gluon Reggeization

TL;DR

This work advances the high-energy QCD description by computing the quark contribution to the generalized non-forward BFKL kernel at momentum transfer $t$ in the next-to-leading logarithmic approximation, including quark corrections to the gluon trajectory and to Reggeon-Reggeon production channels. It provides explicit, dimensionally regulated expressions for the quark-induced real-kernel pieces in both the octet (gluon) and singlet (Pomeron) channels, analyzes their infrared properties, and demonstrates the bootstrap consistency of gluon Reggeization at NLLA within the quark sector. The results offer a rigorous cross-check of the NLLA kernel and are applicable to arbitrary color representations in the $t$-channel, with implications for both Pomeron and Odderon dynamics. The paper also discusses reconciliation with related work and presents detailed appendices to support the technical derivations.

Abstract

We calculate the quark part of the kernel of the generalized non-forward BFKL equation at non-zero momentum transfer $t$ in the next-to-leading logarithmic approximation. Along with the quark contribution to the gluon Regge trajectory, this part includes pieces coming from the quark-antiquark production and from the quark contribution to the radiative corrections in one-gluon production in the Reggeon-Reggeon collisions. The results obtained can be used for an arbitrary representation of the colour group in the $t-$channel. Using the results for the adjoint representation, we demonstrate explicitly the fulfillment of the ``bootstrap'' condition for the gluon Reggeization in the next-to-leading logarithmic approximation in the part concerning the quark contribution.

Figures (1)

• Figure 1: Diagrammatic representation of the elastic scattering amplitude $A + B \rightarrow A' + B'$.