One-loop Reggeon-Reggeon-gluon vertex at arbitrary space-time dimension

TL;DR

This work provides the first complete one-loop calculation of the Reggeon-Reggeon-gluon vertex in arbitrary space-time dimension $D$, derived from gluon production in multi-Regge kinematics. The authors express the result through a compact set of transverse-momentum integrals, some of which are evaluated for general $D$ while others are handled via epsilon-expansions and longitudinal reductions, with full details in the Appendices. They present gauge-invariant decompositions of the RRG vertex into right/left contributions and supply explicit, dimensionally regularized expressions, including forward-limit simplifications and consistency with known results. Furthermore, the one-gluon contribution to the non-forward BFKL kernel in the singlet and octet channels is computed, enabling NLO bootstrap checks of gluon Reggeization and applications to Odderon studies in $D=4+2\e$. These results furnish essential $D$-dependent building blocks for high-energy QCD factorization and Reggeized-gluon dynamics at NLO.

Abstract

In order to check the compatibility of the gluon Reggeization in QCD with the $s$-channel unitarity, the one-loop correction to the Reggeon-Reggeon-gluon vertex must be known at arbitrary space-time dimension $D$. We obtain this correction from the gluon production amplitude in the multi-Regge kinematics and present an explicit expression for it in terms of a few integrals over the transverse momenta of virtual particles. The one-gluon contribution to the non-forward BFKL kernel at arbitrary $D$ is also obtained.