The Generalized Non-forward BFKL Equation and the ``Bootstrap'' Condition for the Gluon Reggeization in the NLLA

TL;DR

The paper tackles high-energy QCD scattering with fixed momentum transfer in the non-forward region, seeking a next-to-leading logarithmic generalization of the BFKL equation. It builds a representation of amplitudes in terms of impact factors and a Reggeized-gluon Green function, where the kernel is determined by the gluon trajectory and Reggeon-particle production vertices. A key feature is the imposition of bootstrap conditions, ensuring the Reggeization picture remains self-consistent at NLLA, leading to relations between the real- and virtual-parts of the kernel and the one-loop corrections to production vertices. The work collects known two-loop trajectory results and one-loop kernels/vertices and outlines explicit bootstrap equations to be checked in future studies.

Abstract

The generalization of the BFKL equation for the case of non-forward scattering is considered. The kernel of the generalized equation in the next-to-leading approximation is expressed in terms of the gluon Regge trajectory and the effective vertices for particle production in Reggeon collisions. The ``bootstrap'' equations for the gluon Reggeization are presented.