Rapidity veto effects in the NLO BFKL equation

TL;DR

This paper analyzes the impact of imposing a rapidity veto on the next-to-leading order BFKL equation. It first addresses the problem of unphysical collinear logarithms in the NLO kernel and reviews Salam's schemes to restore physical behaviour, highlighting schemes 3 and 4 as the most realistic. The authors then implement a rapidity veto and show that, once the collinear singularities are removed, the veto’s effect on the kernel is greatly diminished, preserving the saddle-point dynamics near $\gamma=1/2$ and supporting multi-Regge or quasi-MRK kinematics. The results provide theoretical justification for using (quasi-)multi-Regge kinematics in high-energy QCD analyses, as the veto does not undermine the high-energy asymptotics.

Abstract

We examine the effect of suppressing the emission of gluons which are close by in rapidity in the BFKL framework. We show that, after removing the unphysical collinear logarithms which typically arise in formally higher orders of the perturbative expansion, the effect of the rapidity veto is greatly reduced. This is an important result, since it supports the use of multi-Regge and quasi-multi-Regge kinematics which are implemented in the leading and next-to-leading order BFKL formalism.

Figures (10)

• Figure 1: Behaviour of the collinear improved kernels described in the text
• Figure 2: Dependence of the LO kernel plus veto upon $\nu$, for $\bar{\alpha}_s=0.2$
• Figure 3: Dependence of the NLO kernel plus veto upon $\nu$, for $\bar{\alpha}_s=0.2$
• Figure 4: Dependence of the LO kernel plus veto upon $\bar{\alpha}_s$, for $\nu=0$
• Figure 5: Dependence of the NLO kernel plus veto upon $\bar{\alpha}_s$, for $\nu=0$