The Effect of the Infrared Phase of the Discrete BFKL Pomeron on Transverse Momentum Diffusion

TL;DR

This paper investigates how infrared boundary conditions affect the BFKL equation with running coupling, revealing significant impacts on gluon Green functions, transverse momentum diffusion, and the infrared behavior of QCD scattering amplitudes.

Contribution

It introduces a method to incorporate infrared boundary conditions into the BFKL equation, transforming the complex cut into a series of Regge poles and analyzing their effects.

Findings

Infrared boundary conditions significantly influence the asymptotic intercepts.

The approach reduces random walks into the infrared region.

The diffusion in transverse momentum becomes asymmetric due to the boundary conditions.

Abstract

Imposing infrared boundary conditions on the BFKL equation with running coupling transforms the complex momentum w-plane cut present in the gluon Green function into an infinite series of positive Regge poles. In addition, a cut on the negative w line remains. We consider a Hermitian kernel at leading order with running coupling and construct the gluon Green function performing the w integration away from the real axis. We find a strong dependence of the asymptotic intercepts and collinear behaviour on the non-perturbative choice of the boundary conditions, in the form of an infrared phase. This is particularly manifest in the asymmetric infrared/ultraviolet structure of the associated diffusion in transverse momentum. We find that random walks into the infrared region are largely reduced in this approach.