On the conformal spin dependence of the perturbative QCD vacuum singularity

TL;DR

This paper investigates the conformal spin dependence of the perturbative QCD vacuum singularity by analyzing the four-gluon scattering amplitude, revealing the importance of both even and odd conformal spins and deriving new mathematical representations.

Contribution

It introduces a comprehensive conformal expansion of the four-gluon amplitude, including both even and odd spins, and derives novel hypergeometric function forms and connections to Bessel kernels.

Findings

Inclusion of both even and odd conformal spins is essential.

Derived a new hypergeometric function representation of the amplitude.

Connected Fourier expansion with Bessel kernels from number theory.

Abstract

We study the four-gluon scattering amplitude in the high energy limit of QCD written in terms of its conformal expansion. We highlight the need to include both even and odd conformal spin contributions in order to map it to an iterative representation in rapidity and transverse momentum space which we have evaluated numerically. By Fourier expanding in a set of three azimuthal angles, we find a new form for the amplitude in terms of $_4F_3$ hypergeometric functions. An alternative formulation is possible when connecting this Fourier expansion with Bessel kernels studied in analytic number theory.