Difference between standard and quasi-conformal BFKL kernels

TL;DR

This paper investigates the difference between standard and quasi-conformal BFKL kernels, revealing that the simplicity of the quasi-conformal form is largely due to the impact parameter space representation.

Contribution

It calculates the difference between the standard and quasi-conformal BFKL kernels in momentum space, showing its simplicity and clarifying the kernel's structure.

Findings

The difference between the kernels is simple.

The quasi-conformal kernel's simplicity is mainly due to impact parameter space.

The total kernel is fully determined by its Moebius representation.

Abstract

As it was recently shown, the colour singlet BFKL kernel, taken in Moebius representation in the space of impact parameters, can be written in quasi-conformal shape, which is unbelievably simple compared with the conventional form of the BFKL kernel in momentum space. It was also proved that the total kernel is completely defined by its Moebius representation. In this paper we calculated the difference between standard and quasi-conformal BFKL kernels in momentum space and discovered that it is rather simple. Therefore we come to the conclusion that the simplicity of the quasi-conformal kernel is caused mainly by using the impact parameter space.