Numerical analysis of the unintegrated double gluon distribution

TL;DR

This paper provides a detailed numerical analysis of the unintegrated double gluon distribution, exploring its dependence on transverse momenta, momentum fractions, and scales, and demonstrating factorization properties at small x.

Contribution

It introduces a numerical approach to compute the unintegrated double gluon distribution using the Kimber-Martin-Ryskin method, including the effects of splitting and sum rules.

Findings

Unintegrated gluon distribution factorizes at small x when splitting is included.

The distribution depends on transverse momenta, momentum fractions, and scales.

Factorization holds under certain conditions, validating the approach.

Abstract

We present detailed numerical analysis of the unintegrated double gluon distribution which includes the dependence on the transverse momenta of partons. The unintegrated double gluon distribution was obtained following the Kimber-Martin-Ryskin method as a convolution of the perturbative gluon splitting function with the collinear integrated double gluon distribution and the Sudakov form factors. We analyze the dependence on the transverse momenta, longitudinal momentum fractions and hard scales. We find that the unintegrated gluon distribution factorizes into a product of two single unintegrated gluon distributions in the region of small values of $x$, provided the splitting contribution is included and the momentum sum rule is satisfied.