Constraining the double gluon distribution by the single gluon distribution

TL;DR

This paper develops a method to construct initial conditions for double gluon distribution functions in QCD, ensuring they satisfy the momentum sum rule and analyzing their evolution with scale.

Contribution

It introduces a parameter-free, sum rule-compliant initial condition for double gluon distributions based on the single gluon distribution.

Findings

Double gluon distributions approximately factorize at small x

Factorization is violated at large x

Constructed distributions satisfy the momentum sum rule

Abstract

We show how to consistently construct initial conditions for the QCD evolution equations for double parton distribution functions in the pure gluon case. We use to momentum sum rule for this purpose and a specific form of the known single gluon distribution function in the MSTW parameterization. The resulting double gluon distribution satisfies exactly the momentum sum rule and is parameter free. We also study numerically its evolution with a hard scale and show the approximate factorization into product of two single gluon distributions at small values of x, whereas at large values of x the factorization is always violated in agreement with the sum rule.