The double gluon distribution from the single gluon distribution

TL;DR

This paper demonstrates that the double gluon distribution function can be uniquely derived from the single gluon distribution using the momentum sum rule, and analyzes its evolution and factorization properties.

Contribution

It provides a method to constrain the double gluon distribution from the single gluon distribution and examines its evolution, highlighting the limitations of the factorized approximation.

Findings

Double gluon distribution can be constrained by single gluon distribution.

Factorized ansatz works well at small x but fails at larger x.

Numerical evolution shows the behavior of the double gluon distribution with scale.

Abstract

Using momentum sum rule for evolution equations for Double Parton Distribution Functions (DPDFs) in the leading logarithmic approximation, we find that the double gluon distribution function can be uniquely constrained via the single gluon distribution function. We also study numerically its evolution with a hard scale and show that an approximately factorized ansatz into the product of two single gluon distributions performs quite well at small values of $x$ but is always violated for larger values, as expected.