Momentum sum rule and factorization of double parton distributions

TL;DR

This paper demonstrates that the momentum sum rule is essential for the factorization of double parton distributions into single distributions at small x and high Q, revealing a fundamental link between these distributions.

Contribution

It establishes that the momentum sum rule is a necessary condition for factorization of double parton distributions at small x and large Q, a novel insight in parton distribution theory.

Findings

Momentum sum rule is necessary for factorization.

Factorization holds at small x and high Q.

Provides a fundamental relation between double and single distributions.

Abstract

We show that the momentum sum rule is a necessary condition for factorization of double parton distributions into a product of two single parton distributions for small values of the parton momentum fractions x and large enough values of the evolution scale Q. This is a somewhat surprising result since the momentum sum rule involves integration over all values of the momentum fraction. In essence, the momentum sum rule provides a proper relation between the double and single parton distributions, which is necessary for the small x factorization at large $Q$.