Two-loop splitting in double parton distributions: the colour non-singlet case

TL;DR

This paper calculates the next-to-leading order two-loop splitting contributions to double parton distributions for all colour states, analyzing their behavior and impact in various kinematic regimes.

Contribution

It provides the first comprehensive NLO two-loop calculation of double parton splitting for all colour configurations, including divergence handling methods.

Findings

Two-loop contributions vary across different channels.

Rapidity divergences are effectively managed with Wilson lines or delta regulator.

Results inform the understanding of parton correlations at small distances.

Abstract

At small inter-parton distances, double parton distributions receive their dominant contribution from the splitting of a single parton. We compute this mechanism at next-to-leading order in perturbation theory for all colour configurations of the observed parton pair. Rapidity divergences are handled either by using spacelike Wilson lines or by applying the delta regulator. We investigate the behaviour of the two-loop contributions in different kinematic limits, and we illustrate their impact in different channels.