# Two-loop splitting in double parton distributions

## TL;DR

This paper calculates the next-to-leading order two-loop splitting functions for double parton distributions, providing essential ingredients for precise double parton scattering predictions at NLO.

## Contribution

It presents the first two-loop matching calculations of DPDs onto PDFs and derives NLO 1->2 splitting functions for all partonic channels.

## Key findings

- Computed two-loop matching of DPDs onto PDFs.
- Derived NLO 1->2 splitting functions for all channels.
- Verified sum rules and kinematic limits for the splitting functions.

## Abstract

Double parton distributions (DPDs) receive a short-distance contribution from a single parton splitting to yield the two observed partons. We investigate this mechanism at next-to-leading order (NLO) in perturbation theory. Technically, we compute the two-loop matching of both the position and momentum space DPDs onto ordinary PDFs. This also yields the 1 -> 2 splitting functions appearing in the evolution of momentum-space DPDs at NLO. We give results for the unpolarised, colour-singlet DPDs in all partonic channels. These quantities are required for calculations of double parton scattering at full NLO. We discuss various kinematic limits of our results, and we verify that the 1 -> 2 splitting functions are consistent with the number and momentum sum rules for DPDs.