Transverse momentum in double parton scattering: factorisation, evolution and matching

TL;DR

This paper extends the theoretical framework for double parton scattering by incorporating transverse momentum dependence, deriving evolution equations, and analyzing factorisation and resummation at one-loop accuracy.

Contribution

It develops a formalism for transverse momentum dependent double parton distributions, including evolution equations and perturbative kernels, enhancing understanding of double parton scattering.

Findings

Derived evolution equations for soft factors and double parton distributions.

Expressed transverse momentum dependent distributions in terms of nonperturbative quantities.

Analyzed resummation possibilities for large transverse momenta.

Abstract

We give a description of double parton scattering with measured transverse momenta in the final state, extending the formalism for factorisation and resummation developed by Collins, Soper and Sterman for the production of colourless particles. After a detailed analysis of their colour structure, we derive and solve evolution equations in rapidity and renormalisation scale for the relevant soft factors and double parton distributions. We show how in the perturbative regime, transverse momentum dependent double parton distributions can be expressed in terms of simpler nonperturbative quantities and compute several of the corresponding perturbative kernels at one-loop accuracy. We then show how the coherent sum of single and double parton scattering can be simplified for perturbatively large transverse momenta, and we discuss to which order resummation can be performed with presently available results. As an auxiliary result, we derive a simple form for the square root factor in the Collins construction of transverse momentum dependent parton distributions.