Advances in High Energy Physics

Volume 2019, Article ID 3797394, 9 pages

https://doi.org/10.1155/2019/3797394

## Transverse Momentum Dependence in Double Parton Scattering

^{1}CERN Theory Division, 1211 Geneva 23, Switzerland^{2}PRISMA Cluster of Excellence & Mainz Institute for Theoretical Physics Johannes Gutenberg University, 55099 Mainz, Germany

Correspondence should be addressed to Jonathan R. Gaunt; hc.nrec@tnuag.drahcir.nahtanoj

Received 21 December 2018; Accepted 14 February 2019; Published 12 March 2019

Guest Editor: Alexey Vladimirov

Copyright © 2019 Jonathan R. Gaunt and Tomas Kasemets. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP^{3}.

#### Abstract

In this review, we describe the status of transverse momentum dependence (TMD) in double parton scattering (DPS). The different regions of TMD DPS are discussed, and expressions are given for the DPS cross section contributions that make use of as much perturbative information as possible. The regions are then combined with each other as well as single parton scattering to obtain a complete expression for the cross section. Particular emphasis is put on the differences and similarities to transverse momentum dependence in single parton scattering. We further discuss the status of the factorisation proof for double colour singlet production in DPS, which is now on a similar footing to the proofs for TMD factorisation in single Drell-Yan, discuss parton correlations, and give an outlook on possible research on DPS in the near future.

#### 1. Introduction

Double parton scattering (DPS) is the process in which one has two hard scatterings, producing two sets of particles that we can label as ‘’ and ‘’, in an individual proton-proton collision (one allows any possibility for the final-state particles accompanying ‘’ and ‘’; these are often denoted by the symbol and are typically the products of additional soft scatterings and soft/collinear radiation from the partons active in the hard processes. The proof of factorisation for double colour-singlet production in DPS relies on this inclusive definition [1].). The region in which the transverse momenta of systems 1 and 2, and , are small is particularly important in studies of DPS, since DPS is especially prominent in this region compared to the usual single parton scattering (SPS) mechanism [2, 3] (note that here we use boldface symbols to denote transverse momentum vectors). Indeed, many experimental extractions of DPS use variables sensitive to this ‘double back-to-back’ configuration, for example, the variable in [4]. In the small , region a description in terms of double parton transverse momentum dependent (TMD) distributions is appropriate. There are many parallels between the treatment of TMD cross sections in single parton scattering (SPS) and double parton scattering (DPS). There are however also clear differences, with direct physical consequences. In this review, we aim to highlight these differences and similarities in order to facilitate researchers interested in spin and TMD physics to make important contributions to the field of DPS.

While TMD factorisation in SPS has been rigorously proven for colour singlet production (see, e.g., [5]), it runs into problems for hadron collisions producing coloured final states [6–8]. These issues are expected to be important also for DPS, and we will therefore restrict ourselves to double colour-singlet production, i.e., where each of the two hard collisions separately produces a colour singlet final state.

In the production of two colour singlets, such as two vector bosons, the TMD SPS factorisation theorem can be applied as usual to study the region where the sum of the two transverse momenta is small. If, however, the transverse momenta of both bosons are measured to be much smaller than the hard scale, standard TMD factorisation alone is no longer sufficient. For these observables, DPS contributes at the same power as SPS, and no leading-power factorisation theorem can be derived without simultaneously taking care of SPS and DPS, including their interference. An overview of the different factorisation theorems in hadron collisions and the treatment of the initial state in different regions of the sum and difference of the transverse momenta of the two colour singlets is shown in Figure 1. Once we integrate over the transverse momentum difference DPS is degraded to a power correction to the SPS cross section. Nonetheless, there are several processes in high energy collisions where DPS can compete with or surpass the SPS contribution even for the total cross section. This is usually due to enhancements caused by the large increase in parton densities at small momentum fractions and/or that the SPS cross section is suppressed by additional small coupling constants.