Abstract

An essential part of any factorisation proof is the demonstration that the exchange of Glauber gluons cancels for the considered observable. We show this cancellation at all orders for double Drell-Yan production (the double parton scattering process in which a pair of electroweak gauge bosons is produced) both for the integrated cross section and for the cross section differential in the transverse boson momenta. In the process of constructing this proof, we also revisit and clarify some issues regarding the Glauber cancellation argument and its relation to the rest of the factorisation proof for the single Drell-Yan process.

Highlights

  • As the LHC continues to run after its energy upgrade, hopes are high that signals for physics beyond the Standard Model will show up in the coming years

  • Using light-front ordered version of QCD perturbation theory (LCPT) we show that, whilst individual cut graphs in GR may have pinched poles at small l−j, the sum over all cuts GR is free from such pinches, and all poles in l−j that originate from A(lj) are in the lower half plane

  • LCPT gives the same results as conventional covariant perturbation theory and may be derived from it [8, 80], as we show

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Summary

Introduction

As the LHC continues to run after its energy upgrade, hopes are high that signals for physics beyond the Standard Model will show up in the coming years. Together with model assumptions connecting these multi-parton distributions with their single-parton counterparts, this forms the basis of most phenomenological investigations, see for instance [13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45] To put this framework on a more solid footing, it is necessary to understand whether factorisation holds for multiple hard scattering.

Overview of the factorisation proof
Overall strategy
Scaling of soft momenta
Approximations for soft gluons
Scope and general method
Grammer-Yennie approximation and rearrangement of terms
Explicit calculations in a simplified setting
Double box graph
Lightlike Wilson lines
Alternative momentum routings
Wilson lines with finite rapidity
Gauge boson vertex correction
General prescription for avoiding the Glauber region
All-order proof of Glauber gluon cancellation
Derivation of LCPT from covariant perturbation theory
Absence of pinched poles in the Glauber region
Single Drell-Yan
Double Drell-Yan
Including longitudinally polarised collinear gluons
Independence of the remainder R on partitioning of soft vertices
Summary
A Evaluation of Feynman integrals in light-cone coordinates
B Alternative approach to the double scattering collinear factor
C Timelike Wilson lines
Full Text
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