Probing factorization violation with vector angularities

TL;DR

This paper introduces vector angularities, a new class of observables to study factorization violation in high-energy collisions, providing a baseline for experimental tests and analyzing effects via simulations.

Contribution

It proposes vector angularities as a novel observable family, develops a factorization formula excluding Glauber gluon effects, and compares predictions with Pythia simulations to study factorization violation.

Findings

Negligible factorization violation where established

Sizable effects away from established factorization

Good agreement between NLL' predictions and Pythia without MPI

Abstract

Factorization underlies all predictions at the Large Hadron Collider, but has only been rigorously proven in a few cases. One of these cases is the Drell-Yan process, $pp \to Z/\gamma + X$, in the limit of small boson transverse momentum. We introduce a one-parameter family of observables, that we call vector angularities, of which the transverse momentum is a special case. This enables the study of factorization violation, with a smooth transition to the limit for which factorization has been established. Like the angularity event shapes, vector angularities are a sum of transverse momenta weighted by rapidity, but crucially this is a vector sum rather than a sum of the magnitude of transverse momenta. We study these observables in Pythia, using the effect of multi-parton interactions (MPI) as a proxy factorization violation, finding a negligible effect in the case where factorization is established but sizable effects away from it. We also present a factorization formula for the cross section, that does not include factorization violating contributions from Glauber gluons, and thus offers a baseline for studying factorization violation experimentally using vector angularities. Our predictions at next-to-leading logarithmic accuracy (NLL$'$) are in good in agreement with Pythia (not including MPI), and can be extended to higher order.