  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.
