LAUSR

A bstractWe consider Drell-Yan production pp → Z/γ∗ → ℓ+ℓ− with the simultaneous measurement of the Z-boson transverse momentum qT and 0-jettiness T0$$ {\mathcal{T}}_0 $$. Since both observables resolve the initial-state QCD radiation, the double-differential cross section in qT and T0$$ {\mathcal{T}}_0 $$ contains Sudakov double logarithms of both qT/Q and T0/Q$$ {\mathcal{T}}_0/Q $$, where Q ∼ mZ is the dilepton invariant mass. We simultaneously resum the logarithms in qT and T0$$ {\mathcal{T}}_0 $$ to next-to-next-to-leading logarithmic order (NNLL) matched to next-to-leading fixed order (NLO). Our results provide the first genuinely two-dimensional analytic Sudakov resummation for initial-state radiation. Integrating the resummed double-differential spectrum with an appropriate scale choice over either T0$$ {\mathcal{T}}_0 $$ or qT recovers the corresponding single-differential resummation for the remaining variable. We discuss in detail the required effective field theory setups and their combination using two-dimensional resummation profile scales. We also introduce a new method to perform the qT resummation where the underlying resummation is carried out in impact-parameter space, but is consistently turned off depending on the momentum-space target value for qT. Our methods apply at any order and for any color-singlet production process, such that our results can be systematically extended when the relevant perturbative ingredients become available.