Joint two-dimensional resummation in qT and 0-jettiness at NNLL

We consider Drell-Yan production pp Z/ (+-) with the simultaneous measurement of the Z-boson transverse momentum q(T) and 0-jettiness T0. Since both observables resolve the initial-state QCD radiation, the double-differential cross section in q(T) and T0 contains Sudakov double logarithms of both q(T)/Q and T0/Q, where Q approximate to m(Z) is the dilepton invariant mass. We simultaneously resum the logarithms in q(T) and T0 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 or q(T) 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 q(T) 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 q(T). 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.