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

Abstract

We consider Drell-Yan production pp → Z/γ^∗ → ℓ⁺ℓ⁻ with the simultaneous measurement of the Z-boson transverse momentum q_T and 0-jettiness ${\mathcal{T}}_0$. Since both observables resolve the initial-state QCD radiation, the double-differential cross section in q_T and ${\mathcal{T}}_0$ contains Sudakov double logarithms of both q_T/Q and ${\mathcal{T}}_0/Q$, where Q ∼ m_Z is the dilepton invariant mass. We simultaneously resum the logarithms in q_T and ${\mathcal{T}}_0$ 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 ${\mathcal{T}}_0$ 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.