Matching NNLO to parton shower using N$^3$LL colour-singlet transverse momentum resummation in GENEVA

We extend the GENEVA Monte Carlo framework using the transverse momentum of a colour-singlet system as the resolution variable. This allows us to use next-to-next-to-next-to leading logarithm (N$^3$LL) resummation via the \radish formalism to obtain precise predictions for any colour-singlet production process at the fully exclusive level. Thanks to the implementation of two different resolution variables within the GENEVA framework, we are able to assess the impact of such a choice on differential observables for the first time. As a first application we present predictions for Drell-Yan lepton pair production at next-to-next-to-leading order (NNLO) in QCD interfaced to a parton shower simulation that includes additional all-order radiative corrections. We provide fully showered and hadronised events using PYTHIA8, while retaining the NNLO QCD accuracy for observables which are inclusive over the additional radiation. We also show that it is possible to obtain a numerically good agreement between showered GENEVA predictions and the N$^3$LL resummation for the transverse momentum spectrum by choosing a more local recoil scheme. We compare our final predictions to LHC data at 13 TeV, finding good agreement across several distributions.