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The production of weak gauge bosons, $W^{\pm}$ and $Z$, are at the core ofthe LHC precision measurement program. Their transverse momentum spectra aswell as their pairwise ratios are key theoretical inputs to many high-precisionanalyses, ranging from the $W$ mass measurement to the determination of partondistribution functions. Owing to the different properties of the $W$ and $Z$boson and the different accessible fiducial regions for their measurement, asimple one-dimensional correlation is insufficient to capture the differingvector and axial-vector dynamics of the produced lepton pair. We propose tocorrelate them in two observables, the transverse momentum $q_T$ of the leptonpair and its azimuthal separation $\Delta\phi$. Both quantities are purelytransverse and therefore accessible in all three processes, either directly orby utilising the missing transverse momentum of the event. We calculate all thesingle-differential $q_T$ and $\Delta\phi$ as well as the double-differential$(q_T,\Delta\phi)$ spectra for all three processes at N$^3$LL'+N$^2$LOaccuracy, resumming small transverse momentum logarithms in the soft-collineareffective theory approach and including all singlet and non-singletcontributions. Using the double-differential cross sections we build thepairwise ratios$\mathcal{R}_{W^+/Z},~\mathcal{R}_{W^-/Z},~\mathcal{R}_{W^+/W^-}$ and determinetheir uncertainties assuming fully correlated, partially correlated, anduncorrelated uncertainties in the respective numerators and denominators. Inthe preferred partially correlated case we find uncertainties of less than 1%in most phase space regions and up to 3% in the lowest $q_T$ region.

The $q_T$ and $\Delta\phi$ spectra in W and Z production at the LHC at N$^3$LL'+N$^2$LO