The transverse momentum spectrum of weak gauge bosons at N$^3$LL$+$NNLO

We present accurate QCD predictions for the transverse momentum ( $p_\perp $ ) spectrum of electroweak gauge bosons at the LHC for $13~\mathrm {TeV} $ collisions, based on a consistent combination of a NNLO calculation at large $p_\perp $ and N$^3$ LL resummation in the small $p_\perp $ limit. The inclusion of higher order corrections leads to substantial changes in the shape of the differential distributions, and the residual perturbative uncertainties are reduced to the few percent level across the whole transverse momentum spectrum. We examine the ratio of $p_\perp $ distributions in charged- and neutral-current Drell–Yan production, and study different prescriptions for the estimate of perturbative uncertainties that rely on different degrees of correlation between these processes. We observe an excellent stability of the ratios with respect to the perturbative order, indicating a strong correlation between the corresponding QCD corrections.