Differential N$^3$LO QCD corrections to charged current production at the LHC

Charged current Drell-Yan production at hadron colliders is a benchmark electroweak process. A recent measurement of the W boson mass by the CDF experiment displays a large deviation from the Standard Model prediction. To enable precision phenomenology for this process, we compute the third-order (N$^3$LO) QCD corrections to the rapidity distribution in W boson production and to the transverse mass distribution of its decay products. We study kinematic regions relevant for the LHC experiments and assess the numerical magnitude of uncertainties from electroweak input parameters and parton distribution functions.