Drell-Yan lepton-pair production: $q_T$ resummation at N$^3$LL accuracy and fiducial cross sections at N$^3$LO

We present high-accuracy QCD predictions for the transverse-momentum ($q_T$) distribution and fiducial cross sections of Drell-Yan lepton pairs produced in hadronic collisions. At small value of $q_T$ we resum to all perturbative orders the logarithmically enhanced contributions up to next-to-next-to-next-to-leading logarithmic (N$^3$LL) accuracy, including all the next-to-next-to-next-to-leading order (N$^3$LO) (i.e. $\mathcal{O}(\alpha_S^3)$) terms. Our resummed calculation has been implemented in the public numerical program DYTurbo, which produces fast and precise predictions with the full dependence on the final-state leptons kinematics. We consistently combine our resummed results with the known $\mathcal{O}(\alpha_S^3)$ fixed-order predictions at large values of $q_T$ thus obtaining full N$^3$LO accuracy also for fiducial cross sections. We show numerical results at LHC energies discussing the reduction of the perturbative uncertainty with respect to lower-order calculations.