Drell-Yan cross-sections with fiducial cuts: impact of linear power corrections and $q_T$-resummation in PDF determination

Measurement at Hadron colliders of neutral- and charged-current Drell-Yan production provide essential constraints in the determination of parton distribution functions. Experimentally, they have reached percent level precision, challenging the accuracy of the theoretical predictions. In this work we benchmark the novel implementation in $\texttt{DYTurbo}$ of linear fiducial power corrections in the $q_T$-subtraction formalism at NLO and NNLO in QCD. We illustrate how the inclusion of linear fiducial power corrections impacts predictions for precise $W$ and $Z$ measurements from the LHC and affects their description by modern global parton distribution functions. The further inclusion of $q_T$-resummation corrections in the theoretical predictions leads to a better modelling of the lepton $p_T$ distribution and we study how this improve the description of the data.