Squeezing the proton: estimating and improving parton distribution uncertainties for precision electroweak measurements

We consider the production of a lepton and a neutrino each with large transverse momentum at the LHC and the Tevatron, in the so called charged current Drell-Yan process. We propagate the uncertainties due to the knowledge of the proton structure to the prediction of several observables defined for this scattering process. We study the covariance with respect to variations of the proton parameterisation of the bins of the considered kinematical distributions. We introduce this covariance in the formulation of a fit that determines the preferred value of the W boson mass from the analysis of the experimental data and apply this procedure to different sets of proton parameterisations. We study the robustness of the determination of the PDF covariance matrix from Monte Carlo data. We study the covariance matrix under the variation of mW to understand the difference in the dependence of the differential distributions between mW and the PDF uncertainty.