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Parton Density Uncertainties and the Determination of Electroweak Parameters at Hadron Colliders

We discuss the determination of electroweak parameters from hadron collider observables, focusing on the $W$ boson mass measurement. We revise the procedures adopted in the literature to include in the experimental analysis the uncertainty due to our imperfect knowledge of the proton structure. We show how the treatment of the proton parton density functions (PDFs) uncertainty as a source of systematic error, leads to the automatic inclusion in the fit of the bin-bin correlation of the kinematic distributions with respect to PDF variations. In the case of the determination of $M_W$ from the charged lepton transverse momentum distribution, we observe that the inclusion of this correlation factor yields a strong reduction of the PDF uncertainty, given a sufficiently good control over all the other error sources. This improvement depends on a systematic accounting of the features of the QCD-based PDF model, and it is achieved relying only on the information available in current PDF sets. While a realistic quantitative estimate requires to take into account the details of the experimental systematics, we argue that, in perspective, the proton PDF uncertainty will not be a bottleneck for precision measurements.