PDF uncertainties in the determination of the W boson mass and of the effective lepton mixing angle at the LHC

The precision measurement of the W boson mass allows to perform stringent consistency tests of the Standard Model by means of global electroweak fits. The accurate determination of the W boson mass is one of the legacy results of the Tevatron, where the experimental accuracy is such that $M_W$ is now limited by theoretical uncertainties related to the parton distributions of the proton. In this contribution, we show how to quantify the impact of PDF uncertainties in the measurement of $M_W$ at the Tevatron and the LHC by means of a template method, and study both the use of the W transverse mass and the lepton pT kinematical distributions to generate these templates. We also present preliminary results on the quantification of the PDF uncertainties in the determination of the effective lepton mixing angle at the LHC, based on the same template method as for the W mass determination