Understanding PDF uncertainty in W boson mass measurements

We study the dependence of the transverse mass distribution of charged leptons and the missing energy on parton distributions(PDFs)adapted to W boson mass measurements at the CDF and ATLAS experiments.We compare the shape variations of the distribution induced by different PDFs and find that the spread of predictions from different PDF sets can be significantly larger than the PDF uncertainty predicted by a specific PDF set.We suggest analyzing the experimental data using up-to-date PDFs to gain a better understanding of the PDF uncertainties in W boson mass measurements.We also perform a series of Lagrange multiplier scans to identify the constraints on the transverse mass distribution imposed by individual data sets in the CT18 global analysis.In the case of the CDF measurement,the distribution is mostly sensitive to d-quark PDFs in the intermediate x region,which are largely constrained by DIS and Drell-Yan data on deuteron targets and Tevatron lepton charge asymmetry data.