  We reexamine the dominant contribution of parton distribution function (PDF)
uncertainties to the W mass measurement, and determine their contribution is
+-39(30) MeV when running the Large Hadron Collider at 7(13) TeV. We find that
spurious correlations in older PDF sets led to over-optimistic assumptions
regarding normalization to Z observables. In order to understand the origin of
the large uncertainties we break down the contribution of the PDF errors into
effects at the hard matrix element level, in showering, and in sensitivity to
finite detector resolutions.
  Using CT10, CT10W, and charm enhanced PDF sets in comparison to older PDF
sets, we develop a robust analysis that examines correlations between
transverse mass reconstructions of W and Z decays (scaled by cos $\theta_W$) to
leptons. We find that central leptons (|$\eta_l$| < 1.3) from W and Z bosons
carry the most weight in reducing the PDF uncertainty, and estimate a PDF error
of +10/-12 MeV is achievable in a W mass measurement at the LHC. Further
reductions of the W mass uncertainty will require improved fits to the parton
distribution functions.
