Parton distributions and the $W$ mass measurement

Abstract

We examine the sources of parton distribution errors in the $W$ mass measurement, and point out shortcomings in the existing literature. Optimistic assumptions about strategies to reduce the error by normalizing to $Z$ observables are examined and found to rely too heavily on assumptions about the parametrization and degrees of freedom of the parton distribution functions (PDFs). We devise a strategy to combine measurements as efficiently as possible using error correlations to reduce the overall uncertainty of the measurement, including $Z$ data, and estimate a PDF error of ${}_{-12}^{+10}$ 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.

27 pgs, 4 figs, v2 added clarifications and derivation to Sec. 5, to appear in PRD, v3 fixes Ref. typo

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