Parton distributions and the $W$ mass measurement

TL;DR

This paper analyzes the impact of parton distribution function errors on the precision of the W boson mass measurement at the LHC, highlighting limitations of current methods and proposing a combined measurement strategy to reduce uncertainties.

Contribution

It introduces a new strategy to combine measurements using error correlations and estimates a potential reduction of PDF-related errors in W mass measurements.

Findings

Estimated PDF error of +10/-12 MeV in W mass measurement at the LHC.

Critique of existing normalization strategies relying on Z observables.

Emphasis on the need for improved PDF fits for further precision.

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 $^{+10}_{-12}$ 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.