PDF uncertainties on the W boson mass measurement from the lepton transverse momentum distribution

TL;DR

This study quantifies how proton PDF uncertainties propagate to the W boson mass measurement extracted from the lepton transverse momentum distribution in charged-current Drell-Yan events. Using a template-fit approach with multiple global PDF sets and reweighting, it assesses the one- to a few-dozen MeV impact on $m_W$, showing that the combined PDF4LHC uncertainty lies in the 18–24 MeV range for typical selections, with larger spreads across PDF groups. The analysis also demonstrates that tighter cuts on lepton-pair kinematics can reduce the MW uncertainty to roughly 6–18 MeV, while newer PDFs modestly improve the envelope. The results underscore the critical role of precise PDFs for achieving sub-10 MeV MW precision and suggest that future PDF improvements are essential for exploiting high-precision MW measurements at hadron colliders.

Abstract

We study the charged current Drell-Yan process and we evaluate the proton parton densities uncertainties on the lepton transverse momentum distribution and their impact on the determination of the W-boson mass. We consider the global PDF sets CT10, MSTW2008CPdeut, NNPDF2.3, NNPDF3.0, MMHT2014, and apply the PDF4LHC recipe to combine the individual results, obtaining an uncertainty on MW that ranges between +-18 and +-24 MeV, depending on the final state, collider energy and kind. We discuss the dependence of the uncertainty on the acceptance cuts and the role of the individual parton densities in the final result. We remark that some PDF sets predict an uncertainty on MW of O(10 MeV); this encouraging result is spoiled, in the combined analysis of the different sets, by an important spread of the central values predicted by each group.

Figures (8)

• Figure 1: Ratio of lepton transverse momentum distributions which have been generated with different $W$ boson masses.
• Figure 2: Percentage size of the PDF uncertainty on the lepton transverse momentum distribution, computed with different PDF sets. In addition to the basic acceptance criteria of Table \ref{['tab:selection']}, a cut $p_\perp^W< 15$ GeV on the lepton pair has been applied. The lower lines refer to the normalized distributions of Equation \ref{['eq:normdistr']}, the upper lines to the standard ones. Results for $W^+$ (left) and $W^-$ (right) production at the LHC 8 TeV (middle plots) and 13 TeV (lower plots); results for the Tevatron in the upper plot.
• Figure 3: Percentage size of the PDF uncertainty on the lepton transverse momentum distribution, computed with the NNPDF3.0 set at the LHC at different energies. Results for $W^+$ (left) and $W^-$ (right) production, in the case of absolute (upper lines) or normalized (lower lines) distributions.
• Figure 4: Summary of the PDF uncertainty on $m_{ W}$ computed with different PDF sets, colliders and final states. The basic acceptance criteria have been used in the left plot, while in the right plot an additional cut $p_\perp^W<15$ GeV has been applied.
• Figure 5: Shape of the normalized differential distribution $d\sigma/dx$ for different $p_\perp^W$ cuts (left plot). Ratio of the previous shapes with different $p_\perp^W$ cuts with respect to the inclusive (no $p_\perp^W$ cut) distribution (right plot).