# A Study of the PDF uncertainty on the LHC W-boson mass measurement

## TL;DR

This paper quantifies the uncertainty in measuring the W-boson mass at the LHC caused by parton distribution functions, using advanced calculations and simulations to provide precise estimates at different energies.

## Contribution

It provides a detailed, quantitative assessment of PDF-induced uncertainties on the W-boson mass measurement at various LHC energies using NNLO PDFs and NNLL+NNLO calculations.

## Key findings

- PDF uncertainties are around 13-17 MeV at 7 TeV.
- Uncertainties are similar at 8 TeV and 13 TeV energies.
- The study offers specific uncertainty estimates for different kinematic cuts.

## Abstract

The determination of the $W$-boson mass through an analysis of the decay charged-lepton transverse momentum distribution has a sizable uncertainty due to the imperfect knowledge of the relevant parton distribution functions (PDFs). In this paper, a quantitative assessment of the $W$-boson mass uncertainty at the LHC resulting from the PDF uncertainty is examined. We use the CT14 NNLO PDFs with a NNLL + NNLO calculation (ResBos) to simulate the $W$-boson production and decay kinematics. The uncertainty of the $W$-boson mass determination is then determined as a function of the boson and lepton kinematics. For $W^{+}$ production using $P_{T}^{W} < 15$ GeV and $35 < P_{T}^{l}$ (GeV) $< 45$, PDF uncertainties (at the 68% CL) of $^{+16.0}_{-17.5}$ MeV, $^{+13.9}_{-14.8}$ MeV, and $^{+12.2}_{-19.2}$ MeV, are determined at 7 TeV, 8 TeV and 13 TeV respectively. The uncertainties of $W^{-}$ for the same cuts are found to be $^{+15.9}_{-15.6}$ MeV, $^{+15.0}_{-12.7}$ MeV and $^{+14.8}_{-15.3}$ MeV, at 7 TeV, 8 TeV and 13 TeV respectively.