Understanding PDF uncertainty on the $W$ boson mass measurements in CT18 global analysis

TL;DR

This paper investigates how different parton distribution functions (PDFs) influence the measurement of the $W$ boson mass, highlighting the importance of using updated PDFs to accurately assess uncertainties in experimental results.

Contribution

It compares shape variations from different PDFs and uses Lagrange multiplier scans to identify data constraints on the $W$ mass measurement in the CT18 global analysis.

Findings

Spread of predictions from different PDFs exceeds individual PDF uncertainties.

CDF measurement is sensitive to $d$-quark PDFs at intermediate $x$.

DIS, Drell-Yan, and charge asymmetry data constrain key PDFs.

Abstract

We study the dependence of the transverse mass distribution of the charged lepton and the missing energies on the parton distributions (PDFs) adapted to the $W$ boson mass measurements at the CDF and ATLAS experiments. We compare the shape variations of the distribution induced by different PDFs and find that spread of predictions from different PDF sets can be much larger than the PDF uncertainty predicted by a specific PDF set. We suggest analyzing the experimental data using up-to-date PDFs for a better understanding of the PDF uncertainties in the $W$ boson mass measurements. We further carry out a series of Lagrange multiplier scans to identify the constraints on the transverse mass distribution imposed by individual data sets in the CT18 global analysis. In the case of CDF measurement, the distribution is mostly sensitive to the $d$-quark PDFs at the intermediate $x$ region that is largely constrained by the DIS and Drell-Yan data on the deuteron target, as well as the Tevatron lepton charge asymmetry data.