# Understanding and constraining the PDF uncertainties in a W boson mass measurement with forward muons at the LHC

## TL;DR

This paper investigates the impact of PDF uncertainties on the precision measurement of the W boson mass at the LHC, proposing methods to reduce these uncertainties significantly using LHCb data.

## Contribution

It provides a detailed analysis of PDF uncertainty sources in W mass measurements and proposes a strategy to halve this uncertainty with LHCb Run 2 data.

## Key findings

- PDF uncertainties limit W mass measurement precision.
- A new approach can reduce PDF uncertainties by about 50%.
- LHCb's forward acceptance enhances W mass measurement accuracy.

## Abstract

Precision electroweak tests are a powerful probe of physics beyond the Standard Model, but the sensitivity is limited by the precision with which the $W$ boson mass ($M_W$) has been measured. The Parton Distribution Function (PDF) uncertainties are a potential limitation for measurements of $M_W$ with LHC data. It has recently been pointed out that, thanks to LHCb's unique forward rapidity acceptance, a new measurement of $M_W$ by LHCb can improve this situation. Here we report on a detailed study on the mechanism driving the PDF uncertainty in the LHCb measurement of $M_W$, and propose an approach which should reduce this uncertainty by roughly a factor of two using LHCb Run 2 data.