Proton-PDF uncertainties in extracting nuclear PDFs from $W^\pm$ production in p+Pb collisions

TL;DR

This paper evaluates how uncertainties in free-proton PDFs affect the extraction of nuclear PDFs from W boson production data in p+Pb collisions, proposing methods to mitigate these effects and highlighting future challenges with increased data precision.

Contribution

It introduces a covariance-matrix and reweighting approach to quantify free-proton PDF uncertainties and proposes a new charge asymmetry ratio with minimal proton-PDF dependence.

Findings

Residual free-proton PDF effects are small with current data.

Self-normalization and ratios reduce but do not eliminate uncertainties.

A new charge asymmetry ratio shows excellent cancellation of proton-PDF uncertainties.

Abstract

We discuss the recent CMS Collaboration measurement of $W^\pm$ boson production in p+Pb collisions at 8.16 TeV in terms of the constraining power on nuclear parton distribution functions (PDFs). The impact of the free-proton PDF uncertainties on the nuclear PDF extraction is quantified by using a theoretical covariance-matrix method and Hessian PDF reweighting. We discuss different ways to mitigate these theoretical uncertainties, including self-normalization, forward-to-backward ratios and nuclear-modification ratios. It is found that none of these methods offer perfect cancellation of the free-proton PDFs but, with the present data uncertainties, the residual free-proton-PDF dependence has, conveniently for the global analyses, little effect on the extraction of the nuclear modifications. Based on a simple estimate of obtainable statistics at the LHC Run 3, we argue that this will change in the near future and it becomes more important to propagate the proton-PDF uncertainties accordingly. Using the obtained information on the correlations of the free-proton uncertainties, we also identify a new charge asymmetry ratio, where the cancellation of the proton-PDF uncertainties is found to be extremely good.