Estimating the impact of mixed QCD-electroweak corrections on the $W$-mass determination at the LHC

TL;DR

This paper assesses how mixed QCD-electroweak corrections influence the precision measurement of the W boson mass at the LHC, finding potential shifts up to 20 MeV that could affect current and future analyses.

Contribution

It provides the first estimate of the impact of mixed QCD-electroweak corrections on W mass extraction using simplified observables, highlighting the need for detailed differential calculations.

Findings

Mixed QCD-electroweak corrections can shift the W mass by up to 20 MeV.

The shift depends on the kinematic cuts used in fiducial cross section definitions.

Current target precision for W mass measurement is around 10 MeV, close to the estimated correction.

Abstract

We study the impact of the recently computed mixed QCD-electroweak corrections to the production of $W$ and $Z$ bosons at the LHC on the value of the $W$ mass extracted from the transverse momentum distribution of charged leptons from $W$ decays. Using the average lepton transverse momenta in $W$ and $Z$ decays as simplified observables for the determination of the $W$ mass, we estimate that mixed QCD-electroweak corrections can shift the extracted value of the $W$ mass by up to ${\cal O}(20)~{\rm MeV}$, depending on the kinematic cuts employed to define fiducial cross sections for $Z$ and $W$ production. Since the target precision of the $W$-mass measurement at the LHC is ${\cal O}(10)~{\rm MeV}$, our results emphasize the need for fully-differential computations of mixed QCD-electroweak corrections and a careful analysis of their potential impact on the determination of the $W$ mass.