Simultaneously determining the $W^{\pm}$ boson mass and parton shower model parameters

We explore the possibility of simultaneously determining the $W$ boson mass, $m_{W}$, and QCD-related nuisance parameters that affect the $W$ boson $p_{\mathrm{T}}$ spectrum from a fit to the $p_{\mathrm{T}}$ spectrum of the muon in the leptonic decay $W\rightarrow\mu\nu$. The study is performed using pseudodata generated using Pythia and the muon is required to fall in a kinematic region corresponding to the approximate acceptance of the LHCb detector. We find that the proposed method performs well and has little trouble disentangling variations in the muon $p_{\mathrm{T}}$ spectrum due to $m_{W}$ from those due to the $W$ boson $p_{\mathrm{T}}$ model.