Muon $q/ p_{\mathrm{T}} $ distribution in simulated $ W \rightarrow \mu\nu$ events with variations in (left) $m_W$ and (right) the $A_3$ coefficient. The dashed vertical lines indicate the two $ p_{\mathrm{T}}$ ranges that are included in the $m_W$ fit.

Curvature corrections as a function of the detector region index (depends on $\eta$, $\phi$ and tracking detector, as described in the text) for (left) data and (right) simulation. The corrections are shown for both polarity configurations. The periodic pattern corresponds to a dependence on pseudorapidity that repeats in the intervals of the azimuthal angle.

Dimuon mass distributions for selected $J/\psi$, $\Upsilon (1S)$ and $ Z$ boson candidates. All categories with both muons in the $2.2 < \eta < 4.4$ region are combined. The data are compared with the fit model. The red histogram delineates the model before the application of the smearing.

Trigger efficiency ratios in data relative to simulation in intervals of $\eta$ for a single interval of $\phi$. The points are presented as a function of $1/ p_{\mathrm{T}} $ and are overlaid with best-fit linear functions of $ p_{\mathrm{T}} $. Points from each $\eta$ interval are separated for readability by an offset of half the integer index $i$ for that interval. The uncertainties on most of the points are too small for the error bars to be visible.

Isolation efficiencies as a function of the observables (left) $u$ and (right) $1/ p_{\mathrm{T}} $ of the muon. The grey histograms indicate the, arbitrarily normalised, shapes of each distribution in simulated $ W$ boson events. In the lower panels the ratios of the isolation efficiency with respect to the uncorrected simulation are shown.

Weighted $ p_{\mathrm{T}}$ spectra of the samples of (left) positively and (right) negatively charged hadron candidates. The fit results are overlaid.

Distributions of $ p_{\mathrm{T}} ^Z$ (left) before and (right) after the fit for the different candidate models of the unpolarised cross-sections. The fit only considers the region $ p_{\mathrm{T}} ^Z < 30\text{ Ge V} $, indicated by the dashed vertical line. In the lower panels the ratios with respect to the POWHEGPythia model are shown.

Distribution of $ p_{\mathrm{T}} ^Z$ compared to the POWHEGPythia model prior to the parametric correction, which is delineated by the red line in the lower panel.

Logarithm of the relative energy loss of the dilepton system due to final-state radiation for (left) $ W$ boson events and (right) $ Z$ boson events. An energy loss of below $10^{-6}$ is considered unresolvable and is accounted for in the underflow bin to the left of the dashed vertical line. In the lower panel the ratio with respect to Pythia is shown.

Projections of the (left) $q/ p_{\mathrm{T}} $ and (right) $\phi^*$ distributions for the challenge datasets. The four dashed vertical lines indicate the two fit regions in the $q/ p_{\mathrm{T}} $ distribution.

Distributions of (left) $q/ p_{\mathrm{T}} $ and (right) $\phi^{\ast}$ compared to the model after the $m_W$ fit.

Projections of the (left) $q/ p_{\mathrm{T}} $ and (right) rapidity distributions for the $ Z$ boson selection. A final state muon is only included in the $q/ p_{\mathrm{T}} $ distribution if it satisfies the $ W$ boson selection requirements.

Measured value of $m_W$ compared to those from the ALEPH [62], DELPHI [63], L3 [64], OPAL [65], CDF [10], D0 [11] and ATLAS [12] experiments. The current prediction of $m_W$ from the global electroweak fit is also included.

Animated gif made out of all figures.

Parameters in the momentum smearing model where the uncertainties quoted are statistical.

Results of fits of different models to the $ p_{\mathrm{T}} ^Z$ distribution. The uncertainties quoted are statistical, and the $\chi^2$ comparison of the different models to the data is evaluated considering only statistical uncertainties. The right-hand column lists the fit values of the $ k_{\rm T}^{\rm intr}$ parameter or, for DYTurbo , the analogous $g$ parameter. The fit with DYTurbo has one more degree of freedom than the fits with the other models since only one tuning parameter ($g$) is used for DYTurbo .

Fit results with the same default fit model used for the templates but with different models used for the pseudodata. The POWHEGPythia pseudodata correspond to $\alpha_s=0.125$ and $ k_{\rm T}^{\rm intr} =1.8\text{ Ge V} $. The Herwig and POWHEGHerwig pseudodata correspond to $\alpha_s=0.136$ and $ k_{\rm T}^{\rm intr}$ =1.3 $\text{ Ge V}$ . The Pythia pseudodata correspond to $\alpha_s=0.127$ and $ k_{\rm T}^{\rm intr} =2.7\text{ Ge V} $. The DYTurbo pseudodata correspond to $\alpha_s=0.118$ and $g=1\text{ Ge V} ^2$. The contributions to the total $\chi^2$ from the $q/ p_{\mathrm{T}} $ and $\phi^*$ distributions are denoted $\chi^2_W$ and $\chi^2_Z$, respectively. The shift in the $m_W$ value with respect to the POWHEGPythia pseudodata is denoted $\delta m_W$. The uncertainties quoted are statistical.

Values of the parameters determined in the $m_W$ fit with the \texttt{NNPDF31\_nlo\_as\_0118} PDF set. The uncertainties quoted are statistical.

Uncertainties for the NNPDF3.1, CT18 and MSHT20 sets. The contributions from the PDF uncertainty with fixed $\alpha_s$ and from the $\alpha_s$ variation are quoted separately as is their sum in quadrature, which defines the total uncertainty for each PDF set.

Contributions to the systematic uncertainty in $m_W$. Negligible contributions below $1 \text{ Me V} $ are not listed.

Fit results where the data and simulation samples are split into two orthogonal subsets. For a given split, the first row is defined as the reference with respect to which the difference in $m_W$, denoted by $\delta m_W$, is defined. The uncertainties quoted on $\delta m_W$ are statistical.

Fit results with variations in the fit range around the default $ p_{\mathrm{T}} ^{\rm min} = 28$ $\text{ Ge V}$ and $ p_{\mathrm{T}} ^{\rm min} = 52$ $\text{ Ge V}$ . The second column lists the $\chi^2$ values, the third column lists the shifts in $m_W$ with respect to the default fit and the third column lists the statistical uncertainties in $m_W$.

Fit results with variations in which physics parameters are varying freely.

This ZIP file contains supplementary material for LHCb-PAPER-2021-024 supplementary.pdf: The supplementary material available on CDS with captions *.pdf, *.eps, *.png, *.C: Each figure in multiple formats