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: : Simulated kinematic distributions of (a) \ptl and (b) \mt in $W^\pm \to \mu^\pm\nu$ events, for $W$-boson mass and width values of $\mW = 80399$~\MeV and $\GW = 2085$~\MeV. The ratio panels represent the relative effect of varying these parameters by $\pm 60$~\MeV and $\pm 200$~\MeV, respectively.

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: : Overview of the \mW fit results in all categories for the (a) \ptl and (b) \mt distributions, with the CT10nnlo PDF set, where $q$ denotes the charge of the decay lepton. The results of the PLH fit are compared with the $\chi^2$ fit, where systematic uncertainties are propagated using the offset method~\cite{STDM-2014-18}. The points labelled as `Combination' correspond to the result of a joint PLH fit to all categories and to a combination of individual $\chi^2$ fits.

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: : (a) Distribution of the difference $\Delta \mW$ between the nominal \mW PLH fit result and results obtained for pseudo-experiments using random variations of the sources of systematic uncertainty. The \ptl distribution is used. (b) Distribution of pull significances for the NPs in the combined PLH fit to the \ptl distribution.

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: : Relative effect, with respect to CT10nnlo, of the indicated PDF extrapolations on the detector-level, $\eta$-inclusive \ptl distributions in (a,c) $W^+$ events and (b,d) $W^-$ events. The thick lines show the central PDF set, and the envelopes show the associated 68\% CL uncertainty.

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: : Variation of the fitted value of \mW with the PDF set used in the fit, for the (a)~\ptl and (b)~\mt distributions and different scalings of the pre-fit PDF uncertainties. The reference value is defined by the CT18 PDF set.

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: : Overview of the \mW PLH fit results in all categories for the (a) \ptl and (b) \mt distributions, with the CT18 PDF set. The points labelled as `Combination' correspond to the result of a joint PLH fit to all categories.

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: : Post-fit distributions of \ptl with data and MC for (a) $W^+\rightarrow e^+\nu_e$, (b) $W^-\rightarrow e^-\overline{\nu}_e$, (c) $W^+\rightarrow \mu^+\nu_{\mu}$ and (d) $W^-\rightarrow \mu^-\overline{\nu}_{\mu}$, inclusive over all $\eta$ regions, and using the CT18 PDF set. In the bottom panels, the darker points represent the post-fit ratio of data to MC, while the lighter points indicate the ratio before the fit. The hatched band represents the total uncertainty of the data.

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: : Difference $\Delta \mW$ between the $W$-boson mass measured using the (a) \ptl and (b) \mt distribution fit ranges indicated in the figure and the nominal fit range. The nominal ranges are $30<\ptl<50$~\GeV and $60<\mt<100$~\GeV, respectively. The outer dashed lines indicate the total measurement uncertainty for the nominal range. Results are shown for the combined fit over all categories, and for the CT18 PDF set.

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: : The ten nuisance parameters inducing the largest shifts on the fitted value of \mW in the combined PLH fits, using the (a) \ptl and (b) \mt distributions and the CT18 PDF set. For a given NP $\theta$, the shift is defined as the product of its post-fit value $\hat \theta$ and its pre-fit impact on \mW. The points, which are plotted according to the bottom horizontal scale, show $\hat \theta$ for each of the nuisance parameters. The error bars show the corresponding post-fit uncertainties, $\sigma_{\hat\theta}$. The nuisance parameters are ranked according to the shift induced on \mW, the NPs with the largest shifts at the top.

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: : (a) Present measured value of \mW, compared to SM prediction from the global electroweak fit~\cite{deBlas:2021wap}, and to the measurements of LEP~\cite{ALEPH:2013dgf}, Tevatron~\cite{Aaltonen:2012bp, D0:2013jba} and the LHC~\cite{STDM-2014-18, LHCb:2021bjt}. (b) The 68\% and 95\% confidence level contours of the \mW and $m_{t}$ indirect determinations from the global electroweak fit~\cite{Haller:2018nnx}, compared to the 68\% and 95\% confidence-level contours of the present ATLAS measurement of \mW, the ATLAS measurement of $m_H$~\cite{ATLAS:2023oaq} and the LHC measurement of $m_t$~\cite{CMS:2023wnd}.

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: : Overview of the \GW PLH fit results in all categories for the (a) \ptl and (b) \mt distributions, with the CT18 PDF set. The points labelled as `Combination' correspond to the result of a joint PLH fit to all categories.

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: : Difference $\Delta \GW$ between the $W$-boson width measured using the (a) \ptl and (b) \mt distribution fit ranges indicated in the figure and the nominal fit range. The nominal ranges are $30<\ptl<50$~\GeV and $60<\mt<100$~\GeV, respectively. The outer dashed lines indicate the total measurement uncertainty for the nominal range. Results are shown for the combined fit over all categories, and for the CT18 PDF set.

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: : The ten nuisance parameters inducing the largest shifts on the fitted value of \GW in the combined PLH fits, using the (a) \ptl and (b) \mt distributions and the CT18 PDF set. For a given NP $\theta$, the shift is defined as the product of its post-fit value $\hat \theta$ and its pre-fit impact on \GW. The points, which are plotted according to the bottom horizontal scale, show $\hat \theta$ for each of the nuisance parameters. The error bars show the corresponding post-fit uncertainties, $\sigma_{\hat\theta}$. The nuisance parameters are ranked according to the shift induced on \GW, the NPs with the largest shifts at the top.

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: : Post-fit distributions of \mt with data and MC for (a) $W^+\rightarrow e^+\nu_e$, (b) $W^-\rightarrow e^-\overline{\nu}_e$, (c) $W^+\rightarrow \mu^+\nu_{\mu}$ and (d) $W^-\rightarrow \mu^-\overline{\nu}_{\mu}$, inclusive over all $\eta$ regions, and using the CT18 PDF set. In the bottom panels, the darker points represent the post-fit ratio of data to MC, while the lighter points indicate the ratio before the fit. The hatched band represents the total uncertainty of the data.

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: : (a) Present measurement of \GW, compared to the SM prediction from the global electroweak fit~\cite{deBlas:2021wap}, and to the measurements of LEP~\cite{ALEPH:2013dgf} and Tevatron~\cite{thetevatronelectroweakworkinggroup2010combination}. (b) 68\% and 95\% CL uncertainty contours for the simultaneous determination of \mW and \GW using the CT18 PDF set and combining results from the \ptl and \mt distributions. The triangular marker represents the best fit, while the star corresponds to the SM prediction of Ref.~\cite{deBlas:2021wap}.