CMS-PAS-HIN-17-007

CMS-PAS-HIN-17-007
Constraints on nuclear parton distributions from W boson production in pPb collisions at ${\sqrt {s_{_{\mathrm {NN}}}}} =$ 8.16 TeV
CMS Collaboration
May 2018

Abstract: The production of W bosons has been measured in proton-lead collisions at a nucleon-nucleon center-of-mass energy of ${\sqrt {s_{_{\mathrm {NN}}}}} =$ 8.16 TeV. The measurement of W bosons is performed in the $\mathrm{W}\rightarrow\mu\nu_{\mu}$ channel, using a data sample with integrated luminosity of 173.4 $\pm$ 8.7 nb $^{-1}$ collected by the CMS experiment at the CERN LHC. The number of positive and negative W bosons is determined in the muon pseudorapidity region $\|\eta_{\mathrm{lab}}\| <$ 2.4 and transverse momentum $p_{\mathrm{T}}^{\mu} >$ 25 GeV/ $c$ . The W boson differential cross sections, muon charge asymmetry, and the ratios of W boson yields on the p-going over the Pb-going directions are reported as a function of the muon pseudorapidity in the center-of-mass frame. The measurements are compared to the predictions from theoretical calculations based on parton distribution functions (PDF). The results of this analysis favor PDF calculations including nuclear modifications and provide constraints on the nuclear PDF global fits.
Links: CDS record (PDF) ; CADI line (restricted) ; These preliminary results are superseded in this paper, PLB 800 (2020) 135048. The superseded preliminary plots can be found here.

Figures & Tables	Summary	Additional Figures	References	CMS Publications

Figures
png pdf	Figure 1: The missing transverse momentum ${{p_{\mathrm {T}}} ^\text {miss}}$ distribution for ${{\mathrm {W^+}}\to {\mu ^+} {\nu _ {\mu}}}$ events within the $-0.2 < {\eta ^{\mu}_{\textrm {CM}}} < 0.0$ (left) and $1.8 < {\eta ^{\mu}_{\textrm {CM}}} < 1.93$ (right) ranges. Unbinned fits to the data (black points) are performed with six contributions, stacked from bottom to top: ${{\mathrm {t}\overline {\mathrm {t}}}}$ (orange), ${{\mathrm {Z}/\gamma } \to {{\tau} {\overline {\tau}}}}$ (dark blue), ${{\mathrm {W^+}}\to {\overline {\tau}} {\nu _ {\tau}}}$ (red), ${{\mathrm {Z}/\gamma } \to {\mu ^+\mu ^-}}$ (green), QCD multijet (light blue) and ${{\mathrm {W^+}}\to {\mu ^+} {\nu _ {\mu}}}$ (yellow). The ${\eta ^{\mu}_{\textrm {CM}}}$ regions are defined such that the proton is moving towards positive pseudorapidity. Error bars represent statistical uncertainties. The lower panels display the data divided by the result of the fit, for each ${{p_{\mathrm {T}}} ^\text {miss}}$ bin.
png pdf	Figure 1-a: The missing transverse momentum ${{p_{\mathrm {T}}} ^\text {miss}}$ distribution for ${{\mathrm {W^+}}\to {\mu ^+} {\nu _ {\mu}}}$ events within the $-0.2 < {\eta ^{\mu}_{\textrm {CM}}} < 0.0$ range. Unbinned fits to the data (black points) are performed with six contributions, stacked from bottom to top: ${{\mathrm {t}\overline {\mathrm {t}}}}$ (orange), ${{\mathrm {Z}/\gamma } \to {{\tau} {\overline {\tau}}}}$ (dark blue), ${{\mathrm {W^+}}\to {\overline {\tau}} {\nu _ {\tau}}}$ (red), ${{\mathrm {Z}/\gamma } \to {\mu ^+\mu ^-}}$ (green), QCD multijet (light blue) and ${{\mathrm {W^+}}\to {\mu ^+} {\nu _ {\mu}}}$ (yellow). The ${\eta ^{\mu}_{\textrm {CM}}}$ regions are defined such that the proton is moving towards positive pseudorapidity. Error bars represent statistical uncertainties. The lower panel displays the data divided by the result of the fit, for each ${{p_{\mathrm {T}}} ^\text {miss}}$ bin.
png pdf	Figure 1-b: The missing transverse momentum ${{p_{\mathrm {T}}} ^\text {miss}}$ distribution for ${{\mathrm {W^+}}\to {\mu ^+} {\nu _ {\mu}}}$ events within the $1.8 < {\eta ^{\mu}_{\textrm {CM}}} < 1.93$ range. Unbinned fits to the data (black points) are performed with six contributions, stacked from bottom to top: ${{\mathrm {t}\overline {\mathrm {t}}}}$ (orange), ${{\mathrm {Z}/\gamma } \to {{\tau} {\overline {\tau}}}}$ (dark blue), ${{\mathrm {W^+}}\to {\overline {\tau}} {\nu _ {\tau}}}$ (red), ${{\mathrm {Z}/\gamma } \to {\mu ^+\mu ^-}}$ (green), QCD multijet (light blue) and ${{\mathrm {W^+}}\to {\mu ^+} {\nu _ {\mu}}}$ (yellow). The ${\eta ^{\mu}_{\textrm {CM}}}$ regions are defined such that the proton is moving towards positive pseudorapidity. Error bars represent statistical uncertainties. The lower panel displays the data divided by the result of the fit, for each ${{p_{\mathrm {T}}} ^\text {miss}}$ bin.
png pdf	Figure 2: Production cross sections for ${{\mathrm {W^+}}\to {\mu ^+} {\nu _ {\mu}}}$ (left) and ${{\mathrm {W^-}}\to {\mu ^-} {\overline {\nu}_ {\mu}}}$ (right), as a function of the muon pseudorapidity in the center-of-mass frame. The brackets represent the statistical and systematic uncertainties summed in quadrature, while the error bars show the statistical uncertainties only. The global luminosity uncertainty of $\pm$ 5.0% is not shown. Calculations using with CT14 PDF (red line), CT14+EPPS16 nPDF (green line) and CT14+nCTEQ15 nPDF (brown line), are also displayed, including their PDF uncertainty bands at 68% confidence interval. The bottom panels show the ratio of data (black points), CT14+EPPS16 (green line) and CT14+nCTEQ15 (brown line) with respect to CT14.
png pdf	Figure 2-a: Production cross sections for ${{\mathrm {W^+}}\to {\mu ^+} {\nu _ {\mu}}}$ , as a function of the muon pseudorapidity in the center-of-mass frame. The brackets represent the statistical and systematic uncertainties summed in quadrature, while the error bars show the statistical uncertainties only. The global luminosity uncertainty of $\pm$ 5.0% is not shown. Calculations using with CT14 PDF (red line), CT14+EPPS16 nPDF (green line) and CT14+nCTEQ15 nPDF (brown line), are also displayed, including their PDF uncertainty bands at 68% confidence interval. The bottom panel shows the ratio of data (black points), CT14+EPPS16 (green line) and CT14+nCTEQ15 (brown line) with respect to CT14.
png pdf	Figure 2-b: Production cross sections for ${{\mathrm {W^-}}\to {\mu ^-} {\overline {\nu}_ {\mu}}}$ , as a function of the muon pseudorapidity in the center-of-mass frame. The brackets represent the statistical and systematic uncertainties summed in quadrature, while the error bars show the statistical uncertainties only. The global luminosity uncertainty of $\pm$ 5.0% is not shown. Calculations using with CT14 PDF (red line), CT14+EPPS16 nPDF (green line) and CT14+nCTEQ15 nPDF (brown line), are also displayed, including their PDF uncertainty bands at 68% confidence interval. The bottom panel shows the ratio of data (black points), CT14+EPPS16 (green line) and CT14+nCTEQ15 (brown line) with respect to CT14.
png pdf	Figure 3: Forward-backward ratios, $N_{{{\mu}}}(+ {\eta ^{\mu}_{\textrm {CM}}})/N_{{{\mu}}}(- {\eta ^{\mu}_{\textrm {CM}}})$ , for the positive (left) and negative (right) muons. The brackets represent the statistical and systematic uncertainties summed in quadrature, while the error bars show the statistical uncertainties only. Calculations using with CT14 PDF (red line), CT14+EPPS16 nPDF (green line) and CT14+nCTEQ15 nPDF (brown line), are also displayed, including their PDF uncertainty bands at 68% confidence interval.
png pdf	Figure 3-a: Forward-backward ratios, $N_{{{\mu}}}(+ {\eta ^{\mu}_{\textrm {CM}}})/N_{{{\mu}}}(- {\eta ^{\mu}_{\textrm {CM}}})$ , for the positive muons. The brackets represent the statistical and systematic uncertainties summed in quadrature, while the error bars show the statistical uncertainties only. Calculations using with CT14 PDF (red line), CT14+EPPS16 nPDF (green line) and CT14+nCTEQ15 nPDF (brown line), are also displayed, including their PDF uncertainty bands at 68% confidence interval.
png pdf	Figure 3-b: Forward-backward ratios, $N_{{{\mu}}}(+ {\eta ^{\mu}_{\textrm {CM}}})/N_{{{\mu}}}(- {\eta ^{\mu}_{\textrm {CM}}})$ , for the negative muons. The brackets represent the statistical and systematic uncertainties summed in quadrature, while the error bars show the statistical uncertainties only. Calculations using with CT14 PDF (red line), CT14+EPPS16 nPDF (green line) and CT14+nCTEQ15 nPDF (brown line), are also displayed, including their PDF uncertainty bands at 68% confidence interval.
png pdf	Figure 4: The forward-backward ratio of all muons, $N_{{\mu}}(+ {\eta ^{\mu}_{\textrm {CM}}})/N_{{\mu}}(- {\eta ^{\mu}_{\textrm {CM}}})$ , as a function of ${\eta ^{\mu}_{\textrm {CM}}}$ . The brackets represent the statistical and systematic uncertainties summed in quadrature, while the error bars show the statistical uncertainties only. Calculations using with CT14 PDF (red line), CT14+EPPS16 nPDF (green line) and CT14+nCTEQ15 nPDF (brown line), are also displayed, including their PDF uncertainty bands at 68% confidence interval.
png pdf	Figure 5: Muon charge asymmetry, $(N_{{{\mu}}}^{+} - N_{{{\mu}}}^{-})/(N_{{{\mu}}}^{+} + N_{{{\mu}}}^{-})$ , as a function of the muon pseudorapidity in the center-of-mass frame. The brackets represent the statistical and systematic uncertainties summed in quadrature, while the error bars show the statistical uncertainties only. Calculations using with CT14 PDF (red line), CT14+EPPS16 nPDF (green line) and CT14+nCTEQ15 nPDF (brown line), are also displayed, including their PDF uncertainty bands at 68% confidence interval.
png pdf	Figure 6: Comparison of the muon charge asymmetry measured at 8.16 TeV (black points) and at 5.02 TeV [12] (blue squares). The muon pseudorapidity has been shifted according to ${{\eta ^{\mu}_{\textrm {ref}}} = {\eta ^{\mu}_{\textrm {CM}}} \pm \textrm {ln} (8.16~\mathrm{TeV} / {\sqrt {s_{_{\text {NN}}}}} )}$ . The brackets represent the statistical and systematic uncertainties summed in quadrature, while the error bars show the statistical uncertainties only. Calculations using with CT14+EPPS16 nPDF at 8.16 TeV (green line) and at 5.02 TeV (brown line), are also displayed, including their PDF uncertainty bands at 68% confidence interval.
png pdf	Figure 7: Distribution of the $\chi ^2$ /ndf values from the comparison of data (absolute cross sections) and theoretical calculations, for the CT14, nCTEQ15 and EPPS16 individual sets. The vertical dashed lines represent the prediction corresponding to the central set of CT14, nCTEQ15, and EPPS16.

Tables
png pdf	Table 1: Maximum uncertainty of the measured observables as a function of ${\eta ^{\mu}_{\textrm {CM}}}$ determined for each category. The uncertainties of the cross sections are relative while for the asymmetries are absolute. The global luminosity uncertainty of $\pm$ 5.0% is not included in the total systematic uncertainty of the cross sections.
png pdf	Table 2: Results of the $\chi ^{2}$ statistical test between the measurements and the theory calculations from the CT14 PDF, CT14+EPPS16 nPDF and CT14+nCTEQ15 nPDF calculations. The value of the $\chi ^{2}$ , the number of degrees of freedom (ndf) and the $\chi ^{2}$ probability (Prob.), are presented for the W differential cross sections, the muon charge asymmetry, the charged muon forward-backward ratios, and the forward-backward ratio of all muons, respectively.

Summary

A measurement of W boson production in pPb collisions at

${\sqrt {s_{_{\mathrm {NN}}}}} =$ 8.16 TeV is reported, using the muon decay channel for muons with

${p_{\mathrm{T}}}$ greater than 25 GeV/

$c$ and

$|{{\eta_{\textrm{lab}}} }| <$ 2.4. The absolute differential production cross sections for positive and negative

$\mathrm{W} \to\mu\nu_{\mu}$ decays, the muon charge asymmetry and the muon forward-backward ratios, are measured as a function of the muon pseudorapidity in the center-of-mass frame, in the range

${\eta^{\mu}_{\textrm{CM}}} \in [-2.86, 1.93]$ .

The measurements are compared to theoretical predictions assuming both proton PDF (CT14) and nuclear PDF (CT14+EPPS16, CT14+nCTEQ15) sets. The absolute cross sections and the forward-backward asymmetries exhibit significant deviations from the CT14 case, revealing nuclear modifications of the PDFs unambiguously for the first time in the production of weak bosons in nuclear collisions. On the contrary, both the CT14+EPPS16 and the CT14+nCTEQ15 calculations show a good overall agreement with data, though the data favors the former global fit. In the latter case, nevertheless, only the individual sets which exhibit the smallest nuclear PDF modifications at small values of

$x$ (in the shadowing region) turn out to be compatible with experimental measurements. The small experimental uncertainties reported in the measurements will enable a significant reduction of the current uncertainties of the quark and antiquark nPDFs, in the range

$10^{-3}$ -

$10^{-1}$ .

Additional Figures
png pdf	Additional Figure 1: Comparison of the production cross section for $\mathrm {W}^{-}\rightarrow \mu ^{-}\bar{\nu}_{\mu}$ (left) and $\mathrm {W}^{+}\rightarrow \mu ^{+}\nu _{\mu}$ (right) measured at 8.16 TeV (black points) and at 5.02 TeV [Phys. Lett. B 750 (2015) 565] (blue squares). The brackets represent the statistical and systematic uncertainties summed in quadrature, while the error bars show the statistical uncertainties only. The global luminosity uncertainty of $\pm$ 5.0% for the data at 8.16 TeV and of $\pm$ 3.5% for the data at 5.02 TeV are not shown. Calculations using with CT14+EPPS16 nPDF [Eur. Phys. J. C 77, 163 (2017)] at 8.16 TeV (green line) and at 5.02 TeV (brown line), are also displayed, including their PDF uncertainty bands at 68% confidence interval.
png pdf	Additional Figure 1-a: Comparison of the production cross section for $\mathrm {W}^{-}\rightarrow \mu ^{-}\bar{\nu}_{\mu}$ measured at 8.16 TeV (black points) and at 5.02 TeV [Phys. Lett. B 750 (2015) 565] (blue squares). The brackets represent the statistical and systematic uncertainties summed in quadrature, while the error bars show the statistical uncertainties only. The global luminosity uncertainty of $\pm$ 5.0% for the data at 8.16 TeV and of $\pm$ 3.5% for the data at 5.02 TeV are not shown. Calculations using with CT14+EPPS16 nPDF [Eur. Phys. J. C 77, 163 (2017)] at 8.16 TeV (green line) and at 5.02 TeV (brown line), are also displayed, including their PDF uncertainty bands at 68% confidence interval.
png pdf	Additional Figure 1-b: Comparison of the production cross section for $\mathrm {W}^{+}\rightarrow \mu ^{+}\nu _{\mu}$ measured at 8.16 TeV (black points) and at 5.02 TeV [Phys. Lett. B 750 (2015) 565] (blue squares). The brackets represent the statistical and systematic uncertainties summed in quadrature, while the error bars show the statistical uncertainties only. The global luminosity uncertainty of $\pm$ 5.0% for the data at 8.16 TeV and of $\pm$ 3.5% for the data at 5.02 TeV are not shown. Calculations using with CT14+EPPS16 nPDF [Eur. Phys. J. C 77, 163 (2017)] at 8.16 TeV (green line) and at 5.02 TeV (brown line), are also displayed, including their PDF uncertainty bands at 68% confidence interval.
png pdf	Additional Figure 2: Comparison of the muon charge asymmetry measured at 8.16 TeV (black points) and at 5.02 TeV [Phys. Lett. B 750 (2015) 565] (blue squares). The brackets represent the statistical and systematic uncertainties summed in quadrature, while the error bars show the statistical uncertainties only. Calculations using with CT14+EPPS16 nPDF [Eur. Phys. J. C 77, 163 (2017)] at 8.16 TeV (green line) and at 5.02 TeV (brown line), are also displayed, including their PDF uncertainty bands at 68% confidence interval.
png pdf	Additional Figure 3: Comparison of the production cross section for $\mathrm {W}^{-}\rightarrow \mu ^{-}\bar{\nu}_{\mu}$ measured at 8.16 TeV (black points) and at 5.02 TeV [Phys. Lett. B 750 (2015) 565] (blue squares). The comparison is presented in two muon pseudorapidity regions: $\eta _{\mathrm {CM}} <$ 0 (left plot) and $\eta _{\mathrm {CM}} >$ 0 (right plot). The brackets represent the statistical and systematic uncertainties summed in quadrature, while the error bars show the statistical uncertainties only. The global luminosity uncertainty of $\pm$ 5.0% for the data at 8.16 TeV and of $\pm$ 3.5% for the data at 5.02 TeV are not shown.
png pdf	Additional Figure 3-a: Comparison of the production cross section for $\mathrm {W}^{-}\rightarrow \mu ^{-}\bar{\nu}_{\mu}$ measured at 8.16 TeV (black points) and at 5.02 TeV [Phys. Lett. B 750 (2015) 565] (blue squares). The comparison is presented in pseudorapidity regions $\eta _{\mathrm {CM}} <$ 0. The brackets represent the statistical and systematic uncertainties summed in quadrature, while the error bars show the statistical uncertainties only. The global luminosity uncertainty of $\pm$ 5.0% for the data at 8.16 TeV and of $\pm$ 3.5% for the data at 5.02 TeV are not shown.
png pdf	Additional Figure 3-b: Comparison of the production cross section for $\mathrm {W}^{-}\rightarrow \mu ^{-}\bar{\nu}_{\mu}$ measured at 8.16 TeV (black points) and at 5.02 TeV [Phys. Lett. B 750 (2015) 565] (blue squares). The comparison is presented in pseudorapidity regions $\eta _{\mathrm {CM}} >$ 0. The brackets represent the statistical and systematic uncertainties summed in quadrature, while the error bars show the statistical uncertainties only. The global luminosity uncertainty of $\pm$ 5.0% for the data at 8.16 TeV and of $\pm$ 3.5% for the data at 5.02 TeV are not shown.
png pdf	Additional Figure 4: Comparison of the production cross section for $\mathrm {W}^{+}\rightarrow \mu ^{+}\nu _{\mu}$ measured at 8.16 TeV (black points) and at 5.02 TeV [Phys. Lett. B 750 (2015) 565] (blue squares). The comparison is presented in two muon pseudorapidity regions: $\eta _{\mathrm {CM}} <$ 0 (left plot) and $\eta _{\mathrm {CM}} >$ 0 (right plot). The brackets represent the statistical and systematic uncertainties summed in quadrature, while the error bars show the statistical uncertainties only. The global luminosity uncertainty of $\pm$ 5.0% for the data at 8.16 TeV and of $\pm$ 3.5% for the data at 5.02 TeV are not shown.
png pdf	Additional Figure 4-a: Comparison of the production cross section for $\mathrm {W}^{+}\rightarrow \mu ^{+}\nu _{\mu}$ measured at 8.16 TeV (black points) and at 5.02 TeV [Phys. Lett. B 750 (2015) 565] (blue squares). The comparison is presented in muon pseudorapidity region $\eta _{\mathrm {CM}} <$ 0. The brackets represent the statistical and systematic uncertainties summed in quadrature, while the error bars show the statistical uncertainties only. The global luminosity uncertainty of $\pm$ 5.0% for the data at 8.16 TeV and of $\pm$ 3.5% for the data at 5.02 TeV are not shown.
png pdf	Additional Figure 4-b: Comparison of the production cross section for $\mathrm {W}^{+}\rightarrow \mu ^{+}\nu _{\mu}$ measured at 8.16 TeV (black points) and at 5.02 TeV [Phys. Lett. B 750 (2015) 565] (blue squares). The comparison is presented in muon pseudorapidity region $\eta _{\mathrm {CM}} >$ 0. The brackets represent the statistical and systematic uncertainties summed in quadrature, while the error bars show the statistical uncertainties only. The global luminosity uncertainty of $\pm$ 5.0% for the data at 8.16 TeV and of $\pm$ 3.5% for the data at 5.02 TeV are not shown.
png pdf	Additional Figure 5: Comparison of the muon charge asymmetry measured at 8.16 TeV (black points) and at 5.02 TeV [Phys. Lett. B 750 (2015) 565] (blue squares). The muon pseudorapidity has been shifted according to ${{\eta ^{\mu}_{\textrm {ref}}} = {\eta ^{\mu}_{\textrm {CM}}} \pm \textrm {ln}\left (8.16~\text{TeV}/ {\sqrt {s_{_{\text {NN}}}}} \right)}$ . The brackets represent the statistical and systematic uncertainties summed in quadrature, while the error bars show the statistical uncertainties only.
png pdf	Additional Figure 6: Comparison of the production cross section for $\mathrm {W}^{-}\rightarrow \mu ^{-}\bar{\nu}_{\mu}$ measured at 8.16 TeV (black points) and at 5.02 TeV [Phys. Lett. B 750 (2015) 565] (blue squares). The comparison is presented in two muon pseudorapidity regions: $\eta _{\mathrm {CM}} <$ 0 (left plot) and $\eta _{\mathrm {CM}} >$ 0 (right plot). The brackets represent the statistical and systematic uncertainties summed in quadrature, while the error bars show the statistical uncertainties only. The global luminosity uncertainty of $\pm$ 5.0% for the data at 8.16 TeV and of $\pm$ 3.5% for the data at 5.02 TeV are not shown. Calculations using with CT14+EPPS16 nPDF [Eur. Phys. J. C 77, 163 (2017)] at 8.16 TeV (green line) and at 5.02 TeV (brown line), are also displayed, including their PDF uncertainty bands at 68% confidence interval.
png pdf	Additional Figure 6-a: Comparison of the production cross section for $\mathrm {W}^{-}\rightarrow \mu ^{-}\bar{\nu}_{\mu}$ measured at 8.16 TeV (black points) and at 5.02 TeV [Phys. Lett. B 750 (2015) 565] (blue squares). The comparison is presented in muon pseudorapidity region $\eta _{\mathrm {CM}} <$ 0. The brackets represent the statistical and systematic uncertainties summed in quadrature, while the error bars show the statistical uncertainties only. The global luminosity uncertainty of $\pm$ 5.0% for the data at 8.16 TeV and of $\pm$ 3.5% for the data at 5.02 TeV are not shown. Calculations using with CT14+EPPS16 nPDF [Eur. Phys. J. C 77, 163 (2017)] at 8.16 TeV (green line) and at 5.02 TeV (brown line), are also displayed, including their PDF uncertainty bands at 68% confidence interval.
png pdf	Additional Figure 6-b: Comparison of the production cross section for $\mathrm {W}^{-}\rightarrow \mu ^{-}\bar{\nu}_{\mu}$ measured at 8.16 TeV (black points) and at 5.02 TeV [Phys. Lett. B 750 (2015) 565] (blue squares). The comparison is presented in muon pseudorapidity region $\eta _{\mathrm {CM}} >$ 0. The brackets represent the statistical and systematic uncertainties summed in quadrature, while the error bars show the statistical uncertainties only. The global luminosity uncertainty of $\pm$ 5.0% for the data at 8.16 TeV and of $\pm$ 3.5% for the data at 5.02 TeV are not shown. Calculations using with CT14+EPPS16 nPDF [Eur. Phys. J. C 77, 163 (2017)] at 8.16 TeV (green line) and at 5.02 TeV (brown line), are also displayed, including their PDF uncertainty bands at 68% confidence interval.
png pdf	Additional Figure 7: Comparison of the production cross section for $\mathrm {W}^{+}\rightarrow \mu ^{+}\nu _{\mu}$ measured at 8.16 TeV (black points) and at 5.02 TeV [Phys. Lett. B 750 (2015) 565] (blue squares). The comparison is presented in two muon pseudorapidity regions: $\eta _{\mathrm {CM}} <$ 0 (left plot) and $\eta _{\mathrm {CM}} >$ 0 (right plot). The brackets represent the statistical and systematic uncertainties summed in quadrature, while the error bars show the statistical uncertainties only. The global luminosity uncertainty of $\pm$ 5.0% for the data at 8.16 TeV and of $\pm$ 3.5% for the data at 5.02 TeV are not shown. Calculations using with CT14+EPPS16 nPDF [Eur. Phys. J. C 77, 163 (2017)] at 8.16 TeV (green line) and at 5.02 TeV (brown line), are also displayed, including their PDF uncertainty bands at 68% confidence interval.
png pdf	Additional Figure 7-a: Comparison of the production cross section for $\mathrm {W}^{+}\rightarrow \mu ^{+}\nu _{\mu}$ measured at 8.16 TeV (black points) and at 5.02 TeV [Phys. Lett. B 750 (2015) 565] (blue squares). The comparison is presented in muon pseudorapidity region $\eta _{\mathrm {CM}} <$ 0. The brackets represent the statistical and systematic uncertainties summed in quadrature, while the error bars show the statistical uncertainties only. The global luminosity uncertainty of $\pm$ 5.0% for the data at 8.16 TeV and of $\pm$ 3.5% for the data at 5.02 TeV are not shown. Calculations using with CT14+EPPS16 nPDF [Eur. Phys. J. C 77, 163 (2017)] at 8.16 TeV (green line) and at 5.02 TeV (brown line), are also displayed, including their PDF uncertainty bands at 68% confidence interval.
png pdf	Additional Figure 7-b: Comparison of the production cross section for $\mathrm {W}^{+}\rightarrow \mu ^{+}\nu _{\mu}$ measured at 8.16 TeV (black points) and at 5.02 TeV [Phys. Lett. B 750 (2015) 565] (blue squares). The comparison is presented in muon pseudorapidity region $\eta _{\mathrm {CM}} >$ 0. The brackets represent the statistical and systematic uncertainties summed in quadrature, while the error bars show the statistical uncertainties only. The global luminosity uncertainty of $\pm$ 5.0% for the data at 8.16 TeV and of $\pm$ 3.5% for the data at 5.02 TeV are not shown. Calculations using with CT14+EPPS16 nPDF [Eur. Phys. J. C 77, 163 (2017)] at 8.16 TeV (green line) and at 5.02 TeV (brown line), are also displayed, including their PDF uncertainty bands at 68% confidence interval.
png pdf	Additional Figure 8: Distribution of the $\chi ^2$ /ndf values from the comparison of data (muon charge asymmetry) and theoretical calculations, for the CT14 [Phys. Rev. D 93, 033006 (2016)], nCTEQ15 [Phys. Rev. D 93, 085037 (2016)] and EPPS16 [Eur. Phys. J. C 77, 163 (2017)] individual sets. The vertical dashed lines represent the prediction corresponding to the central set of CT14, nCTEQ15, and EPPS16.
png pdf	Additional Figure 9: Distribution of the $\chi ^2$ /ndf values from the comparison of data (muon forward-backward ratio) and theoretical calculations, for the CT14 [Phys. Rev. D 93, 033006 (2016)], nCTEQ15 [Phys. Rev. D 93, 085037 (2016)] and EPPS16 [Eur. Phys. J. C 77, 163 (2017)] individual sets. The vertical dashed lines represent the prediction corresponding to the central set of CT14, nCTEQ15, and EPPS16.
png pdf	Additional Figure 10: Distribution of the $\chi ^2$ /ndf values from the comparison of data (forward-backward ratio of all muons) and theoretical calculations, for the CT14 [Phys. Rev. D 93, 033006 (2016)], nCTEQ15 [Phys. Rev. D 93, 085037 (2016)] and EPPS16 [Eur. Phys. J. C 77, 163 (2017)] individual sets. The vertical dashed lines represent the prediction corresponding to the central set of CT14, nCTEQ15, and EPPS16.
png pdf	Additional Figure 11: Distribution of the simulated Bjorken x in the Pb ion as a function of the muon pseudorapidity for $\mathrm {W}^{-}\rightarrow \mu ^{-}\bar{\nu}_{\mu}$ (left) and $\mathrm {W}^{+}\rightarrow \mu ^{+}\nu _{\mu}$ (right) generated at 8.16 TeV. The W boson production have been simulated using the NLO generator POWHEG v2 with the POWHEG BOX W.ew.BMNNP using the CT14+EPPS16 nPDF [Eur. Phys. J. C 77, 163 (2017)].
png pdf	Additional Figure 11-a: Distribution of the simulated Bjorken x in the Pb ion as a function of the muon pseudorapidity for $\mathrm {W}^{-}\rightarrow \mu ^{-}\bar{\nu}_{\mu}$ generated at 8.16 TeV. The W boson production have been simulated using the NLO generator POWHEG v2 with the POWHEG BOX W.ew.BMNNP using the CT14+EPPS16 nPDF [Eur. Phys. J. C 77, 163 (2017)].
png pdf	Additional Figure 11-b: Distribution of the simulated Bjorken x in the Pb ion as a function of the muon pseudorapidity for $\mathrm {W}^{+}\rightarrow \mu ^{+}\nu _{\mu}$ generated at 8.16 TeV. The W boson production have been simulated using the NLO generator POWHEG v2 with the POWHEG BOX W.ew.BMNNP using the CT14+EPPS16 nPDF [Eur. Phys. J. C 77, 163 (2017)].
png pdf	Additional Figure 12: Correlation matrix of the W boson production cross section measurements. The statistical and systematic uncertainties have been included except for the luminosity uncertainty. The black lines are used to distinguish the different bins of muon charge which are ordered from top to bottom as: Minus-Minus, Minus-Plus, Plus-Minus and Plus-Plus.

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