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| CMS-SMP-18-013 ; CERN-EP-2021-206 | ||
| Measurements of the associated production of a W boson and a charm quark in proton-proton collisions at $ \sqrt{s}= $ 8 TeV | ||
| CMS Collaboration | ||
| 2 December 2021 | ||
| Eur. Phys. J. C 82 (2022) 1094 | ||
| Abstract: Measurements of the associated production of a W boson and a charm (c) quark in proton-proton collisions at a centre-of-mass energy of 8 TeV are reported. The analysis uses a data sample corresponding to a total integrated luminosity of 19.7 fb$ ^{-1} $ collected by the CMS detector at the LHC. The W bosons are identified through their leptonic decays to an electron or a muon, and a neutrino. Charm quark jets are selected using distinctive signatures of charm hadron decays. The product of the cross section and branching fraction $ \sigma(\mathrm{p}\mathrm{p} \to \mathrm{W} + \mathrm{c} + \mathrm{X}) \mathcal {B}(\mathrm{W} \to \ell \nu) $, where $ \ell = \mathrm{e} $ or $ \mu $, and the cross section ratio $ \sigma(\mathrm{p}\mathrm{p} \to {\mathrm{W^+} + \overline{\mathrm{c}} + \mathrm{X}}) / \sigma(\mathrm{p}\mathrm{p} \to {\mathrm{W^-} + \mathrm{c} + \mathrm{X}}) $ are measured in a fiducial volume and differentially as functions of the pseudorapidity and of the transverse momentum of the lepton from the W boson decay. The results are compared with theoretical predictions. The impact of these measurements on the determination of the strange quark distribution is assessed. | ||
| Links: e-print arXiv:2112.00895 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; | ||
| Figures & Tables | Summary | Additional Figures | References | CMS Publications |
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| Figures | |
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Figure 1:
Leading order diagrams for the associated production of a W boson and a charm (anti)quark. |
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Figure 2:
Distributions after OS-SS subtraction of the impact parameter significance, IPS, (left) and $ p_{\mathrm{T}} $ (right), of the muon inside the $ \mathrm{c}\text{ jet} $ for events in the SL sample, summing up the contributions of the two W boson decay channels. The IPS distribution is shown after all selection requirements except the one on this variable. The last bin of the distribution includes all events with $ \text{IPS} > $ 7.5. The $ p_{\mathrm{T}} $ distribution includes the selection requirement $ \text{IPS} > $ 1.0 for the $ \mathrm{W} \to \mu\nu $ channel. The contributions of the various processes are estimated with the simulated samples. Vertical bars on data points represent statistical uncertainty in the data. The hatched areas represent the sum in quadrature of statistical and systematic uncertainties in the MC simulation. The ratio of data to simulation is shown in the lower panels. The uncertainty band in the ratio includes the statistical uncertainty in the data, and the statistical and systematic uncertainties in the MC simulation. |
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Figure 2-a:
Distributions after OS-SS subtraction of the impact parameter significance, IPS, (left) and $ p_{\mathrm{T}} $ (right), of the muon inside the $ \mathrm{c}\text{ jet} $ for events in the SL sample, summing up the contributions of the two W boson decay channels. The IPS distribution is shown after all selection requirements except the one on this variable. The last bin of the distribution includes all events with $ \text{IPS} > $ 7.5. The $ p_{\mathrm{T}} $ distribution includes the selection requirement $ \text{IPS} > $ 1.0 for the $ \mathrm{W} \to \mu\nu $ channel. The contributions of the various processes are estimated with the simulated samples. Vertical bars on data points represent statistical uncertainty in the data. The hatched areas represent the sum in quadrature of statistical and systematic uncertainties in the MC simulation. The ratio of data to simulation is shown in the lower panels. The uncertainty band in the ratio includes the statistical uncertainty in the data, and the statistical and systematic uncertainties in the MC simulation. |
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Figure 2-b:
Distributions after OS-SS subtraction of the impact parameter significance, IPS, (left) and $ p_{\mathrm{T}} $ (right), of the muon inside the $ \mathrm{c}\text{ jet} $ for events in the SL sample, summing up the contributions of the two W boson decay channels. The IPS distribution is shown after all selection requirements except the one on this variable. The last bin of the distribution includes all events with $ \text{IPS} > $ 7.5. The $ p_{\mathrm{T}} $ distribution includes the selection requirement $ \text{IPS} > $ 1.0 for the $ \mathrm{W} \to \mu\nu $ channel. The contributions of the various processes are estimated with the simulated samples. Vertical bars on data points represent statistical uncertainty in the data. The hatched areas represent the sum in quadrature of statistical and systematic uncertainties in the MC simulation. The ratio of data to simulation is shown in the lower panels. The uncertainty band in the ratio includes the statistical uncertainty in the data, and the statistical and systematic uncertainties in the MC simulation. |
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Figure 3:
Distributions after OS-SS subtraction of the secondary-vertex displacement significance (left) and corrected secondary-vertex mass (right). For each distribution all selection requirements are applied except the one on the displayed variable. The last bin of each plot includes all events beyond the bin. The contributions from all processes are estimated with the simulated samples. Vertical bars on data points represent the statistical uncertainty in the data. The hatched areas represent the sum in quadrature of statistical and systematic uncertainties in the MC simulation. The ratio of data to simulation is shown in the lower panels. The uncertainty band in the ratio includes the statistical uncertainty in the data, and the statistical and systematic uncertainties in the MC simulation. |
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Figure 3-a:
Distributions after OS-SS subtraction of the secondary-vertex displacement significance (left) and corrected secondary-vertex mass (right). For each distribution all selection requirements are applied except the one on the displayed variable. The last bin of each plot includes all events beyond the bin. The contributions from all processes are estimated with the simulated samples. Vertical bars on data points represent the statistical uncertainty in the data. The hatched areas represent the sum in quadrature of statistical and systematic uncertainties in the MC simulation. The ratio of data to simulation is shown in the lower panels. The uncertainty band in the ratio includes the statistical uncertainty in the data, and the statistical and systematic uncertainties in the MC simulation. |
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Figure 3-b:
Distributions after OS-SS subtraction of the secondary-vertex displacement significance (left) and corrected secondary-vertex mass (right). For each distribution all selection requirements are applied except the one on the displayed variable. The last bin of each plot includes all events beyond the bin. The contributions from all processes are estimated with the simulated samples. Vertical bars on data points represent the statistical uncertainty in the data. The hatched areas represent the sum in quadrature of statistical and systematic uncertainties in the MC simulation. The ratio of data to simulation is shown in the lower panels. The uncertainty band in the ratio includes the statistical uncertainty in the data, and the statistical and systematic uncertainties in the MC simulation. |
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Figure 4:
Comparison of the theoretical predictions for $ \sigma(\mathrm{W}\,\mathrm{c}) $ (left) and $ \sigma(\mathrm{W^+}\,\overline{\mathrm{c}})/\sigma(\mathrm{W^-}\,\mathrm{c}) $ (right) computed with MCFM and several sets of PDFs with the current experimental measurements. |
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Figure 4-a:
Comparison of the theoretical predictions for $ \sigma(\mathrm{W}\,\mathrm{c}) $ (left) and $ \sigma(\mathrm{W^+}\,\overline{\mathrm{c}})/\sigma(\mathrm{W^-}\,\mathrm{c}) $ (right) computed with MCFM and several sets of PDFs with the current experimental measurements. |
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Figure 4-b:
Comparison of the theoretical predictions for $ \sigma(\mathrm{W}\,\mathrm{c}) $ (left) and $ \sigma(\mathrm{W^+}\,\overline{\mathrm{c}})/\sigma(\mathrm{W^-}\,\mathrm{c}) $ (right) computed with MCFM and several sets of PDFs with the current experimental measurements. |
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Figure 5:
Differential cross sections, $ \mathrm{d}\sigma(\mathrm{W}\,\mathrm{c})/\mathrm{d}|\eta^\ell| $ (left) and $ \mathrm{d}\sigma(\mathrm{W}\,\mathrm{c})/\mathrm{d}{p_{\mathrm{T}}^\ell} $ (right). The data points are the combination of the results with the four different samples: SL and SV samples in $ \mathrm{W} \to \mathrm{e}\nu $ and $ \mathrm{W} \to \mu\nu $ events. Theoretical predictions at NLO computed with MCFM and four different NLO PDF sets are also shown. Symbols showing the theoretical expectations are slightly displaced in the horizontal axis for better visibility. The error bars in the MCFM predictions include PDF, $ \alpha_\mathrm{S} $, and scale uncertainties. The inset in the right plot, $ \mathrm{d}\sigma(\mathrm{W}\,\mathrm{c})/\mathrm{d}{p_{\mathrm{T}}^\ell} $, zooms into the measurement-prediction comparison for the last bin, 100 $ < p_{\mathrm{T}}^{\ell} < $ 200 GeV. Predictions from MADGRAPH using the PDF set MSTW2008NNLO are also presented. |
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Figure 5-a:
Differential cross sections, $ \mathrm{d}\sigma(\mathrm{W}\,\mathrm{c})/\mathrm{d}|\eta^\ell| $ (left) and $ \mathrm{d}\sigma(\mathrm{W}\,\mathrm{c})/\mathrm{d}{p_{\mathrm{T}}^\ell} $ (right). The data points are the combination of the results with the four different samples: SL and SV samples in $ \mathrm{W} \to \mathrm{e}\nu $ and $ \mathrm{W} \to \mu\nu $ events. Theoretical predictions at NLO computed with MCFM and four different NLO PDF sets are also shown. Symbols showing the theoretical expectations are slightly displaced in the horizontal axis for better visibility. The error bars in the MCFM predictions include PDF, $ \alpha_\mathrm{S} $, and scale uncertainties. The inset in the right plot, $ \mathrm{d}\sigma(\mathrm{W}\,\mathrm{c})/\mathrm{d}{p_{\mathrm{T}}^\ell} $, zooms into the measurement-prediction comparison for the last bin, 100 $ < p_{\mathrm{T}}^{\ell} < $ 200 GeV. Predictions from MADGRAPH using the PDF set MSTW2008NNLO are also presented. |
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Figure 5-b:
Differential cross sections, $ \mathrm{d}\sigma(\mathrm{W}\,\mathrm{c})/\mathrm{d}|\eta^\ell| $ (left) and $ \mathrm{d}\sigma(\mathrm{W}\,\mathrm{c})/\mathrm{d}{p_{\mathrm{T}}^\ell} $ (right). The data points are the combination of the results with the four different samples: SL and SV samples in $ \mathrm{W} \to \mathrm{e}\nu $ and $ \mathrm{W} \to \mu\nu $ events. Theoretical predictions at NLO computed with MCFM and four different NLO PDF sets are also shown. Symbols showing the theoretical expectations are slightly displaced in the horizontal axis for better visibility. The error bars in the MCFM predictions include PDF, $ \alpha_\mathrm{S} $, and scale uncertainties. The inset in the right plot, $ \mathrm{d}\sigma(\mathrm{W}\,\mathrm{c})/\mathrm{d}{p_{\mathrm{T}}^\ell} $, zooms into the measurement-prediction comparison for the last bin, 100 $ < p_{\mathrm{T}}^{\ell} < $ 200 GeV. Predictions from MADGRAPH using the PDF set MSTW2008NNLO are also presented. |
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Figure 6:
Cross section ratio, $ R_{\mathrm{c}}^{\pm} $, as functions of $ |\eta^{\ell}| $ (left) and $ p_{\mathrm{T}}^{\ell} $ (right). The data points are the combination of the results from the SL and SV samples in $ \mathrm{W} \to \mathrm{e}\nu $ and $ \mathrm{W} \to \mu\nu $ events. Theoretical predictions at NLO computed with MCFM and four different NLO PDF sets are also shown. Symbols showing the theoretical expectations are slightly displaced in the horizontal axis for better visibility. The error bars in the MCFM predictions include PDF, $ \alpha_\mathrm{S} $, and scale uncertainties. Predictions from MADGRAPH using the PDF set MSTW2008NNLO are also presented. |
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Figure 6-a:
Cross section ratio, $ R_{\mathrm{c}}^{\pm} $, as functions of $ |\eta^{\ell}| $ (left) and $ p_{\mathrm{T}}^{\ell} $ (right). The data points are the combination of the results from the SL and SV samples in $ \mathrm{W} \to \mathrm{e}\nu $ and $ \mathrm{W} \to \mu\nu $ events. Theoretical predictions at NLO computed with MCFM and four different NLO PDF sets are also shown. Symbols showing the theoretical expectations are slightly displaced in the horizontal axis for better visibility. The error bars in the MCFM predictions include PDF, $ \alpha_\mathrm{S} $, and scale uncertainties. Predictions from MADGRAPH using the PDF set MSTW2008NNLO are also presented. |
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Figure 6-b:
Cross section ratio, $ R_{\mathrm{c}}^{\pm} $, as functions of $ |\eta^{\ell}| $ (left) and $ p_{\mathrm{T}}^{\ell} $ (right). The data points are the combination of the results from the SL and SV samples in $ \mathrm{W} \to \mathrm{e}\nu $ and $ \mathrm{W} \to \mu\nu $ events. Theoretical predictions at NLO computed with MCFM and four different NLO PDF sets are also shown. Symbols showing the theoretical expectations are slightly displaced in the horizontal axis for better visibility. The error bars in the MCFM predictions include PDF, $ \alpha_\mathrm{S} $, and scale uncertainties. Predictions from MADGRAPH using the PDF set MSTW2008NNLO are also presented. |
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Figure 7:
The strange quark distribution (upper left) and the strangeness suppression factor (upper right) as a function of $ x $ at the factorization scale of $ m^2_{\mathrm{W}} $. The corresponding relative total uncertainties are compared in the lower plots (strange quark distribution, lower left, and strangeness suppression factor, lower right). The results from the QCD analysis, shown as a filled area, use as input the combination of the inclusive deep inelastic scattering (DIS) cross sections [71], the CMS measurements of the lepton charge asymmetry in W boson production at $ \sqrt{s}= $ 7 and 8 TeV [72,73], and the CMS measurements of $ \mathrm{W}\,\mathrm{c} $ production at $ \sqrt{s}= $ 7 [5], 8 (this analysis) and 13 TeV [6]. The $ \mathrm{W}\,\mathrm{c} $ measurement at $ \sqrt{s}= $ 8 TeV is not used for the fit shown in hatched style. |
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Figure 7-a:
The strange quark distribution (upper left) and the strangeness suppression factor (upper right) as a function of $ x $ at the factorization scale of $ m^2_{\mathrm{W}} $. The corresponding relative total uncertainties are compared in the lower plots (strange quark distribution, lower left, and strangeness suppression factor, lower right). The results from the QCD analysis, shown as a filled area, use as input the combination of the inclusive deep inelastic scattering (DIS) cross sections [71], the CMS measurements of the lepton charge asymmetry in W boson production at $ \sqrt{s}= $ 7 and 8 TeV [72,73], and the CMS measurements of $ \mathrm{W}\,\mathrm{c} $ production at $ \sqrt{s}= $ 7 [5], 8 (this analysis) and 13 TeV [6]. The $ \mathrm{W}\,\mathrm{c} $ measurement at $ \sqrt{s}= $ 8 TeV is not used for the fit shown in hatched style. |
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Figure 7-b:
The strange quark distribution (upper left) and the strangeness suppression factor (upper right) as a function of $ x $ at the factorization scale of $ m^2_{\mathrm{W}} $. The corresponding relative total uncertainties are compared in the lower plots (strange quark distribution, lower left, and strangeness suppression factor, lower right). The results from the QCD analysis, shown as a filled area, use as input the combination of the inclusive deep inelastic scattering (DIS) cross sections [71], the CMS measurements of the lepton charge asymmetry in W boson production at $ \sqrt{s}= $ 7 and 8 TeV [72,73], and the CMS measurements of $ \mathrm{W}\,\mathrm{c} $ production at $ \sqrt{s}= $ 7 [5], 8 (this analysis) and 13 TeV [6]. The $ \mathrm{W}\,\mathrm{c} $ measurement at $ \sqrt{s}= $ 8 TeV is not used for the fit shown in hatched style. |
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Figure 7-c:
The strange quark distribution (upper left) and the strangeness suppression factor (upper right) as a function of $ x $ at the factorization scale of $ m^2_{\mathrm{W}} $. The corresponding relative total uncertainties are compared in the lower plots (strange quark distribution, lower left, and strangeness suppression factor, lower right). The results from the QCD analysis, shown as a filled area, use as input the combination of the inclusive deep inelastic scattering (DIS) cross sections [71], the CMS measurements of the lepton charge asymmetry in W boson production at $ \sqrt{s}= $ 7 and 8 TeV [72,73], and the CMS measurements of $ \mathrm{W}\,\mathrm{c} $ production at $ \sqrt{s}= $ 7 [5], 8 (this analysis) and 13 TeV [6]. The $ \mathrm{W}\,\mathrm{c} $ measurement at $ \sqrt{s}= $ 8 TeV is not used for the fit shown in hatched style. |
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Figure 7-d:
The strange quark distribution (upper left) and the strangeness suppression factor (upper right) as a function of $ x $ at the factorization scale of $ m^2_{\mathrm{W}} $. The corresponding relative total uncertainties are compared in the lower plots (strange quark distribution, lower left, and strangeness suppression factor, lower right). The results from the QCD analysis, shown as a filled area, use as input the combination of the inclusive deep inelastic scattering (DIS) cross sections [71], the CMS measurements of the lepton charge asymmetry in W boson production at $ \sqrt{s}= $ 7 and 8 TeV [72,73], and the CMS measurements of $ \mathrm{W}\,\mathrm{c} $ production at $ \sqrt{s}= $ 7 [5], 8 (this analysis) and 13 TeV [6]. The $ \mathrm{W}\,\mathrm{c} $ measurement at $ \sqrt{s}= $ 8 TeV is not used for the fit shown in hatched style. |
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Figure 8:
The strange quark distribution (left) and the strangeness suppression factor (right) as a function of $ x $ at the factorization scale of $ m^2_{\mathrm{W}} $. The results of the current analysis are shown together with those from the global NLO PDFs, ABMP16 and NNPDF3.1 in the upper plot, and CT18 and MSHT20 in the lower one. This QCD analysis uses as input the combination of the inclusive deep inelastic scattering (DIS) cross sections [71], the CMS measurements of the lepton charge asymmetry in W boson production at $ \sqrt{s}= $ 7 and 8 TeV [72,73], and the CMS measurements of $ \mathrm{W}\,\mathrm{c} $ production at $ \sqrt{s}= $ 7 [5], 8 (this analysis) and 13 TeV [6]. |
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Figure 8-a:
The strange quark distribution (left) and the strangeness suppression factor (right) as a function of $ x $ at the factorization scale of $ m^2_{\mathrm{W}} $. The results of the current analysis are shown together with those from the global NLO PDFs, ABMP16 and NNPDF3.1 in the upper plot, and CT18 and MSHT20 in the lower one. This QCD analysis uses as input the combination of the inclusive deep inelastic scattering (DIS) cross sections [71], the CMS measurements of the lepton charge asymmetry in W boson production at $ \sqrt{s}= $ 7 and 8 TeV [72,73], and the CMS measurements of $ \mathrm{W}\,\mathrm{c} $ production at $ \sqrt{s}= $ 7 [5], 8 (this analysis) and 13 TeV [6]. |
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Figure 8-b:
The strange quark distribution (left) and the strangeness suppression factor (right) as a function of $ x $ at the factorization scale of $ m^2_{\mathrm{W}} $. The results of the current analysis are shown together with those from the global NLO PDFs, ABMP16 and NNPDF3.1 in the upper plot, and CT18 and MSHT20 in the lower one. This QCD analysis uses as input the combination of the inclusive deep inelastic scattering (DIS) cross sections [71], the CMS measurements of the lepton charge asymmetry in W boson production at $ \sqrt{s}= $ 7 and 8 TeV [72,73], and the CMS measurements of $ \mathrm{W}\,\mathrm{c} $ production at $ \sqrt{s}= $ 7 [5], 8 (this analysis) and 13 TeV [6]. |
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Figure 8-c:
The strange quark distribution (left) and the strangeness suppression factor (right) as a function of $ x $ at the factorization scale of $ m^2_{\mathrm{W}} $. The results of the current analysis are shown together with those from the global NLO PDFs, ABMP16 and NNPDF3.1 in the upper plot, and CT18 and MSHT20 in the lower one. This QCD analysis uses as input the combination of the inclusive deep inelastic scattering (DIS) cross sections [71], the CMS measurements of the lepton charge asymmetry in W boson production at $ \sqrt{s}= $ 7 and 8 TeV [72,73], and the CMS measurements of $ \mathrm{W}\,\mathrm{c} $ production at $ \sqrt{s}= $ 7 [5], 8 (this analysis) and 13 TeV [6]. |
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Figure 8-d:
The strange quark distribution (left) and the strangeness suppression factor (right) as a function of $ x $ at the factorization scale of $ m^2_{\mathrm{W}} $. The results of the current analysis are shown together with those from the global NLO PDFs, ABMP16 and NNPDF3.1 in the upper plot, and CT18 and MSHT20 in the lower one. This QCD analysis uses as input the combination of the inclusive deep inelastic scattering (DIS) cross sections [71], the CMS measurements of the lepton charge asymmetry in W boson production at $ \sqrt{s}= $ 7 and 8 TeV [72,73], and the CMS measurements of $ \mathrm{W}\,\mathrm{c} $ production at $ \sqrt{s}= $ 7 [5], 8 (this analysis) and 13 TeV [6]. |
| Tables | |
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Table 1:
Summary of the selection requirements for the four analysis categories. |
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Table 2:
Simulated flavour composition (in %) of the SL sample after the selection summarized in Table 1 and OS-SS subtraction, for the electron and muon decay channels of the W boson. $ \mathrm{W} + {\mathrm{Q} \overline{\mathrm{Q}} } $ is the sum of the contributions of $ \mathrm{W} + \mathrm{c}\overline{\mathrm{c}} $ and $ \mathrm{W} + \mathrm{b}\overline{\mathrm{b}} $; its negative value is an effect of the OS-SS subtraction. Quoted uncertainties are statistical only. |
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Table 3:
Simulated flavour composition (in %) of the SV sample after the selection summarized in Table 1, including OS-SS subtraction, for the electron and muon W boson decay channels. $ \mathrm{W} + {\mathrm{Q} \overline{\mathrm{Q}} } $ is the sum of the contributions of $ \mathrm{W} + \mathrm{c}\overline{\mathrm{c}} $ and $ \mathrm{W} + \mathrm{b}\overline{\mathrm{b}} $. Quoted uncertainties are statistical only. |
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Table 4:
Results in the SL (upper) and SV (lower) channels for the $ \mathrm{W} \to \mathrm{e}\nu $ and $ \mathrm{W} \to \mu\nu $ decays separately. Here $ Y_{\text{sel}}(1-f_{\text{bkg}}) $ is the estimate for the signal event yield after background subtraction, $ \mathcal{C} $ is the acceptance times efficiency correction factor, and $ \sigma(\mathrm{W}\,\mathrm{c}) $ is the measured production cross section. |
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Table 5:
Measured production cross sections $ \sigma(\mathrm{W^+}\,\overline{\mathrm{c}}) $, $ \sigma(\mathrm{W^-}\,\mathrm{c}) $, and their ratio, $ R_{\mathrm{c}}^{\pm} $, in the SL (upper) and SV (lower) channels for the electron and muon W boson decay modes. |
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Table 6:
Impact of the sources of systematic uncertainty in the combined $ \sigma(\mathrm{W}\,\mathrm{c}) $ measurement. |
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Table 7:
Measured differential cross section as a function of $ |\eta^{\ell}| $, $ \mathrm{d}\sigma(\mathrm{W}\,\mathrm{c})/\mathrm{d}|\eta^\ell| $ from the combination of all four channels. |
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Table 8:
Measured differential cross section as a function of $ p_{\mathrm{T}}^{\ell} $, $ \mathrm{d}\sigma(\mathrm{W}\,\mathrm{c})/\mathrm{d}{p_{\mathrm{T}}^\ell} $ from the combination of all four channels. |
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Table 9:
Measured cross section ratio $ R_{\mathrm{c}}^{\pm} $ as a function of $ |\eta^{\ell}| $, from the combination of all four channels. |
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Table 10:
Measured cross section ratio $ R_{\mathrm{c}}^{\pm} $ as a function of $ p_{\mathrm{T}}^{\ell} $, from the combination of all four channels. |
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Table 11:
Theoretical predictions for $ \sigma(\mathrm{W}\,\mathrm{c}) $ from MCFM at NLO. The kinematic selection follows the fiducial phase space definition: $ p_{\mathrm{T}}^{\ell} > $ 30 GeV, $ |\eta^{\ell}| < $ 2.1, $ p_{\mathrm{T}}^{\mathrm{c}} > $ 25 GeV, $ |\eta^{\mathrm{c}}| < $ 2.5, and $ \Delta R(\mathrm{c},\ell) > $ 0.5. For each PDF set, the central value of the prediction is given, together with the relative uncertainty as prescribed from the PDF set, and the uncertainties associated with the scale variations and with the value of $ \alpha_\mathrm{S} $. The total uncertainty is given in the last column. The last row in the table gives the experimental results presented in this paper. |
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Table 12:
Theoretical predictions for $ R_{\mathrm{c}}^{\pm} $ calculated with MCFM at NLO. The kinematic selection follows the experimental requirements: $ p_{\mathrm{T}}^{\ell} > $ 30 GeV, $ |\eta^{\ell}| < $ 2.1, $ p_{\mathrm{T}}^{\mathrm{c}} > $ 25 GeV, $ |\eta^{\mathrm{c}}| < $ 2.5, and $ \Delta R(\mathrm{c},\ell) > $ 0.5. For each PDF set, the central value of the prediction is given, together with the relative uncertainty as prescribed from the PDF set, and the uncertainties associated with the scale variations and with the value of $ \alpha_\mathrm{S} $. The total uncertainty is given in the last column. The last row in the table gives the experimental results presented in this paper. |
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Table 13:
The partial $ \chi^2 $ per number of data points, $ n_{\mathrm{dp}} $, and the global $ \chi^2 $ per number of degrees of freedom, $ n_{\mathrm{dof}} $, resulting from the PDF fit. |
| Summary |
| The associated production of a W boson with a charm quark ($ \mathrm{W}\,\mathrm{c} $) in proton-proton (pp) collisions at a centre-of-mass energy of 8 TeV is studied with a data sample collected by the CMS experiment corresponding to an integrated luminosity of 19.7 fb$ ^{-1} $. The $ \mathrm{W}\,\mathrm{c} $ process is selected based on the presence of a high transverse momentum lepton (electron or muon) coming from a W boson decay and a charm hadron decay. Charm hadron decays are identified either by the presence of a muon inside a jet or by reconstructing a secondary decay vertex within a jet. Inclusive and differential fiducial cross section measurements are performed with four different data samples (electron and muon W boson decay channels and reconstruction of semileptonic and inclusive decays of charm hadrons). Cross section measurements are unfolded to the parton level. The ratio of the cross sections of $ \mathrm{W^+}\,\overline{\mathrm{c}} $ and $ \mathrm{W^-}\,\mathrm{c} $ is also measured. The results from the four different channels are consistent and are combined. <\b><\b>The measurements are compared with the predictions of the MADGRAPH MC simulation normalized to the NNLO cross section prediction of inclusive W production from FEWZ. They are consistent within uncertainties. The measurements are also compared with analytical NLO calculations from the MCFM program using different NLO PDF sets. A fair agreement is seen in the differential cross section as a function of the absolute value of the pseudorapidity of the lepton from the W boson. Differences of $ {\sim}10% $ occur in the differential cross section as a function of the transverse momentum of the lepton in the 30--50 GeV range. The combined measurement of the $ \mathrm{W}\,\mathrm{c} $ production cross section as a function of the absolute value of the pseudorapidity of the lepton from the W boson decay is used in a QCD analysis at NLO, together with inclusive deep inelastic scattering measurements from HERA and earlier results from CMS on $ \mathrm{W}\,\mathrm{c} $ production and the lepton charge asymmetry in W boson production. The strange quark distribution $ x\mathrm{s}(x,\mu_f^2) $ and the strangeness suppression factor $ R_{\mathrm{s}}(x,\mu_f^2) $ = $ (\mathrm{s}+\overline{\mathrm{s}})/(\overline{\mathrm{u}}+\overline{\mathrm{d}}) $ are determined and agree with other NLO PDF sets such as ABMP16 [69], NNPDF3.1 [68], CT18 [90], and MSHT20 [91]. The inclusion of the present results further constrains the strange quark distribution and the strangeness suppression factor. |
| Additional Figures | |
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Additional Figure 1:
Relative total uncertainties for the strange quark distribution (left) and strangeness suppression factor (right) as functions of $x$ at the factorization scale of 1.9 GeV$ ^2$. |
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Additional Figure 1-a:
Relative total uncertainties for the strange quark distribution as functions of $x$ at the factorization scale of 1.9 GeV$ ^2$. |
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Additional Figure 1-b:
Relative total uncertainties for the strangeness suppression factor as functions of $x$ at the factorization scale of 1.9 GeV$ ^2$. |
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Additional Figure 2:
Comparison of the results of this analysis with the most recent ATLAS next-to-next-to-leading order PDF set ATLASepWZVjet20 for the strange quark distribution (left) and strangeness suppression factor (right) as functions of $x$ at the factorization scale of $m_{\mathrm{W}}^2$. |
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Additional Figure 2-a:
Comparison of the results of this analysis with the most recent ATLAS next-to-next-to-leading order PDF set ATLASepWZVjet20 for the strange quark distribution as functions of $x$ at the factorization scale of $m_{\mathrm{W}}^2$. |
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Additional Figure 2-b:
Comparison of the results of this analysis with the most recent ATLAS next-to-next-to-leading order PDF set ATLASepWZVjet20 for the strangeness suppression factor as functions of $x$ at the factorization scale of $m_{\mathrm{W}}^2$. |
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