CMSSMP20004 ; CERNEP2024134  
Measurement of the inclusive cross sections for W and Z boson production in protonproton collisions at $ \sqrt{s}= $ 5.02 and 13 TeV  
CMS Collaboration  
7 August 2024  
Submitted to J. High Energy Phys.  
Abstract: Measurements of fiducial and total inclusive cross sections for W and Z boson production are presented in protonproton collisions at $ \sqrt{s}= $ 5.02 and 13 TeV. Electron and muon decay modes ($ \ell=\mathrm{e} $ or $ \mu $) are studied in the data collected with the CMS detector in 2017, in dedicated runs with reduced instantaneous luminosity. The data sets correspond to integrated luminosities of 298 $ \pm $ 6 pb$^{1}$ at 5.02 TeV and 206 $ \pm $ 5 pb$^{1}$ at 13 TeV. Measured values of the products of the total inclusive cross sections and the branching fractions at 5.02 TeV are $ \sigma(\mathrm{p}\mathrm{p} \to \mathrm{W} + \mathrm{X})\mathcal{B}(\mathrm{W} \to \ell\nu) = $ 7300 $ \pm $ 10 (stat) $ \pm $ 60 (syst) $ \pm $ 140 (lumi) pb, and $ \sigma(\mathrm{p}\mathrm{p} \to \mathrm{Z} + \mathrm{X})\mathcal{B}(\mathrm{Z}\to\ell^+\ell^) = $ 669 $ \pm $ 2 (stat) $ \pm $ 6 (syst) $ \pm $ 13 (lumi) pb for the dilepton invariant mass in the range of 60120 GeV. The corresponding results at 13 TeV are 20480 $ \pm $ 10 (stat) $ \pm $ 170 (syst) $ \pm $ 470 (lumi) pb and 1952 $ \pm $ 4 (stat) $ \pm $ 18 (syst) $ \pm $ 45 (lumi) pb. The measured values agree with cross section calculations at nexttonexttoleadingorder in perturbative quantum chromodynamics. Fiducial and total inclusive cross sections, ratios of cross sections of W$^{+}$ and W$^{}$ production as well as inclusive W and Z boson production, and ratios of these measurements at 5.02 and 13 TeV are reported.  
Links: eprint arXiv:2408.03744 [hepex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ; 
Figures  
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Figure 1:
Distributions of $ m_{\mathrm{T}} $ in the W$^{+}$ signal selection for electron (left) and muon (right) final states for the pp collisions at $ \sqrt{s}= $ 5.02 TeV (upper) and 13 TeV (lower) after the maximum likelihood fit. The vertical bars on the observed data represent corresponding statistical uncertainties. The EW backgrounds include the contributions from DY, $ \mathrm{W}\to\tau\nu $, and diboson processes. The lower panel in each plot shows the ratio of the number of observed events to that of the total signal and background predictions. The gray band represents the uncertainty in the total prediction after the fit. 
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Figure 1a:
Distributions of $ m_{\mathrm{T}} $ in the W$^{+}$ signal selection for electron (left) and muon (right) final states for the pp collisions at $ \sqrt{s}= $ 5.02 TeV (upper) and 13 TeV (lower) after the maximum likelihood fit. The vertical bars on the observed data represent corresponding statistical uncertainties. The EW backgrounds include the contributions from DY, $ \mathrm{W}\to\tau\nu $, and diboson processes. The lower panel in each plot shows the ratio of the number of observed events to that of the total signal and background predictions. The gray band represents the uncertainty in the total prediction after the fit. 
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Figure 1b:
Distributions of $ m_{\mathrm{T}} $ in the W$^{+}$ signal selection for electron (left) and muon (right) final states for the pp collisions at $ \sqrt{s}= $ 5.02 TeV (upper) and 13 TeV (lower) after the maximum likelihood fit. The vertical bars on the observed data represent corresponding statistical uncertainties. The EW backgrounds include the contributions from DY, $ \mathrm{W}\to\tau\nu $, and diboson processes. The lower panel in each plot shows the ratio of the number of observed events to that of the total signal and background predictions. The gray band represents the uncertainty in the total prediction after the fit. 
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Figure 1c:
Distributions of $ m_{\mathrm{T}} $ in the W$^{+}$ signal selection for electron (left) and muon (right) final states for the pp collisions at $ \sqrt{s}= $ 5.02 TeV (upper) and 13 TeV (lower) after the maximum likelihood fit. The vertical bars on the observed data represent corresponding statistical uncertainties. The EW backgrounds include the contributions from DY, $ \mathrm{W}\to\tau\nu $, and diboson processes. The lower panel in each plot shows the ratio of the number of observed events to that of the total signal and background predictions. The gray band represents the uncertainty in the total prediction after the fit. 
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Figure 1d:
Distributions of $ m_{\mathrm{T}} $ in the W$^{+}$ signal selection for electron (left) and muon (right) final states for the pp collisions at $ \sqrt{s}= $ 5.02 TeV (upper) and 13 TeV (lower) after the maximum likelihood fit. The vertical bars on the observed data represent corresponding statistical uncertainties. The EW backgrounds include the contributions from DY, $ \mathrm{W}\to\tau\nu $, and diboson processes. The lower panel in each plot shows the ratio of the number of observed events to that of the total signal and background predictions. The gray band represents the uncertainty in the total prediction after the fit. 
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Figure 2:
Distributions of $ m_{\mathrm{T}} $ in the W$^{}$ signal selection for electron (left) and muon (right) final states for the pp collisions at $ \sqrt{s}= $ 5.02 TeV (upper) and 13 TeV (lower) after the maximum likelihood fit. The EW backgrounds include the contributions from DY, $ \mathrm{W}\to\tau\nu $, and diboson processes. Notations are as in Fig. 1. 
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Figure 2a:
Distributions of $ m_{\mathrm{T}} $ in the W$^{}$ signal selection for electron (left) and muon (right) final states for the pp collisions at $ \sqrt{s}= $ 5.02 TeV (upper) and 13 TeV (lower) after the maximum likelihood fit. The EW backgrounds include the contributions from DY, $ \mathrm{W}\to\tau\nu $, and diboson processes. Notations are as in Fig. 1. 
png pdf 
Figure 2b:
Distributions of $ m_{\mathrm{T}} $ in the W$^{}$ signal selection for electron (left) and muon (right) final states for the pp collisions at $ \sqrt{s}= $ 5.02 TeV (upper) and 13 TeV (lower) after the maximum likelihood fit. The EW backgrounds include the contributions from DY, $ \mathrm{W}\to\tau\nu $, and diboson processes. Notations are as in Fig. 1. 
png pdf 
Figure 2c:
Distributions of $ m_{\mathrm{T}} $ in the W$^{}$ signal selection for electron (left) and muon (right) final states for the pp collisions at $ \sqrt{s}= $ 5.02 TeV (upper) and 13 TeV (lower) after the maximum likelihood fit. The EW backgrounds include the contributions from DY, $ \mathrm{W}\to\tau\nu $, and diboson processes. Notations are as in Fig. 1. 
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Figure 2d:
Distributions of $ m_{\mathrm{T}} $ in the W$^{}$ signal selection for electron (left) and muon (right) final states for the pp collisions at $ \sqrt{s}= $ 5.02 TeV (upper) and 13 TeV (lower) after the maximum likelihood fit. The EW backgrounds include the contributions from DY, $ \mathrm{W}\to\tau\nu $, and diboson processes. Notations are as in Fig. 1. 
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Figure 3:
Distributions of $ m_{\mathrm{e}^+\mathrm{e}^} $ (left) and $ m_{\mu^{+}\mu^{}} $ (right) for the pp collisions at $ \sqrt{s}= $ 5.02 TeV (upper) and 13 TeV (lower), after the maximum likelihood fit. The EW backgrounds include the contributions from diboson processes. Notations are as in Fig. 1. 
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Figure 3a:
Distributions of $ m_{\mathrm{e}^+\mathrm{e}^} $ (left) and $ m_{\mu^{+}\mu^{}} $ (right) for the pp collisions at $ \sqrt{s}= $ 5.02 TeV (upper) and 13 TeV (lower), after the maximum likelihood fit. The EW backgrounds include the contributions from diboson processes. Notations are as in Fig. 1. 
png pdf 
Figure 3b:
Distributions of $ m_{\mathrm{e}^+\mathrm{e}^} $ (left) and $ m_{\mu^{+}\mu^{}} $ (right) for the pp collisions at $ \sqrt{s}= $ 5.02 TeV (upper) and 13 TeV (lower), after the maximum likelihood fit. The EW backgrounds include the contributions from diboson processes. Notations are as in Fig. 1. 
png pdf 
Figure 3c:
Distributions of $ m_{\mathrm{e}^+\mathrm{e}^} $ (left) and $ m_{\mu^{+}\mu^{}} $ (right) for the pp collisions at $ \sqrt{s}= $ 5.02 TeV (upper) and 13 TeV (lower), after the maximum likelihood fit. The EW backgrounds include the contributions from diboson processes. Notations are as in Fig. 1. 
png pdf 
Figure 3d:
Distributions of $ m_{\mathrm{e}^+\mathrm{e}^} $ (left) and $ m_{\mu^{+}\mu^{}} $ (right) for the pp collisions at $ \sqrt{s}= $ 5.02 TeV (upper) and 13 TeV (lower), after the maximum likelihood fit. The EW backgrounds include the contributions from diboson processes. Notations are as in Fig. 1. 
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Figure 4:
Comparisons of the fiducial inclusive cross sections and cross section ratios between measurements and the theoretical calculations from DYTURBO with different PDF sets at 5.02 TeV. The gray band represents the total uncertainty of each measurement. The uncertainties in the theoretical predictions include the statistical uncertainty, and the PDF, $ \alpha_\mathrm{S} $, and renormalization and factorization scale uncertainties. The measured values and theoretical predictions (DYTURBO with NNPDF 3.1 as the example) are also shown in the right part of the plot. 
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Figure 5:
Comparisons of the fiducial inclusive cross sections and cross section ratios between measurements and the theoretical calculations from DYTURBO with different PDF sets at 13 TeV. The gray band represents the total uncertainty of each measurement. The uncertainties in the theoretical predictions include the statistical uncertainty, and the PDF, $ \alpha_\mathrm{S} $, and renormalization and factorization scale uncertainties. The measured values and theoretical predictions (DYTURBO with NNPDF 3.1 as the example) are also shown in the right part of the plot. The statistical uncertainty for $ \mathrm{W^+}\to \ell^{+}\nu $ is negligible compared with the other uncertainties, therefore not included in this plot. 
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Figure 6:
Comparisons of the fiducial inclusive cross section ratios and double ratios between 13 and 5.02 TeV, between measurements and the theoretical calculations from DYTURBO with different PDF sets. The gray band represents the total uncertainty of each measurement. The uncertainties in the theoretical predictions include the statistical uncertainty, and the PDF, $ \alpha_\mathrm{S} $, and renormalization and factorization scale uncertainties. The measured values and theoretical predictions (DYTURBO with NNPDF 3.1 as the example) are also shown in the right part of the plot. 
png pdf 
Figure 7:
Comparisons of the total inclusive cross sections and cross section ratios between measurements and the theoretical calculations from DYTURBO with different PDF sets at 5.02 TeV. The gray band represents the total uncertainty of each measurement. The uncertainties in the theoretical predictions include the statistical uncertainty, and the PDF, $ \alpha_\mathrm{S} $, and renormalization and factorization scale uncertainties. The measured values and theoretical predictions (DYTURBO with NNPDF 3.1 as the example) are also shown in the right part of the plot. 
png pdf 
Figure 8:
Comparisons of the total inclusive cross sections and cross section ratios between measurements and the theoretical calculations from DYTURBO with different PDF sets at 13 TeV. The gray band represents the total uncertainty of each measurement. The uncertainties in the theoretical predictions include the statistical uncertainty, and the PDF, $ \alpha_\mathrm{S} $, and renormalization and factorization scale uncertainties. The measured values and theoretical predictions (DYTURBO with NNPDF 3.1 as the example) are also shown in the right part of the plot. 
png pdf 
Figure 9:
Comparisons of the total inclusive cross section ratios and double ratios between 13 and 5.02 TeV, between measurements and the theoretical calculations from DYTURBO with different PDF sets. The gray band represents the total uncertainty of each measurement. The uncertainties in the theoretical predictions include the statistical uncertainty, and the PDF, $ \alpha_\mathrm{S} $, and renormalization and factorization scale uncertainties. The measured values and theoretical predictions (DYTURBO with NNPDF 3.1 as the example) are also shown in the right part of the plot. 
png pdf 
Figure 10:
Summary of the measurements of the total inclusive cross sections for W$^{+}$, W$^{}$, W, and Z boson production times branching fractions versus centerofmass energy from CMS and experiments at lowerenergy colliders. The vertical error bar represents the total uncertainty of each measurement. 
Tables  
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Table 1:
Event yields, after the maximum likelihood fit, in the W$^{+}$, W$^{}$, and Z boson signal regions for electron and muon final states at 5.02 TeV. 
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Table 2:
Event yields, after the maximum likelihood fit, in the W$^{+}$, W$^{}$, and Z boson signal regions for electron and muon final states at 13 TeV. 
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Table 3:
Systematic uncertainties, in percent, for the fiducial inclusive cross sections at 5.02 TeV. The 1.9% integrated luminosity uncertainty, which affects the W and Z boson production cross sections, is not included in the table. 
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Table 4:
Systematic uncertainties, in percent, for the fiducial inclusive cross sections at 13 TeV. The 2.3% integrated luminosity uncertainty, which affects the W and Z boson production cross sections, is not included in the table. 
png pdf 
Table 5:
Systematic uncertainties, in percent, for the fiducial inclusive cross section ratios between 13 and 5.02 TeV. The 2.8% integrated luminosity uncertainty, which affects the W and Z boson production cross section ratios, is not included in the table. 
png pdf 
Table 6:
Systematic uncertainties, in percent, for the total inclusive cross sections at 5.02 TeV. The 1.9% integrated luminosity uncertainty, which affects the W and Z boson production cross sections, is not included in the table. 
png pdf 
Table 7:
Systematic uncertainties, in percent, for the total inclusive cross sections at 13 TeV. The 2.3% integrated luminosity uncertainty, which affects the W and Z boson production cross sections, is not included in the table. 
png pdf 
Table 8:
Systematic uncertainties, in percent, for the total inclusive cross section ratios between 13 and 5.02 TeV. The 2.8% integrated luminosity uncertainty, which affects the W and Z boson production cross section ratios, is not included in the table. 
png pdf 
Table 9:
Comparison of the theoretical calculations and the measured fiducial inclusive cross sections and ratios at 5.02 TeV. The unit for cross sections is always pb. The uncertainties in the theoretical predictions include the statistical uncertainty, and the PDF, $ \alpha_\mathrm{S} $, and renormalization and factorization scale uncertainties. 
png pdf 
Table 10:
Comparison of the theoretical calculations and the measured fiducial inclusive cross sections and ratios at 13 TeV. The unit for cross sections is always pb. The uncertainties in the theoretical predictions include the statistical uncertainty, and the PDF, $ \alpha_\mathrm{S} $, and renormalization and factorization scale uncertainties. The statistical uncertainty for $ \mathrm{W^+}\to \ell^{+}\nu $ is negligible compared with the other uncertainties. 
png pdf 
Table 11:
Comparison of the theoretical calculations and the measured fiducial inclusive cross section ratios between 13 and 5.02 TeV. The uncertainties in the theoretical predictions include the statistical uncertainty, and the PDF, $ \alpha_\mathrm{S} $, and renormalization and factorization scale uncertainties. 
png pdf 
Table 12:
Comparison of the theoretical calculations and the measured total inclusive cross sections and ratios at 5.02 TeV. The unit for cross sections is always pb. The uncertainties in the theoretical predictions include the statistical uncertainty, and the PDF, $ \alpha_\mathrm{S} $, and renormalization and factorization scale uncertainties. 
png pdf 
Table 13:
Comparison of the theoretical calculations and the measured total inclusive cross sections and ratios at 13 TeV. The unit for cross sections is always pb. The uncertainties in the theoretical predictions include the statistical uncertainty, and the PDF, $ \alpha_\mathrm{S} $, and renormalization and factorization scale uncertainties. 
png pdf 
Table 14:
Comparison of the theoretical calculations and the measured total inclusive cross section ratios and double ratios between 13 and 5.02 TeV. The uncertainties in the theoretical predictions include the statistical uncertainty, and the PDF, $ \alpha_\mathrm{S} $, and renormalization and factorization scale uncertainties. 
Summary 
Fiducial and total inclusive cross sections for W and Z boson production measured in protonproton collisions at 5.02 TeV and 13 TeV are presented. Electron and muon decay modes are studied in the data collected with the CMS detector in 2017, in dedicated runs with reduced instantaneous luminosity. The data sets correspond to integrated luminosities of 298 $ \pm $ 6 pb$^{1}$ at 5.02 TeV and 206 $ \pm $ 5 pb$^{1}$ at 13 TeV. Measured values of the products of the total inclusive cross sections and the branching fractions are $ \sigma(\mathrm{p}\mathrm{p} \to \mathrm{W} + \mathrm{X})\mathcal{B}(\mathrm{W} \to \ell\nu ) = $ 7300 $ \pm $ 10 (stat) $ \pm $ 60 (syst) $ \pm $ 140 (lumi) pb, and $ \sigma(\mathrm{p}\mathrm{p} \to \mathrm{Z} + \mathrm{X})\mathcal{B}(\mathrm{Z} \to \ell^+\ell^) = $ 669 $ \pm $ 2 (stat) $ \pm $ 6 (syst) $ \pm $ 13 (lumi) pb for the dilepton invariant mass in the range of 60120 GeV at 5.02 TeV, and correspondingly 20480 $ \pm $ 10 (stat) $ \pm $ 170 (syst) $ \pm $ 470 (lumi) pb and 1952 $ \pm $ 4 (stat) $ \pm $ 18 (syst) $ \pm $ 45 (lumi) pb at 13 TeV. The measured values agree with cross section calculations at nexttonexttoleadingorder in perturbative quantum chromodynamics. Fiducial and total inclusive cross sections, ratios of cross sections of W$^{+}$ to W$^{}$, W to Z, and 13 TeV to 5.02 TeV measurements are reported. The fiducial inclusive cross sections for W and Z boson productions at 5.02 TeV achieve a precision of less than 2%, which is the most precisely measured cross sections from the CMS experiment. 
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