CMS-SMP-22-017

CMS-SMP-22-017 ; CERN-EP-2025-013
Measurements of the inclusive W and Z boson production cross sections and their ratios in proton-proton collisions at $\sqrt{s}=$ 13.6 TeV
CMS Collaboration
12 March 2025
Submitted to J. High Energy Phys.
Abstract: Measurements are presented of the W and Z boson production cross sections in proton-proton collisions at a center-of-mass energy of 13.6 TeV. Data collected in 2022 and corresponding to an integrated luminosity of 5.01 fb $^{-1}$ with one or two identified muons in the final state are analyzed. The results for the products of total inclusive cross sections and branching fractions for muonic decays of W and Z bosons are 11.93 $\pm$ 0.08 (syst) $\pm$ 0.17 (lumi) $\,^{+0.07}_{-0.07}$ (acceptance) nb for $\mathrm{W^+}$ boson production, 8.86 $\pm$ 0.06 (syst) $\pm$ 0.12 (lumi) $\,^{+0.05}_{-0.06}$ (acceptance) nb for $\mathrm{W^-}$ boson production, and 2.021 $\pm$ 0.009 (syst) $\pm$ 0.028 (lumi) $\,^{+0.011}_{-0.013}$ (acceptance) nb for the Z boson production in the dimuon mass range of 60--120 GeV, all with negligible statistical uncertainties. Furthermore, the corresponding fiducial cross sections, as well as cross section ratios for both fiducial and total phase space, are provided. The ratios include charge-separated results for W boson production ( $\mathrm{W^+}$ and $\mathrm{W^-}$ ) and the sum of the two contributions ( $\mathrm{W}^{\pm}$ ), each relative to the measured Z boson production cross section. Additionally, the ratio of the measured cross sections for $\mathrm{W^+}$ and $\mathrm{W^-}$ boson production is reported. All measurements are in agreement with theoretical predictions, calculated at next-to-next-to-leading order accuracy in quantum chromodynamics.
Links: e-print arXiv:2503.09742 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ;

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: Corrected distributions of the $p_{\mathrm{T}}$ of the leading (upper left) and trailing (upper right) muon, as well as $p_{\mathrm{T}}^\text{miss}$ (lower) in the Z boson signal region. The distributions of both data and combined simulation in the upper panels are normalized because the scale of the signal sample is extracted later in the fit. The lower panels show the ratio of the normalized data to the normalized prediction. Overflow entries are included in the rightmost bin, respectively. Differences in the shape between data and prediction are fully covered by the systematic uncertainty band. The systematic uncertainties are described in detail in Section 9. The vertical uncertainty bars on the data represent the statistical uncertainty.
png pdf	Figure 1-a: Corrected distributions of the $p_{\mathrm{T}}$ of the leading (upper left) and trailing (upper right) muon, as well as $p_{\mathrm{T}}^\text{miss}$ (lower) in the Z boson signal region. The distributions of both data and combined simulation in the upper panels are normalized because the scale of the signal sample is extracted later in the fit. The lower panels show the ratio of the normalized data to the normalized prediction. Overflow entries are included in the rightmost bin, respectively. Differences in the shape between data and prediction are fully covered by the systematic uncertainty band. The systematic uncertainties are described in detail in Section 9. The vertical uncertainty bars on the data represent the statistical uncertainty.
png pdf	Figure 1-b: Corrected distributions of the $p_{\mathrm{T}}$ of the leading (upper left) and trailing (upper right) muon, as well as $p_{\mathrm{T}}^\text{miss}$ (lower) in the Z boson signal region. The distributions of both data and combined simulation in the upper panels are normalized because the scale of the signal sample is extracted later in the fit. The lower panels show the ratio of the normalized data to the normalized prediction. Overflow entries are included in the rightmost bin, respectively. Differences in the shape between data and prediction are fully covered by the systematic uncertainty band. The systematic uncertainties are described in detail in Section 9. The vertical uncertainty bars on the data represent the statistical uncertainty.
png pdf	Figure 1-c: Corrected distributions of the $p_{\mathrm{T}}$ of the leading (upper left) and trailing (upper right) muon, as well as $p_{\mathrm{T}}^\text{miss}$ (lower) in the Z boson signal region. The distributions of both data and combined simulation in the upper panels are normalized because the scale of the signal sample is extracted later in the fit. The lower panels show the ratio of the normalized data to the normalized prediction. Overflow entries are included in the rightmost bin, respectively. Differences in the shape between data and prediction are fully covered by the systematic uncertainty band. The systematic uncertainties are described in detail in Section 9. The vertical uncertainty bars on the data represent the statistical uncertainty.
png pdf	Figure 2: Example figures to illustrate the extrapolation procedure to estimate the QCD multijet background from the QCD-enriched control region. The yield in each bin is obtained by subtracting the simulated non-QCD contributions from the measured data. At high values of the transverse mass, the statistical uncertainty of the QCD yield increases, represented by the vertical uncertainty bars, leaving more freedom for the polynomial fit.
png pdf	Figure 2-a: Example figures to illustrate the extrapolation procedure to estimate the QCD multijet background from the QCD-enriched control region. The yield in each bin is obtained by subtracting the simulated non-QCD contributions from the measured data. At high values of the transverse mass, the statistical uncertainty of the QCD yield increases, represented by the vertical uncertainty bars, leaving more freedom for the polynomial fit.
png pdf	Figure 2-b: Example figures to illustrate the extrapolation procedure to estimate the QCD multijet background from the QCD-enriched control region. The yield in each bin is obtained by subtracting the simulated non-QCD contributions from the measured data. At high values of the transverse mass, the statistical uncertainty of the QCD yield increases, represented by the vertical uncertainty bars, leaving more freedom for the polynomial fit.
png pdf	Figure 2-c: Example figures to illustrate the extrapolation procedure to estimate the QCD multijet background from the QCD-enriched control region. The yield in each bin is obtained by subtracting the simulated non-QCD contributions from the measured data. At high values of the transverse mass, the statistical uncertainty of the QCD yield increases, represented by the vertical uncertainty bars, leaving more freedom for the polynomial fit.
png pdf	Figure 2-d: Example figures to illustrate the extrapolation procedure to estimate the QCD multijet background from the QCD-enriched control region. The yield in each bin is obtained by subtracting the simulated non-QCD contributions from the measured data. At high values of the transverse mass, the statistical uncertainty of the QCD yield increases, represented by the vertical uncertainty bars, leaving more freedom for the polynomial fit.
png pdf	Figure 3: Result of the extrapolated $m_{\mathrm{T}}$ distribution for the QCD multijet background in the signal region from the QCD-enriched control region. The template normalization is left freely floating in the fit, as the final normalization is determined in the fit. The vertical uncertainty bars correspond to the extrapolation uncertainty from the fit.
png pdf	Figure 3-a: Result of the extrapolated $m_{\mathrm{T}}$ distribution for the QCD multijet background in the signal region from the QCD-enriched control region. The template normalization is left freely floating in the fit, as the final normalization is determined in the fit. The vertical uncertainty bars correspond to the extrapolation uncertainty from the fit.
png pdf	Figure 3-b: Result of the extrapolated $m_{\mathrm{T}}$ distribution for the QCD multijet background in the signal region from the QCD-enriched control region. The template normalization is left freely floating in the fit, as the final normalization is determined in the fit. The vertical uncertainty bars correspond to the extrapolation uncertainty from the fit.
png pdf	Figure 4: The post-fit distributions of (upper left) $\mu^{+}\nu_{\!\mu}$ , (upper right) $\mu^{-}\overline{\nu}_{\!\mu}$ , and (lower) $\mu^{+} \mu^{-}$ signal regions. The lower panel in each plot shows the ratio of the number of events observed in data to that of the signal and background predictions. Overflow entries are included in the rightmost bin for the two upper plots. The vertical uncertainty bars on the data represent the statistical uncertainty.
png pdf	Figure 4-a: The post-fit distributions of (upper left) $\mu^{+}\nu_{\!\mu}$ , (upper right) $\mu^{-}\overline{\nu}_{\!\mu}$ , and (lower) $\mu^{+} \mu^{-}$ signal regions. The lower panel in each plot shows the ratio of the number of events observed in data to that of the signal and background predictions. Overflow entries are included in the rightmost bin for the two upper plots. The vertical uncertainty bars on the data represent the statistical uncertainty.
png pdf	Figure 4-b: The post-fit distributions of (upper left) $\mu^{+}\nu_{\!\mu}$ , (upper right) $\mu^{-}\overline{\nu}_{\!\mu}$ , and (lower) $\mu^{+} \mu^{-}$ signal regions. The lower panel in each plot shows the ratio of the number of events observed in data to that of the signal and background predictions. Overflow entries are included in the rightmost bin for the two upper plots. The vertical uncertainty bars on the data represent the statistical uncertainty.
png pdf	Figure 4-c: The post-fit distributions of (upper left) $\mu^{+}\nu_{\!\mu}$ , (upper right) $\mu^{-}\overline{\nu}_{\!\mu}$ , and (lower) $\mu^{+} \mu^{-}$ signal regions. The lower panel in each plot shows the ratio of the number of events observed in data to that of the signal and background predictions. Overflow entries are included in the rightmost bin for the two upper plots. The vertical uncertainty bars on the data represent the statistical uncertainty.
png pdf	Figure 5: Comparison of measured product of fiducial (left) and total (right) cross sections and branching fractions with different theoretical predictions at NNLO+NNLL QCD accuracy. The vertical uncertainty bars on the markers represent the total uncertainty of the theoretical prediction.
png pdf	Figure 5-a: Comparison of measured product of fiducial (left) and total (right) cross sections and branching fractions with different theoretical predictions at NNLO+NNLL QCD accuracy. The vertical uncertainty bars on the markers represent the total uncertainty of the theoretical prediction.
png pdf	Figure 5-b: Comparison of measured product of fiducial (left) and total (right) cross sections and branching fractions with different theoretical predictions at NNLO+NNLL QCD accuracy. The vertical uncertainty bars on the markers represent the total uncertainty of the theoretical prediction.
png pdf	Figure 6: Comparison of measured fiducial (left) and total (right) ratios with different theoretical predictions at NNLO+NNLL QCD accuracy. The vertical uncertainty bars on the markers represent the total uncertainty of the theoretical prediction.
png pdf	Figure 6-a: Comparison of measured fiducial (left) and total (right) ratios with different theoretical predictions at NNLO+NNLL QCD accuracy. The vertical uncertainty bars on the markers represent the total uncertainty of the theoretical prediction.
png pdf	Figure 6-b: Comparison of measured fiducial (left) and total (right) ratios with different theoretical predictions at NNLO+NNLL QCD accuracy. The vertical uncertainty bars on the markers represent the total uncertainty of the theoretical prediction.
png pdf	Figure 7: Comparison of measured products of total cross section and branching fractions for W and Z boson production at different center-of-mass energies with the corresponding theoretical prediction at NNLO+NNLL QCD accuracy obtained from DYTURBO. The uncertainties in the theoretical prediction include variations of the renormalization and factorization scales, as well as the PDF uncertainty evaluated with the NNPDF 3.1 set. The vertical uncertainty bars on the markers represent the total uncertainty of the measurement.

Tables
png pdf	Table 1: Predictions for the product of the fiducial and total inclusive cross sections and branching fractions. The first uncertainty is the PDF uncertainty, the second is the QCD scale uncertainty of the calculation, and the third is the integration uncertainty.
png pdf	Table 2: Predictions for the fiducial and total inclusive cross section ratios. The first uncertainty is the PDF uncertainty, the second is the QCD scale uncertainty of the calculation, and the third is the integration uncertainty.
png pdf	Table 3: Post-fit uncertainties in percent for the fiducial cross section measurement. For completeness, also the integrated luminosity and statistical uncertainty are given.
png pdf	Table 4: Post-fit uncertainties in percent for the fiducial cross section ratio measurement. For completeness, also the statistical uncertainty is given.
png pdf	Table 5: Pre-fit event yields in the fiducial region. A dash indicates that the corresponding contribution is found to be negligible in this signal region.
png pdf	Table 6: Post-fit event yields in the fiducial region. The post-fit uncertainties include only statistical and systematic uncertainties, but not the uncertainty in the luminosity. The individual uncertainties in the event yields for a given process are derived by taking the full covariance matrix into account. A dash indicates that the corresponding contribution is found to be negligible in this signal region.
png pdf	Table 7: Results for the product of the fiducial and total inclusive cross sections and branching fractions measurements. For the measured values the quoted uncertainty represents the systematic uncertainty, while the statistical uncertainty is negligible. For the acceptance predictions, as explained in Section 5, the first uncertainty is the PDF uncertainty, the second is the scale uncertainty, and the third is the integration uncertainty of the calculation.
png pdf	Table 8: Ratios of the measured product of the fiducial and total inclusive cross sections and branching fractions along with the corresponding acceptance predictions. Since some contributions of the systematic uncertainty, most prominently the luminosity uncertainty, cancel out in the ratios, the statistical component becomes relevant. For the acceptance predictions, as explained in Section 5, the first uncertainty is the PDF uncertainty, the second is the scale uncertainty, and the third is the integration uncertainty of the calculation.

Summary

Measurements of fiducial and total inclusive W and Z boson production cross sections multiplied by the

$\mathrm{W}\to\mu\nu_{\!\mu}$ and

$\mathrm{Z}\to\mu^{+}\mu^{-}$ branching fractions, respectively, in proton-proton collisions at 13.6 TeV are presented. Muon final states are studied in data samples collected with the CMS detector corresponding to an integrated luminosity of 5.01

$\pm$ 0.07 fb

$^{-1}$ . The measured Z boson cross section is defined as the inclusive Drell--Yan

$\mathrm{Z}/\gamma^\ast$ production of muon pairs in the invariant mass range of 60--120 GeV, where the production of a Z boson is the dominant contribution.

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