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) $^{+0.07}_{-0.07}$ (acc) nb for W$^+$ boson production, 8.86 $\pm$ 0.06 (syst) $\pm$ 0.12 (lumi) $^{+0.05}_{-0.06}$ (acc) nb for W$^-$ boson production, and 2.021 $\pm$ 0.009 (syst) $\pm$ 0.028 (lumi) $^{+0.011}_{-0.013}$ (acc) 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 (W$^+$ and W$^-$) and the sum of the two contributions (W$^\pm$), each relative to the measured Z boson production cross section. Additionally, the ratio of the measured cross sections for W$^+$ and 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.
Corrected normalized distribution of the transverse momentum of the leading muon in the Z boson signal region. Simulated contributions from Z boson, electroweak, and ttbar production, as well as their sum, and the data are shown.
Corrected normalized distribution of the transverse momentum of the trailing muon in the Z boson signal region. Simulated contributions from Z boson, electroweak, and ttbar production, as well as their sum, and the data are shown.
Corrected normalized distribution of the missing transverse momentum in the Z boson signal region. Simulated contributions from Z boson, electroweak, and ttbar production, as well as their sum, and the data are shown.
In the standard model of particle physics, the masses of the carriers of the weak interaction, the W and Z bosons, are uniquely related. Physics beyond the standard model could change this relationship through the effects of quantum loops of virtual particles, thus making it of great importance to measure these masses with the highest possible precision. Although the mass of the Z boson is known to the remarkable precision of 22 parts per million (2.0 MeV), the W boson mass is known much less precisely, given the difficulty of the measurement. A global fit to electroweak data, used to predict the W boson mass in the standard model, yields an uncertainty of 6 MeV. Reaching a comparable experimental precision would be a sensitive and fundamental test of the standard model. Furthermore, a precision measurement of the W boson mass performed by the CDF Collaboration at the Fermilab Tevatron has challenged the standard model by significantly disagreeing with the prediction of the global electroweak fit and the average of other $m_\mathrm{W}$ measurements. We report the first W boson mass measurement by the CMS Collaboration at the CERN LHC, based on a data sample collected in 2016 at the proton-proton collision energy of 13 TeV. The W boson mass is measured using a large sample of W$\to\mu\nu$ events via a highly granular binned maximum likelihood fit to the kinematic properties of the muons produced in the W$^{+}$ and W$^{-}$ boson decays. The significant in situ constraints of theoretical inputs and their corresponding uncertainties, together with an accurate determination of the experimental effects, lead to a precise W boson mass measurement, $m_\mathrm{W} =$ 80$\,$360.2 $\pm$ 9.9 MeV, in agreement with the standard model prediction.
Postfit pulls, constraints, and impacts (both nominal and 'global') for all nuisance parameters in the W boson mass fit, sorted by the absolute value of the nominal impact.
Postfit pulls, constraints, and impacts (both nominal and 'global') for all nuisance parameters in the W boson mass fit (charge difference), sorted by the absolute value of the nominal impact.
Postfit pulls, constraints, and impacts (both nominal and 'global') for all nuisance parameters in the W-like Z boson mass fit, sorted by the absolute value of the nominal impact.
An analysis is presented based on models of the intrinsic transverse momentum (intrinsic $k_\mathrm{T}$) of partons in nucleons by studying the dilepton transverse momentum in Drell-Yan events. Using parameter tuning in event generators and existing data from fixed-target experiments and from hadron colliders, our investigation spans three orders of magnitude in center-of-mass energy and two orders of magnitude in dilepton invariant mass. The results show an energy-scaling behavior of the intrinsic $k_\mathrm{T}$ parameters, independent of the dilepton invariant mass at a given center-of-mass energy.
Tuned intrinsic kT parameters BeamRemnants:PrimordialkThard in Pythia with the underlying-event tune CP5 at nucleon-nucleon center-of-mass energy from 38.8 GeV to 13 TeV.
Tuned intrinsic kT parameters BeamRemnants:PrimordialkThard in Pythia with the underlying-event tune CP4 at nucleon-nucleon center-of-mass energy from 38.8 GeV to 13 TeV.
Tuned intrinsic kT parameters BeamRemnants:PrimordialkThard in Pythia with the underlying-event tune CP3 at nucleon-nucleon center-of-mass energy from 38.8 GeV to 13 TeV.
The forward-backward asymmetry in Drell-Yan production and the effective leptonic electroweak mixing angle are measured in proton-proton collisions at $\sqrt{s}$ = 13 TeV, collected by the CMS experiment and corresponding to an integrated luminosity of 138 fb$^{-1}$. The measurement uses both dimuon and dielectron events, and is performed as a function of the dilepton mass and rapidity. The unfolded angular coefficient $A_4$ is also extracted, as a function of the dilepton mass and rapidity. Using the CT18Z set of parton distribution functions, we obtain $\sin\theta^\ell_\text{eff}$ = 0.23152 $\pm$ 0.00031, where the uncertainty includes the experimental and theoretical contributions. The measured value agrees with the standard model fit result to global experimental data. This is the most precise $\sin\theta^\ell_\text{eff}$ measurement at a hadron collider, with a precision comparable to the results obtained at LEP and SLD.
Measured $A_4(|Y|,M))$ distribution for the combined Run 2 data.
Correlation coefficients for the $A_4(|Y|,M)$ values among different $|Y|-M$ bins. The $A_4(|Y|,M)$ values and total uncertainties are shown in Figure 8 in the paper.
The Large Hadron Collider at CERN, delivering proton-proton collisions at much higher energies and far higher luminosities than previous machines, has enabled a comprehensive programme of measurements of the standard model (SM) processes by the CMS experiment. These unprecedented capabilities facilitate precise measurements of the properties of a wide array of processes, the most fundamental being cross sections. The discovery of the Higgs boson and the measurement of its mass became the keystone of the SM. Knowledge of the mass of the Higgs boson allows precision comparisons of the predictions of the SM with the corresponding measurements. These measurements span the range from one of the most copious SM processes, the total inelastic cross section for proton-proton interactions, to the rarest ones, such as Higgs boson pair production. They cover the production of Higgs bosons, top quarks, single and multibosons, and hadronic jets. Associated parameters, such as coupling constants, are also measured. These cross section measurements can be pictured as a descending stairway, on which the lowest steps represent the rarest processes allowed by the SM, some never seen before.
Cross sections of selected high-energy processes measured by the CMS experiment. Measurements performed at different LHC pp collision energies are marked by unique symbols and the coloured bands indicate the combined statistical and systematic uncertainty of the measurement. Grey bands indicate the uncertainty of the corresponding SM theory predictions. Shaded hashed bars indicate the excluded cross section region for a production process with the measured 95% CL upper limit on the process indicated by the solid line of the same colour.
Summary of production cross section measurements involving top quarks. Measurements performed at different LHC pp collision energies are marked by unique symbols and the coloured bands indicate the combined statistical and systematic uncertainty of the measurement. Grey bands indicate the uncertainty of the corresponding SM theory predictions. Shaded hashed bars indicate the excluded cross section region for a production process with the measured 95% C.L. upper limit on the process indicated by the solid line of the same colour.
Summary of measurements of jet cross sections and electroweak processes in association with jets. Measurements performed at different LHC pp collision energies are marked by unique symbols and the coloured bands indicate the combined statistical and systematic uncertainty of the measurement. Grey bands indicate the uncertainty of the corresponding SM theory predictions. Shaded hashed bars indicate the excluded cross section region for a production process with the measured 95% C.L. upper limit on the process indicated by the solid line of the same colour. Versions of these plots in pdf format with links to the publications can be found at https://cms-results.web.cern.ch/cms-results/public-results/publications/SMP-23-004/.
The first search for the Z boson decay to $\tau\tau\mu\mu$ at the CERN LHC is presented, based on data collected by the CMS experiment at the LHC in proton-proton collisions at a center-of-mass energy of 13 TeV and corresponding to an integrated luminosity of 138 fb$^{-1}$. The data are compatible with the predicted background. For the first time, an upper limit at the 95% confidence level of 6.9 times the standard model expectation is placed on the ratio of the Z $\to$ $\tau\tau\mu\mu$ to Z $\to$ 4$\mu$ branching fractions. Limits are also placed on the six flavor-conserving four-lepton effective-field-theory operators involving two muons and two tau leptons, for the first time testing all such operators.
Distribution of $m_{4\mu}$ after the maximum likelihood fit of the background-only model (stacked histograms) to the data (black points). The nuisance parameters are set to their post-fit values and the signal (black dotted line) is overlaid, scaled to the upper limit on its cross section of 6.9 times the SM expectation. The gray shaded areas in both panels correspond to the total uncertainty in the background prediction. The black vertical bars indicate the statistical uncertainty in the data.
Observed limits at the 95% CL on $C_{\mathrm{LL}}^{2233}$ vs. $C_{\mathrm{LR}}^{2332}$ (red) showing the full range.
Observed limits at the 95% CL on $C_{\mathrm{LR}}^{2233}$ vs. $C_{\mathrm{LL}}^{2332}$ (orange) showing the full range.
A measurement is presented of a ratio observable that provides a measure of the azimuthal correlations among jets with large transverse momentum $p_\mathrm{T}$. This observable is measured in multijet events over the range of $p_\mathrm{T}$ = 360-3170 GeV based on data collected by the CMS experiment in proton-proton collisions at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 134 fb$^{-1}$. The results are compared with predictions from Monte Carlo parton-shower event generator simulations, as well as with fixed-order perturbative quantum chromodynamics (pQCD) predictions at next-to-leading-order (NLO) accuracy obtained with different parton distribution functions (PDFs) and corrected for nonperturbative and electroweak effects. Data and theory agree within uncertainties. From the comparison of the measured observable with the pQCD prediction obtained with the NNPDF3.1 NLO PDFs, the strong coupling at the Z boson mass scale is $\alpha_\mathrm{S}(m_\mathrm{Z})$ = 0.1177 $\pm$ 0.0013 (exp) $_{-0.0073}^{+0.0116}$ (theo) = 0.1177 $_{-0.0074}^{+0.0117}$, where the total uncertainty is dominated by the scale dependence of the fixed-order predictions. A test of the running of $\alpha_\mathrm{S}(m_\mathrm{Z})$ in the TeV region shows no deviation from the expected NLO pQCD behaviour.
Bin-to-bin correlation matrix for the $R_{\Delta\phi}(p_\mathrm{T})$ distribution at the particle level.
The $R_{\Delta\phi}(p_\mathrm{T})$ distribution at the particle level as a function of $p_\mathrm{T}$.
Nonperturbative corrections for the $R_{\Delta\phi}(p_\mathrm{T})$ distribution.
Diboson production in association with jets is studied in the fully leptonic final states, pp $\to$ (Z$\gamma^*$)(Z/$\gamma^*$) + jets $\to$ 2$\ell$2$\ell'$ + jets, ($\ell,\ell'$ = e or $\mu$) in proton-proton collisions at a center-of-mass energy of 13 TeV. The data sample corresponds to an integrated luminosity of 138 fb$^{-1}$ collected with the CMS detector at the LHC. Differential distributions and normalized differential cross sections are measured as a function of jet multiplicity, transverse momentum $p_\mathrm{T}$, pseudorapidity $\eta$, invariant mass and $\Delta\eta$ of the highest-$p_\mathrm{T}$ and second-highest-$p_\mathrm{T}$ jets, and as a function of invariant mass of the four-lepton system for events with various jet multiplicities. These differential cross sections are compared with theoretical predictions that mostly agree with the experimental data. However, in a few regions we observe discrepancies between the predicted and measured values. Further improvement of the predictions is required to describe the ZZ + jets production in the whole phase space.
Differential cross sections normalized to the fiducial cross section as a function of the invariant mass of the four-lepton system, in the on-shell ZZ region
Differential cross sections normalized to the fiducial cross section as a function of the number of jets with $p_T > 30$ GeV
Differential cross sections normalized to the fiducial cross section as a function of the $p_T$ of the highest-$p_T$ jet
The inclusive jet cross section is measured as a function of jet transverse momentum $p_\mathrm{T}$ and rapidity $y$. The measurement is performed using proton-proton collision data at $\sqrt{s}$ = 5.02 TeV, recorded by the CMS experiment at the LHC, corresponding to an integrated luminosity of 27.4 pb$^{-1}$. The jets are reconstructed with the anti-$k_\mathrm{T}$ algorithm using a distance parameter of $R$ = 0.4, within the rapidity interval $\lvert y\rvert$$\lt$ 2, and across the kinematic range 0.06 $\lt$$p_\mathrm{T}$$\lt$ 1 TeV. The jet cross section is unfolded from detector to particle level using the determined jet response and resolution. The results are compared to predictions of perturbative quantum chromodynamics, calculated at both next-to-leading order and next-to-next-to-leading order. The predictions are corrected for nonperturbative effects, and presented for a variety of parton distribution functions and choices of the renormalization / factorization scales and the strong coupling $\alpha_\mathrm{S}$.
The JEC, JER, and total systematic uncertainties in unfolded cross sections as functions of transverse momentum, for |y|<0.5. The total systematic uncertainty includes also the luminosity, jet identification and trigger efficiency uncertainties.
The JEC, JER, and total systematic uncertainties in unfolded cross sections as functions of transverse momentum, for 0.5<|y|<1. The total systematic uncertainty includes also the luminosity, jet identification and trigger efficiency uncertainties.
The JEC, JER, and total systematic uncertainties in unfolded cross sections as functions of transverse momentum, for 1<|y|<1.5. The total systematic uncertainty includes also the luminosity, jet identification and trigger efficiency uncertainties.
A measurement of the dijet production cross section is reported based on proton-proton collision data collected in 2016 at $\sqrt{s}$ = 13 TeV by the CMS experiment at the CERN LHC, corresponding to an integrated luminosity of up to 36.3 fb$^{-1}$. Jets are reconstructed with the anti-$k_\mathrm{T}$ algorithm for distance parameters of $R$ = 0.4 and 0.8. Cross sections are measured double-differentially (2D) as a function of the largest absolute rapidity $\lvert y_\text{max}\rvert$ of the two jets with the highest transverse momenta $p_\mathrm{T}$ and their invariant mass $m_{1,2}$, and triple-differentially (3D) as a function of the rapidity separation $y^*$, the total boost $y_\mathrm{b}$, and either $m_{1,2}$ or the average $p_\mathrm{T}$ of the two jets. The cross sections are unfolded to correct for detector effects and are compared with fixed-order calculations derived at next-to-next-to-leading order in perturbative quantum chromodynamics. The impact of the measurements on the parton distribution functions and the strong coupling constant at the mass of the Z boson is investigated, yielding a value of $\alpha_\mathrm{S}(m_\mathrm{Z})$ = 0.1179 $\pm$ 0.0019.
Double-differential dijet cross section for anti-$k_\text{T}$ jets with R = 0.4 as a function of the dijet invariant mass ($m_{1,2}$) and the absolute rapidity of the outermost jet ($\left| y \right|_\text{max}$)
Electroweak corrections to double-differential dijet cross section for anti-$k_\text{T}$ jets with R = 0.4 as a function of the dijet invariant mass ($m_{1,2}$) and the absolute rapidity of the outermost jet ($\left| y \right|_\text{max}$)
Nonperturbative corrections to double-differential dijet cross section for anti-$k_\text{T}$ jets with R = 0.4 as a function of the dijet invariant mass ($m_{1,2}$) and the absolute rapidity of the outermost jet ($\left| y \right|_\text{max}$)
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