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| CMS-SMP-19-007 ; CERN-EP-2025-134 | ||
| Studies of $ \mathrm{Z} \to 4\ell $ decays in proton-proton collisions at $ \sqrt{s} = $ 8 and 13 TeV | ||
| CMS Collaboration | ||
| 24 May 2026 | ||
| Submitted to Physical Review D | ||
| Abstract: Decays of Z bosons to four charged leptons (electrons and muons) are studied in proton-proton collisions at $ \sqrt{s} = $ 8 and 13 TeV. The analysis is based on data collected with the CMS detector at the LHC corresponding to an integrated luminosity of 19.7 fb$ ^{-1} $ at 8 TeV and 138 fb$ ^{-1} $ at 13 TeV. The measured value of the inclusive branching fraction for all four-lepton decay modes, $ \mathcal{B}(\mathrm{Z} \to 4\ell) $, is $ [ $ 4.67 $ \pm $ 0.11 (stat) $ \pm $ 0.10 (syst) $ ] \times 10^{-6} $, which has a precision of about 3% limited by both statistical and systematic uncertainties. Measurements of the individual branching fractions for the decays $ \mathrm{Z} \to 4\mu $, $ \mathrm{Z} \to 4\mathrm{e} $, and $ \mathrm{Z} \to 2\mu 2\mathrm{e} $ are also reported. Differential decay rates are presented as functions of kinematic and angular quantities in the Z boson rest frame. Measurements of triple-product asymmetries, which are sensitive to possible violations of charge conjugation and parity invariance, are performed for $ \mathrm{Z} \to 4\ell $ decays. The results are compared with standard model predictions and used to set limits on the production of new gauge bosons. | ||
| Links: e-print arXiv:2605.25158 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
The $ \mathrm{Z} \to 4\ell $ decay process in $ \mathrm{p}\mathrm{p} $ collisions. |
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Figure 2:
The $ \mathrm{Z} \to 4\ell $ process mediated by a scalar (left) or vector (right) boson $ \mathrm{U} $. |
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Figure 2-a:
The $ \mathrm{Z} \to 4\ell $ process mediated by a scalar (left) or vector (right) boson $ \mathrm{U} $. |
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Figure 2-b:
The $ \mathrm{Z} \to 4\ell $ process mediated by a scalar (left) or vector (right) boson $ \mathrm{U} $. |
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Figure 3:
Invariant mass distributions for events passing the $ \mathrm{Z} \to 4\ell $ selection for the sum of all 4 $ \ell $ channels (upper left), the 4 $ \mu $ channel (upper right), the 2 $ \mu 2\mathrm{e} $ channel (lower left), and the 4 e channel (lower right). Vertical error bars represent the total uncertainty on each point. The simulations are normalized according to predicted cross sections and the integrated luminosity. |
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Figure 3-a:
Invariant mass distributions for events passing the $ \mathrm{Z} \to 4\ell $ selection for the sum of all 4 $ \ell $ channels (upper left), the 4 $ \mu $ channel (upper right), the 2 $ \mu 2\mathrm{e} $ channel (lower left), and the 4 e channel (lower right). Vertical error bars represent the total uncertainty on each point. The simulations are normalized according to predicted cross sections and the integrated luminosity. |
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Figure 3-b:
Invariant mass distributions for events passing the $ \mathrm{Z} \to 4\ell $ selection for the sum of all 4 $ \ell $ channels (upper left), the 4 $ \mu $ channel (upper right), the 2 $ \mu 2\mathrm{e} $ channel (lower left), and the 4 e channel (lower right). Vertical error bars represent the total uncertainty on each point. The simulations are normalized according to predicted cross sections and the integrated luminosity. |
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Figure 3-c:
Invariant mass distributions for events passing the $ \mathrm{Z} \to 4\ell $ selection for the sum of all 4 $ \ell $ channels (upper left), the 4 $ \mu $ channel (upper right), the 2 $ \mu 2\mathrm{e} $ channel (lower left), and the 4 e channel (lower right). Vertical error bars represent the total uncertainty on each point. The simulations are normalized according to predicted cross sections and the integrated luminosity. |
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Figure 3-d:
Invariant mass distributions for events passing the $ \mathrm{Z} \to 4\ell $ selection for the sum of all 4 $ \ell $ channels (upper left), the 4 $ \mu $ channel (upper right), the 2 $ \mu 2\mathrm{e} $ channel (lower left), and the 4 e channel (lower right). Vertical error bars represent the total uncertainty on each point. The simulations are normalized according to predicted cross sections and the integrated luminosity. |
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Figure 4:
The differential $ \mathrm{Z} \to 4\ell $ decay rate $ \mathrm{d}\Gamma_{\mathrm{Z} \to 4\ell}{\mathrm{d}x} $ as a function of the quantities $ m_{Z_{1}} $ (upper left), $ m_{Z_{2}} $ (upper right), $ p_{\ell_1} $ (lower left), and $ m_{\ell_{2,3,4}} $ (lower right) defined in Section 8.2. These distributions have been unfolded and scaled to the full phase space region using the $ \mathcal{B}(\mathrm{Z} \to 4\ell) $ result of Table 5. For each bin, the total uncertainty is shown. |
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Figure 4-a:
The differential $ \mathrm{Z} \to 4\ell $ decay rate $ \mathrm{d}\Gamma_{\mathrm{Z} \to 4\ell}{\mathrm{d}x} $ as a function of the quantities $ m_{Z_{1}} $ (upper left), $ m_{Z_{2}} $ (upper right), $ p_{\ell_1} $ (lower left), and $ m_{\ell_{2,3,4}} $ (lower right) defined in Section 8.2. These distributions have been unfolded and scaled to the full phase space region using the $ \mathcal{B}(\mathrm{Z} \to 4\ell) $ result of Table 5. For each bin, the total uncertainty is shown. |
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Figure 4-b:
The differential $ \mathrm{Z} \to 4\ell $ decay rate $ \mathrm{d}\Gamma_{\mathrm{Z} \to 4\ell}{\mathrm{d}x} $ as a function of the quantities $ m_{Z_{1}} $ (upper left), $ m_{Z_{2}} $ (upper right), $ p_{\ell_1} $ (lower left), and $ m_{\ell_{2,3,4}} $ (lower right) defined in Section 8.2. These distributions have been unfolded and scaled to the full phase space region using the $ \mathcal{B}(\mathrm{Z} \to 4\ell) $ result of Table 5. For each bin, the total uncertainty is shown. |
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Figure 4-c:
The differential $ \mathrm{Z} \to 4\ell $ decay rate $ \mathrm{d}\Gamma_{\mathrm{Z} \to 4\ell}{\mathrm{d}x} $ as a function of the quantities $ m_{Z_{1}} $ (upper left), $ m_{Z_{2}} $ (upper right), $ p_{\ell_1} $ (lower left), and $ m_{\ell_{2,3,4}} $ (lower right) defined in Section 8.2. These distributions have been unfolded and scaled to the full phase space region using the $ \mathcal{B}(\mathrm{Z} \to 4\ell) $ result of Table 5. For each bin, the total uncertainty is shown. |
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Figure 4-d:
The differential $ \mathrm{Z} \to 4\ell $ decay rate $ \mathrm{d}\Gamma_{\mathrm{Z} \to 4\ell}{\mathrm{d}x} $ as a function of the quantities $ m_{Z_{1}} $ (upper left), $ m_{Z_{2}} $ (upper right), $ p_{\ell_1} $ (lower left), and $ m_{\ell_{2,3,4}} $ (lower right) defined in Section 8.2. These distributions have been unfolded and scaled to the full phase space region using the $ \mathcal{B}(\mathrm{Z} \to 4\ell) $ result of Table 5. For each bin, the total uncertainty is shown. |
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Figure 5:
The differential decay rates $ \mathrm{d}\Gamma_{Z \to 4\ell}/\mathrm{d}{\beta} $ (upper), $ \mathrm{d}\Gamma_{Z \to 4\ell}/\mathrm{d}{\alpha_{\mathrm{Z}_1}} $ (middle left), $ \mathrm{d}\Gamma_{Z \to 4\ell}/\mathrm{d}{\alpha_{\mathrm{Z}_2}} $ (middle right), $ \mathrm{d}\Gamma_{Z \to 4\ell}/\mathrm{d}{\cos\theta_{\mathrm{Z}_1}} $ (lower left), and $ \mathrm{d}\Gamma_{Z \to 4\ell}/\mathrm{d}{\cos\theta_{\mathrm{Z}_2}} $ (lower right). Here, $ \beta $ and $ \alpha_{\mathrm{Z}_1} $ have been scaled so that $ \pi $ radians corresponds to 1.0 on the plot. These distributions have been unfolded and scaled to the full phase space region using the $ \mathcal{B}(\mathrm{Z} \to 4\ell) $ result of Table 5. For each bin, the total uncertainty is shown. |
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Figure 5-a:
The differential decay rates $ \mathrm{d}\Gamma_{Z \to 4\ell}/\mathrm{d}{\beta} $ (upper), $ \mathrm{d}\Gamma_{Z \to 4\ell}/\mathrm{d}{\alpha_{\mathrm{Z}_1}} $ (middle left), $ \mathrm{d}\Gamma_{Z \to 4\ell}/\mathrm{d}{\alpha_{\mathrm{Z}_2}} $ (middle right), $ \mathrm{d}\Gamma_{Z \to 4\ell}/\mathrm{d}{\cos\theta_{\mathrm{Z}_1}} $ (lower left), and $ \mathrm{d}\Gamma_{Z \to 4\ell}/\mathrm{d}{\cos\theta_{\mathrm{Z}_2}} $ (lower right). Here, $ \beta $ and $ \alpha_{\mathrm{Z}_1} $ have been scaled so that $ \pi $ radians corresponds to 1.0 on the plot. These distributions have been unfolded and scaled to the full phase space region using the $ \mathcal{B}(\mathrm{Z} \to 4\ell) $ result of Table 5. For each bin, the total uncertainty is shown. |
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Figure 5-b:
The differential decay rates $ \mathrm{d}\Gamma_{Z \to 4\ell}/\mathrm{d}{\beta} $ (upper), $ \mathrm{d}\Gamma_{Z \to 4\ell}/\mathrm{d}{\alpha_{\mathrm{Z}_1}} $ (middle left), $ \mathrm{d}\Gamma_{Z \to 4\ell}/\mathrm{d}{\alpha_{\mathrm{Z}_2}} $ (middle right), $ \mathrm{d}\Gamma_{Z \to 4\ell}/\mathrm{d}{\cos\theta_{\mathrm{Z}_1}} $ (lower left), and $ \mathrm{d}\Gamma_{Z \to 4\ell}/\mathrm{d}{\cos\theta_{\mathrm{Z}_2}} $ (lower right). Here, $ \beta $ and $ \alpha_{\mathrm{Z}_1} $ have been scaled so that $ \pi $ radians corresponds to 1.0 on the plot. These distributions have been unfolded and scaled to the full phase space region using the $ \mathcal{B}(\mathrm{Z} \to 4\ell) $ result of Table 5. For each bin, the total uncertainty is shown. |
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Figure 5-c:
The differential decay rates $ \mathrm{d}\Gamma_{Z \to 4\ell}/\mathrm{d}{\beta} $ (upper), $ \mathrm{d}\Gamma_{Z \to 4\ell}/\mathrm{d}{\alpha_{\mathrm{Z}_1}} $ (middle left), $ \mathrm{d}\Gamma_{Z \to 4\ell}/\mathrm{d}{\alpha_{\mathrm{Z}_2}} $ (middle right), $ \mathrm{d}\Gamma_{Z \to 4\ell}/\mathrm{d}{\cos\theta_{\mathrm{Z}_1}} $ (lower left), and $ \mathrm{d}\Gamma_{Z \to 4\ell}/\mathrm{d}{\cos\theta_{\mathrm{Z}_2}} $ (lower right). Here, $ \beta $ and $ \alpha_{\mathrm{Z}_1} $ have been scaled so that $ \pi $ radians corresponds to 1.0 on the plot. These distributions have been unfolded and scaled to the full phase space region using the $ \mathcal{B}(\mathrm{Z} \to 4\ell) $ result of Table 5. For each bin, the total uncertainty is shown. |
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Figure 5-d:
The differential decay rates $ \mathrm{d}\Gamma_{Z \to 4\ell}/\mathrm{d}{\beta} $ (upper), $ \mathrm{d}\Gamma_{Z \to 4\ell}/\mathrm{d}{\alpha_{\mathrm{Z}_1}} $ (middle left), $ \mathrm{d}\Gamma_{Z \to 4\ell}/\mathrm{d}{\alpha_{\mathrm{Z}_2}} $ (middle right), $ \mathrm{d}\Gamma_{Z \to 4\ell}/\mathrm{d}{\cos\theta_{\mathrm{Z}_1}} $ (lower left), and $ \mathrm{d}\Gamma_{Z \to 4\ell}/\mathrm{d}{\cos\theta_{\mathrm{Z}_2}} $ (lower right). Here, $ \beta $ and $ \alpha_{\mathrm{Z}_1} $ have been scaled so that $ \pi $ radians corresponds to 1.0 on the plot. These distributions have been unfolded and scaled to the full phase space region using the $ \mathcal{B}(\mathrm{Z} \to 4\ell) $ result of Table 5. For each bin, the total uncertainty is shown. |
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Figure 5-e:
The differential decay rates $ \mathrm{d}\Gamma_{Z \to 4\ell}/\mathrm{d}{\beta} $ (upper), $ \mathrm{d}\Gamma_{Z \to 4\ell}/\mathrm{d}{\alpha_{\mathrm{Z}_1}} $ (middle left), $ \mathrm{d}\Gamma_{Z \to 4\ell}/\mathrm{d}{\alpha_{\mathrm{Z}_2}} $ (middle right), $ \mathrm{d}\Gamma_{Z \to 4\ell}/\mathrm{d}{\cos\theta_{\mathrm{Z}_1}} $ (lower left), and $ \mathrm{d}\Gamma_{Z \to 4\ell}/\mathrm{d}{\cos\theta_{\mathrm{Z}_2}} $ (lower right). Here, $ \beta $ and $ \alpha_{\mathrm{Z}_1} $ have been scaled so that $ \pi $ radians corresponds to 1.0 on the plot. These distributions have been unfolded and scaled to the full phase space region using the $ \mathcal{B}(\mathrm{Z} \to 4\ell) $ result of Table 5. For each bin, the total uncertainty is shown. |
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Figure 6:
Distributions of $ \sin\phi $ for the sum of all 4 $ \ell $ channels (upper left), the 4 $ \mu $ channel (upper right), the 2 $ \mu 2\mathrm{e} $ channel (lower left), and the 4 e channel (lower right). Vertical error bars represent the total uncertainty on each point. The simulations are normalized according to predicted cross sections and the integrated luminosity. |
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Figure 6-a:
Distributions of $ \sin\phi $ for the sum of all 4 $ \ell $ channels (upper left), the 4 $ \mu $ channel (upper right), the 2 $ \mu 2\mathrm{e} $ channel (lower left), and the 4 e channel (lower right). Vertical error bars represent the total uncertainty on each point. The simulations are normalized according to predicted cross sections and the integrated luminosity. |
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Figure 6-b:
Distributions of $ \sin\phi $ for the sum of all 4 $ \ell $ channels (upper left), the 4 $ \mu $ channel (upper right), the 2 $ \mu 2\mathrm{e} $ channel (lower left), and the 4 e channel (lower right). Vertical error bars represent the total uncertainty on each point. The simulations are normalized according to predicted cross sections and the integrated luminosity. |
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Figure 6-c:
Distributions of $ \sin\phi $ for the sum of all 4 $ \ell $ channels (upper left), the 4 $ \mu $ channel (upper right), the 2 $ \mu 2\mathrm{e} $ channel (lower left), and the 4 e channel (lower right). Vertical error bars represent the total uncertainty on each point. The simulations are normalized according to predicted cross sections and the integrated luminosity. |
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Figure 6-d:
Distributions of $ \sin\phi $ for the sum of all 4 $ \ell $ channels (upper left), the 4 $ \mu $ channel (upper right), the 2 $ \mu 2\mathrm{e} $ channel (lower left), and the 4 e channel (lower right). Vertical error bars represent the total uncertainty on each point. The simulations are normalized according to predicted cross sections and the integrated luminosity. |
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Figure 7:
Exclusion contours at 95% CL for a BSM boson $ \mathrm{U} $: (upper left) $ \mathrm{U} $ couples only to electrons, (upper right) $ \mathrm{U} $ couples only to muons, (lower left) $ \mathrm{U} $ couples equally to electrons and muons. The region above and to the left of the curve is excluded. The lower right plot compares the exclusion contour obtain in this analysis to the CMS direct search [14] for a vector $ \mathrm{U} $ boson that couples only to muons. The dashed (solid) lines show the expected (observed) exclusion contours. |
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Figure 7-a:
Exclusion contours at 95% CL for a BSM boson $ \mathrm{U} $: (upper left) $ \mathrm{U} $ couples only to electrons, (upper right) $ \mathrm{U} $ couples only to muons, (lower left) $ \mathrm{U} $ couples equally to electrons and muons. The region above and to the left of the curve is excluded. The lower right plot compares the exclusion contour obtain in this analysis to the CMS direct search [14] for a vector $ \mathrm{U} $ boson that couples only to muons. The dashed (solid) lines show the expected (observed) exclusion contours. |
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Figure 7-b:
Exclusion contours at 95% CL for a BSM boson $ \mathrm{U} $: (upper left) $ \mathrm{U} $ couples only to electrons, (upper right) $ \mathrm{U} $ couples only to muons, (lower left) $ \mathrm{U} $ couples equally to electrons and muons. The region above and to the left of the curve is excluded. The lower right plot compares the exclusion contour obtain in this analysis to the CMS direct search [14] for a vector $ \mathrm{U} $ boson that couples only to muons. The dashed (solid) lines show the expected (observed) exclusion contours. |
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Figure 7-c:
Exclusion contours at 95% CL for a BSM boson $ \mathrm{U} $: (upper left) $ \mathrm{U} $ couples only to electrons, (upper right) $ \mathrm{U} $ couples only to muons, (lower left) $ \mathrm{U} $ couples equally to electrons and muons. The region above and to the left of the curve is excluded. The lower right plot compares the exclusion contour obtain in this analysis to the CMS direct search [14] for a vector $ \mathrm{U} $ boson that couples only to muons. The dashed (solid) lines show the expected (observed) exclusion contours. |
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Figure 7-d:
Exclusion contours at 95% CL for a BSM boson $ \mathrm{U} $: (upper left) $ \mathrm{U} $ couples only to electrons, (upper right) $ \mathrm{U} $ couples only to muons, (lower left) $ \mathrm{U} $ couples equally to electrons and muons. The region above and to the left of the curve is excluded. The lower right plot compares the exclusion contour obtain in this analysis to the CMS direct search [14] for a vector $ \mathrm{U} $ boson that couples only to muons. The dashed (solid) lines show the expected (observed) exclusion contours. |
| Tables | |
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Table 1:
Definitions of the phase space and fiducial regions for four-lepton and for dilepton events. The $ m_{\ell^+ \ell^-} $ requirement for four-lepton events applies to all possible same-flavor, opposite-sign lepton pairs. |
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Table 2:
Systematic uncertainties in the branching fraction, listed by source and by final state. The uncertainty from each source varies by data-taking period. Uncertainties from pileup and theory sources are identical for all final states. |
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Table 3:
Observed event yields and sample composition for the $ \mathrm{Z} \to 4\ell $ signal region listed for the sum of all 4 $ \ell $ channels and for each channel individually. These yields are inclusive of all 8 and 13 TeV data samples. The uncertainties shown are obtained by combining statistical and systematic uncertainties in quadrature. |
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Table 4:
Observed event yields and sample composition for the $ \mathrm{Z} \to \ell^+\ell^-$ signal regions, inclusive of all 8 and 13 TeV data samples. The uncertainties shown are obtained by combining statistical and systematic uncertainties in quadrature. |
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Table 5:
Measured branching fractions. The measured values for individual channels 4 $ \mu $, 2 $ \mu 2\mathrm{e} $, and 4 e are obtained from the BSM fit described in Section 8.1. The value for the combined channel 4 $ \ell $ is obtained from the SM fit. |
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Table 6:
The number of signal $ \mathrm{Z} \to 4\ell $ events $ N_+ $ ($ N_- $) in which $ \sin\phi > $ 0 ($ < $ 0), and the associated asymmetry $ A_{\sin\phi} $ defined in Eq. \refeqeqn:TripleProductAsymmetry. The yields $ N_+ $ and $ N_- $ are reported after subtraction of backgrounds. Uncertainties are computed with respect to $ A_{\sin\phi} = $ 0. |
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Table 7:
Upper limits at 95% CL on the branching fractions listed in Table 5. |
| Summary |
| A detailed study of $ \mathrm{Z} \to 4\ell $ decays (\ell = $ \mathrm{e} $ or $ \mu $) in proton-proton collisions at $ \sqrt{s} = $ 8 and 13 TeV has been presented. The data correspond to an integrated luminosity of 19.7 fb$ ^{-1} $ collected at 8 TeV and 138 fb$ ^{-1} $ at 13 TeV with the CMS detector. A total of 1,877 events is observed in the $ \mathrm{Z} \to 4\ell $ signal region. The signal purity for each of the 4 $ \mu $, 2 $ \mu 2\mathrm{e} $, and 4 e final states is above 97%. A measurement of the branching fraction for the sum of all four-lepton decay modes has been reported: $ \mathcal{B}(\mathrm{Z} \to 4\ell) = ( $ 4.67 $ \pm $ 0.11 (stat) $ \pm $ 0.10 (syst) $) \times 10^{-6} $. This measurement is more precise than all previous CMS and ATLAS results [1,2,3,4,5,6] and has a combined statistical and systematic precision of 3.2%. Measurements of the branching fractions for the decays $ \mathrm{Z} \to 4\mu $, $ \mathrm{Z} \to 4\mathrm{e} $, and $ \mathrm{Z} \to 2\mu 2\mathrm{e} $ have also been reported. All measured branching fractions are consistent with standard model (SM) expectations. Measurements of differential decay rates for the $ \mathrm{Z} \to 4\ell $ decay process as functions of nine kinematic and angular quantities were presented. These measurements are reported in terms of the $ \mathrm{Z} \to 4\ell $ partial width $ \Gamma_{\mathrm{Z} \to 4\ell} $. They are unfolded to correct for the effects of detector resolution and scaled to the full phase space region defined by the four-lepton invariant mass 80 $ < m_{4\ell} < $ 100 GeV and the dilepton invariant mass $ m_{\ell^+ \ell^-} > $ 4 GeV. These differential decay rates characterize the behavior of the $ \mathrm{Z} \to 4\ell $ decay process and are consistent with simulations based on the SM. In the interest of exploring possible contributions of new physics to the $ \mathrm{Z} \to 4\ell $ channel, a triple-product asymmetry measurement was performed. The measurement was made possible by the high statistical precision of the analysis, and may be used to probe for possible violations of charge conjugation and parity invariance in this decay. This asymmetry is observed to be consistent with zero for all 4 $ \ell $ channels, as expected in the SM. Finally, the $ \mathcal{B}(\mathrm{Z} \to 4\mu\!) $, $ \mathcal{B}(\mathrm{Z} \to 4\mathrm{e}\!) $, and $ \mathcal{B}(\mathrm{Z} \to 2\mu 2\mathrm{e}\!) $ measurements were used to set limits on new physics in the form of a scalar or vector boson that may mediate the $ \mathrm{Z} \to 4\ell $ process. These limits are more stringent than those set using previous measurements of $ \mathcal{B}(\mathrm{Z} \to 4\ell) $ [11] and complement direct searches for a narrow-width vector boson decaying to a $ \mu^{+}\mu^{-} $ pair [14]. |
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