CMSPASSMP19007  
Studies of Z $ \to 4\ell $ decays in protonproton collisions at $ \sqrt{s} = $ 8 and 13 TeV  
CMS Collaboration  
22 August 2023  
Abstract: Decays of Z bosons to four charged leptons (electrons and muons) are studied in protonproton 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 fourlepton decay modes, $ \mathcal{B}(\mathrm{Z} \rightarrow 4\ell) $, is ( 4.67 $ \pm $ 0.11 (stat) $ \pm $ 0.10 (sys) ) $ \times $ 10$^{6} $ which has a precision of about 3%. Measurements of the individual branching fractions for the decays Z $ \to 4\mu $, Z $ \to 4\mathrm{e} $, and Z $ \to 2\mu2\mathrm{e} $ are also reported. Differential decay rates as functions of kinematic and angular quantities in the Z boson rest frame are presented. Measurements of tripleproduct asymmetries, which are sensitive to violations of charge conjugation and parity (CP) invariance, are performed for Z $ \to 4\ell $ decays. The results are compared to standard model predictions and used to set limits on the production of new gauge bosons.  
Links: CDS record (PDF) ; CADI line (restricted) ; 
Figures  
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Figure 1:
The Z $ \to 4\ell $ process in pp collisions. 
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Figure 2:
The Z $ \to 4\ell $ process mediated by a scalar (left) or vector (right) boson U. 
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Figure 2a:
The Z $ \to 4\ell $ process mediated by a scalar (left) or vector (right) boson U. 
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Figure 2b:
The Z $ \to 4\ell $ process mediated by a scalar (left) or vector (right) boson U. 
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Figure 3:
Invariant mass distributions for events passing the Z $ \to 4\ell $ selection for the sum of all 4$ \ell $ channels (upper left), the 4$ \mu $ channel (upper right), the 2$ \mu $2e channel (lower left), and the 4 e channel (lower right). The simulations are normalized according to predicted cross sections and the integrated luminosity. 
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Figure 3a:
Invariant mass distributions for events passing the Z $ \to 4\ell $ selection for the sum of all 4$ \ell $ channels (upper left), the 4$ \mu $ channel (upper right), the 2$ \mu $2e channel (lower left), and the 4 e channel (lower right). The simulations are normalized according to predicted cross sections and the integrated luminosity. 
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Figure 3b:
Invariant mass distributions for events passing the Z $ \to 4\ell $ selection for the sum of all 4$ \ell $ channels (upper left), the 4$ \mu $ channel (upper right), the 2$ \mu $2e channel (lower left), and the 4 e channel (lower right). The simulations are normalized according to predicted cross sections and the integrated luminosity. 
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Figure 3c:
Invariant mass distributions for events passing the Z $ \to 4\ell $ selection for the sum of all 4$ \ell $ channels (upper left), the 4$ \mu $ channel (upper right), the 2$ \mu $2e channel (lower left), and the 4 e channel (lower right). The simulations are normalized according to predicted cross sections and the integrated luminosity. 
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Figure 3d:
Invariant mass distributions for events passing the Z $ \to 4\ell $ selection for the sum of all 4$ \ell $ channels (upper left), the 4$ \mu $ channel (upper right), the 2$ \mu $2e channel (lower left), and the 4 e channel (lower right). The simulations are normalized according to predicted cross sections and the integrated luminosity. 
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Figure 4:
The differential Z $ \to 4\ell $ decay rate $ d\Gamma_{\mathrm{Z} \to 4\ell} / dx $ as a function of the quantities $ m_{\mathrm{Z}_{1}} $ (upper left), $ m_{\mathrm{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 4a:
The differential Z $ \to 4\ell $ decay rate $ d\Gamma_{\mathrm{Z} \to 4\ell} / dx $ as a function of the quantities $ m_{\mathrm{Z}_{1}} $ (upper left), $ m_{\mathrm{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 4b:
The differential Z $ \to 4\ell $ decay rate $ d\Gamma_{\mathrm{Z} \to 4\ell} / dx $ as a function of the quantities $ m_{\mathrm{Z}_{1}} $ (upper left), $ m_{\mathrm{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 4c:
The differential Z $ \to 4\ell $ decay rate $ d\Gamma_{\mathrm{Z} \to 4\ell} / dx $ as a function of the quantities $ m_{\mathrm{Z}_{1}} $ (upper left), $ m_{\mathrm{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 4d:
The differential Z $ \to 4\ell $ decay rate $ d\Gamma_{\mathrm{Z} \to 4\ell} / dx $ as a function of the quantities $ m_{\mathrm{Z}_{1}} $ (upper left), $ m_{\mathrm{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 Z $ \to 4\ell $ decay rates $\mathrm{d}\Gamma_{\mathrnm{Z}\to 4\ell}/\mathrm{d}{\beta} $ (upper), $\mathrm{d}\Gamma_{\mathrnm{Z}\to 4\ell}/\mathrm{d}{\alpha_{\mathrm{Z}_1}} $ (middle left), $\mathrm{d}\Gamma_{\mathrnm{Z}\to 4\ell}/\mathrm{d}{\alpha_{\mathrm{Z}_2}} $ (middle right), $\mathrm{d}\Gamma_{\mathrnm{Z}\to 4\ell}/\mathrm{d}{\cos\theta_{\mathrm{Z}_1}} $ (lower left), and $\mathrm{d}\Gamma_{\mathrnm{Z}\to 4\ell}/\mathrm{d}{\cos\theta_{\mathrm{Z}_2}} $ (lower right). For details, see Fig. 4. 
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Figure 5a:
The differential Z $ \to 4\ell $ decay rates $\mathrm{d}\Gamma_{\mathrnm{Z}\to 4\ell}/\mathrm{d}{\beta} $ (upper), $\mathrm{d}\Gamma_{\mathrnm{Z}\to 4\ell}/\mathrm{d}{\alpha_{\mathrm{Z}_1}} $ (middle left), $\mathrm{d}\Gamma_{\mathrnm{Z}\to 4\ell}/\mathrm{d}{\alpha_{\mathrm{Z}_2}} $ (middle right), $\mathrm{d}\Gamma_{\mathrnm{Z}\to 4\ell}/\mathrm{d}{\cos\theta_{\mathrm{Z}_1}} $ (lower left), and $\mathrm{d}\Gamma_{\mathrnm{Z}\to 4\ell}/\mathrm{d}{\cos\theta_{\mathrm{Z}_2}} $ (lower right). For details, see Fig. 4. 
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Figure 5b:
The differential Z $ \to 4\ell $ decay rates $\mathrm{d}\Gamma_{\mathrnm{Z}\to 4\ell}/\mathrm{d}{\beta} $ (upper), $\mathrm{d}\Gamma_{\mathrnm{Z}\to 4\ell}/\mathrm{d}{\alpha_{\mathrm{Z}_1}} $ (middle left), $\mathrm{d}\Gamma_{\mathrnm{Z}\to 4\ell}/\mathrm{d}{\alpha_{\mathrm{Z}_2}} $ (middle right), $\mathrm{d}\Gamma_{\mathrnm{Z}\to 4\ell}/\mathrm{d}{\cos\theta_{\mathrm{Z}_1}} $ (lower left), and $\mathrm{d}\Gamma_{\mathrnm{Z}\to 4\ell}/\mathrm{d}{\cos\theta_{\mathrm{Z}_2}} $ (lower right). For details, see Fig. 4. 
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Figure 5c:
The differential Z $ \to 4\ell $ decay rates $\mathrm{d}\Gamma_{\mathrnm{Z}\to 4\ell}/\mathrm{d}{\beta} $ (upper), $\mathrm{d}\Gamma_{\mathrnm{Z}\to 4\ell}/\mathrm{d}{\alpha_{\mathrm{Z}_1}} $ (middle left), $\mathrm{d}\Gamma_{\mathrnm{Z}\to 4\ell}/\mathrm{d}{\alpha_{\mathrm{Z}_2}} $ (middle right), $\mathrm{d}\Gamma_{\mathrnm{Z}\to 4\ell}/\mathrm{d}{\cos\theta_{\mathrm{Z}_1}} $ (lower left), and $\mathrm{d}\Gamma_{\mathrnm{Z}\to 4\ell}/\mathrm{d}{\cos\theta_{\mathrm{Z}_2}} $ (lower right). For details, see Fig. 4. 
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Figure 5d:
The differential Z $ \to 4\ell $ decay rates $\mathrm{d}\Gamma_{\mathrnm{Z}\to 4\ell}/\mathrm{d}{\beta} $ (upper), $\mathrm{d}\Gamma_{\mathrnm{Z}\to 4\ell}/\mathrm{d}{\alpha_{\mathrm{Z}_1}} $ (middle left), $\mathrm{d}\Gamma_{\mathrnm{Z}\to 4\ell}/\mathrm{d}{\alpha_{\mathrm{Z}_2}} $ (middle right), $\mathrm{d}\Gamma_{\mathrnm{Z}\to 4\ell}/\mathrm{d}{\cos\theta_{\mathrm{Z}_1}} $ (lower left), and $\mathrm{d}\Gamma_{\mathrnm{Z}\to 4\ell}/\mathrm{d}{\cos\theta_{\mathrm{Z}_2}} $ (lower right). For details, see Fig. 4. 
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Figure 5e:
The differential Z $ \to 4\ell $ decay rates $\mathrm{d}\Gamma_{\mathrnm{Z}\to 4\ell}/\mathrm{d}{\beta} $ (upper), $\mathrm{d}\Gamma_{\mathrnm{Z}\to 4\ell}/\mathrm{d}{\alpha_{\mathrm{Z}_1}} $ (middle left), $\mathrm{d}\Gamma_{\mathrnm{Z}\to 4\ell}/\mathrm{d}{\alpha_{\mathrm{Z}_2}} $ (middle right), $\mathrm{d}\Gamma_{\mathrnm{Z}\to 4\ell}/\mathrm{d}{\cos\theta_{\mathrm{Z}_1}} $ (lower left), and $\mathrm{d}\Gamma_{\mathrnm{Z}\to 4\ell}/\mathrm{d}{\cos\theta_{\mathrm{Z}_2}} $ (lower right). For details, see Fig. 4. 
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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 $2e channel (lower left), and the 4 e channel (lower right). The simulations are normalized according to predicted cross sections and the integrated luminosity. 
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Figure 6a:
Distributions of $ \sin\phi $ for the sum of all 4$ \ell $ channels (upper left), the 4$ \mu $ channel (upper right), the 2$ \mu $2e channel (lower left), and the 4 e channel (lower right). The simulations are normalized according to predicted cross sections and the integrated luminosity. 
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Figure 6b:
Distributions of $ \sin\phi $ for the sum of all 4$ \ell $ channels (upper left), the 4$ \mu $ channel (upper right), the 2$ \mu $2e channel (lower left), and the 4 e channel (lower right). The simulations are normalized according to predicted cross sections and the integrated luminosity. 
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Figure 6c:
Distributions of $ \sin\phi $ for the sum of all 4$ \ell $ channels (upper left), the 4$ \mu $ channel (upper right), the 2$ \mu $2e channel (lower left), and the 4 e channel (lower right). The simulations are normalized according to predicted cross sections and the integrated luminosity. 
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Figure 6d:
Distributions of $ \sin\phi $ for the sum of all 4$ \ell $ channels (upper left), the 4$ \mu $ channel (upper right), the 2$ \mu $2e channel (lower left), and the 4 e channel (lower right). 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 U: (upper left) U couples only to electrons, (upper right) U couples only to muons, (lower left) 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 [17] for a vector U boson that couples only to muons. The dashed (solid) lines show the expected (observed) exclusion contours. 
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Figure 7a:
Exclusion contours at 95% CL for a BSM boson U: (upper left) U couples only to electrons, (upper right) U couples only to muons, (lower left) 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 [17] for a vector U boson that couples only to muons. The dashed (solid) lines show the expected (observed) exclusion contours. 
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Figure 7b:
Exclusion contours at 95% CL for a BSM boson U: (upper left) U couples only to electrons, (upper right) U couples only to muons, (lower left) 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 [17] for a vector U boson that couples only to muons. The dashed (solid) lines show the expected (observed) exclusion contours. 
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Figure 7c:
Exclusion contours at 95% CL for a BSM boson U: (upper left) U couples only to electrons, (upper right) U couples only to muons, (lower left) 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 [17] for a vector U boson that couples only to muons. The dashed (solid) lines show the expected (observed) exclusion contours. 
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Figure 7d:
Exclusion contours at 95% CL for a BSM boson U: (upper left) U couples only to electrons, (upper right) U couples only to muons, (lower left) 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 [17] for a vector 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 fourlepton and for dilepton events. The $ m_{\mathrm{L} } $ requirement for fourlepton events applies to all possible sameflavor, oppositesign 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 datataking 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 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. Uncertainties shown are combined statistical and systematic uncertainties. 
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Table 4:
Observed event yields and sample composition for the Z $ \to \mathrm{L} $ signal regions, inclusive of all 8 and 13 TeV data samples. Uncertainties shown are combined statistical and systematic uncertainties. 
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Table 5:
Measured branching fractions. The measured values for individual channels 4$ \mu $, 2$ \mu $2e, and 4 e are obtained from the BSM fit described in Section 8.1, while the value for the combined channel 4$ \ell $ is obtained from the SM fit. 
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Table 6:
The number of signal Z $ \to 4\ell $ events $ N_+ $ ($ N_ $) in which $ \sin\phi > $ 0 ($ < $ 0), and the associated asymmetry $ A_{\sin\phi} $ defined in Eq. (10). 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 Z $ \to 4\ell $ decays (\ell$ = \mathrm{e} $ or $ \mu $) in protonproton 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 of 138 fb$ ^{1} $ at 13 TeV with the CMS detector at the LHC. A total of 1,877 events is observed in the Z $ \to 4\ell $ signal region. The signal purity for each of the 4$ \mu $, 2$ \mu $2e, and 4e final states is above 97%. A measurement of the branching fraction for the sum of all fourlepton decay modes, $ \mathcal{B}(\mathrm{Z} \to 4\ell) $ has been reported. This measurement is more precise than all previous CMS and ATLAS results [5,6,7,8,9,10] and has a combined statistical and systematic precision of about 3%. Measurements of the branching fractions for the decays Z $ \to 4\mu $, Z $ \to 4\mathrm{e} $, and Z $ \to 2\mu 2\mathrm{e} $ are also reported. All measured branching fractions are consistent with the standard model (SM) expectations. Measurements of differential decay rates for the Z $ \to 4\ell $ process as functions of nine kinematic and angular quantities were presented. These measurements are reported in terms of the 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 fourlepton invariant mass 80 $ < m_{4\ell} < $ 100 GeV and the dilepton invariant mass $ m_{\mathrm{L} } > $ 4 GeV. These differential decay rates characterize the behavior of the Z $ \to 4\ell $ process and are consistent with simulations based on the SM. In the interest of exploring possible beyond the SM contributions to the Z $ \to 4\ell $ channel, a tripleproduct 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 ($ {\mathit{CP}} $) invariance in this decay. This asymmetry is observed to be consistent with zero for all 4$ \ell $ channels, as expected in the SM. Finally, the $ \mathcal{B}(\mathrm{Z} \to 4\ell) $, $ \mathcal{B}(\mathrm{Z} \to 4\mu\!) $, and $ \mathcal{B}(\mathrm{Z} \to 4\mathrm{e}\!) $ measurements were used to set limits on new physics in the form of a scalar or vector boson that may mediate the Z $ \to 4\ell $ process. These limits are more stringent than those set using previous measurements of $ \mathcal{B}(\mathrm{Z} \to 4\ell) $ [12] and complement direct searches for a narrow vector boson decaying to a $ \mu^{+}\mu^{} $ pair [17]. 
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