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CMS-EXO-18-008 ; CERN-EP-2018-208
Search for an $L_{\mu}-L_{\tau}$ gauge boson using $\mathrm{Z}\to4\mu$ events in proton-proton collisions at $\sqrt{s} = $ 13 TeV
Phys. Lett. B 792 (2019) 345
Abstract: A search for a narrow Z' gauge boson with a mass between 5 and 70 GeV resulting from an $L_{\mu}-L_{\tau}$ U(1) local gauge symmetry is reported. Theories that predict such a particle have been proposed as an explanation of various experimental discrepancies, including the lack of a dark matter signal in direct-detection experiments, tension in the measurement of the anomalous magnetic moment of the muon, and reports of possible lepton flavor universality violation in B meson decays. A data sample of proton-proton collisions at a center-of-mass energy of 13 TeV is used, corresponding to an integrated luminosity of 77.3 fb$^{-1}$ recorded in 2016 and 2017 by the CMS detector at the LHC. Events containing four muons with an invariant mass near the standard model Z boson mass are analyzed, and the selection is further optimized to be sensitive to the events that may contain $\mathrm{Z} \to \mathrm{Z'}\mu\mu\to4\mu$ decays. The event yields are consistent with the standard model predictions. Upper limits of $ 10^{-8} $-$ 10^{-7} $ at 95% confidence level are set on the product of branching fractions $\mathcal{B}(\mathrm{Z} \to \mathrm{Z'} \mu \mu) \mathcal{B}(\mathrm{Z'} \to\mu \mu)$, depending on the Z' mass, which excludes a Z' boson coupling strength to muons above 0.004-0.3. These are the first dedicated limits on $L_{\mu}-L_{\tau}$ models at the LHC and result in a significant increase in the excluded model parameter space. The results of this search may also be used to constrain the coupling strength of any light Z' gauge boson to muons.
Figures & Tables Summary References CMS Publications
Figures

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Figure 1:
Leading order Feynman diagrams for the signal process (left) and the dominant background process (right), where in each diagram the four-muon final state originates from annihilation.

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Figure 1-a:
Leading order Feynman diagram for the signal process, where the four-muon final state originates from annihilation..

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Figure 1-b:
Leading order Feynman diagram for the dominant background process, where the four-muon final state originates from annihilation..

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Figure 2:
Leading order Feynman diagrams for the subdominant quark-initiated (left) and gluon-initiated (right) background processes, where in each diagram the four-muon final state originates from conversion.

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Figure 2-a:
Leading order Feynman diagram for the subdominant quark-initiated background processes, where the four-muon final state originates from conversion.

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Figure 2-b:
Leading order Feynman diagram for the subdominant gluon-initiated background processes, where the four-muon final state originates from conversion.

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Figure 3:
Distribution of the reconstructed four-muon invariant mass $ {m_{4 {\mu}}} $ in the full mass range and a comparison to the predicted $ {{\mathrm {q}} {\overline {\mathrm {q}}}} / {\mathrm {g}} {\mathrm {g}} \to 4 {{\mu}}$ background. The blue histogram represents the expected SM 4$ {{\mu}}$ background distribution and the gray band shows the systematic uncertainty in its prediction. For illustration, three Z' signal hypotheses with different masses and coupling strengths are shown by colored lines.

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Figure 4:
Distributions of the reconstructed $m({\mathrm {Z}'}_1)$ and $m({\mathrm {Z}'}_2)$ observables and a comparison to the predicted $ {{\mathrm {q}} {\overline {\mathrm {q}}}} / {\mathrm {g}} {\mathrm {g}} \to 4 {{\mu}}$ background. The variable bin width has been chosen according to the expected mass resolution. The blue histogram represents the expected SM 4$ {{\mu}}$ background distributions and the gray band shows the systematic uncertainty in its prediction. For illustration, three Z' signal hypotheses with different masses and coupling strengths are also shown by colored lines.

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Figure 4-a:
Distribution of the reconstructed $m({\mathrm {Z}'}_1)$ observable and a comparison to the predicted $ {{\mathrm {q}} {\overline {\mathrm {q}}}} / {\mathrm {g}} {\mathrm {g}} \to 4 {{\mu}}$ background. The variable bin width has been chosen according to the expected mass resolution. The blue histogram represents the expected SM 4$ {{\mu}}$ background distributions and the gray band shows the systematic uncertainty in its prediction. For illustration, three Z' signal hypotheses with different masses and coupling strengths are also shown by colored lines.

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Figure 4-b:
Distribution of the reconstructed $m({\mathrm {Z}'}_2)$ observable and a comparison to the predicted $ {{\mathrm {q}} {\overline {\mathrm {q}}}} / {\mathrm {g}} {\mathrm {g}} \to 4 {{\mu}}$ background. The variable bin width has been chosen according to the expected mass resolution. The blue histogram represents the expected SM 4$ {{\mu}}$ background distributions and the gray band shows the systematic uncertainty in its prediction. For illustration, three Z' signal hypotheses with different masses and coupling strengths are also shown by colored lines.

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Figure 5:
Expected and observed 95% CL limits on the product of the $ {\mathrm {Z}'}\mu \mu $ production cross section and branching fraction (left y-axis) and $\mathcal {B}({\mathrm {Z}}\to {\mathrm {Z}'} {{\mu}} {{\mu}}) \mathcal {B}({\mathrm {Z}'}\to {{\mu}} {{\mu}})$ (right y-axis). The dashed black curve is the expected upper limit, with one and two standard-deviation bands shown in green and yellow, respectively. The solid black curve is the observed upper limit. The colored lines show the predicted cross section times branching fraction (left y-axis) and $\mathcal {B}({\mathrm {Z}}\to {\mathrm {Z}'} {{\mu}} {{\mu}}) \mathcal {B}({\mathrm {Z}'}\to {{\mu}} {{\mu}})$ (right y-axis) as a function of $m({\mathrm {Z}'})$ for three different coupling strengths, chosen for illustration. The $\mathcal {B}({\mathrm {Z}'}\to {{\mu}} {{\mu}})$ is taken to be $1/3$ to derive the theoretical predictions.

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Figure 6:
Top: Expected and observed 95% CL limits on the gauge coupling strength $g$ as a function of $m({\mathrm {Z}'})$. The dashed black curve is the expected upper limit, with one and two standard-deviation bands shown in green and yellow, respectively. The solid black curve is the observed upper limit. The $\mathcal {B}({\mathrm {Z}}^{\prime} \to {{\mu}} {{\mu}}) = $ 1/3 is used to derive the upper limits. The hatched area shows the region where the narrow width approximation is no longer valid. Bottom: comparison with other experiments sensitive to the same parameter space, with shaded regions being excluded as described in the text. These three constraints are adapted from Ref. [13].

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Figure 6-a:
Expected and observed 95% CL limits on the gauge coupling strength $g$ as a function of $m({\mathrm {Z}'})$. The dashed black curve is the expected upper limit, with one and two standard-deviation bands shown in green and yellow, respectively. The solid black curve is the observed upper limit. The $\mathcal {B}({\mathrm {Z}}^{\prime} \to {{\mu}} {{\mu}}) = $ 1/3 is used to derive the upper limits. The hatched area shows the region where the narrow width approximation is no longer valid.

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Figure 6-b:
Comparison with other experiments sensitive to the same parameter space, with shaded regions being excluded as described in the text. These three constraints are adapted from Ref. [13].
Tables

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Table 1:
The numbers of expected background and signal events and the numbers of observed candidate events after the full selection with 80 $ < {m_{4 {\mu}}} < $ 100 GeV. The signal and $ {{\mathrm {q}} {\overline {\mathrm {q}}}} / {\mathrm {g}} {\mathrm {g}} \to 4 {{\mu}}$ background rates are both estimated from simulation. The signal predictions are reported with systematic uncertainties only, while the background predictions are reported with statistical and systematic uncertainties, respectively. Also shown are the numbers of expected background and signal events and the numbers of observed candidate events in the relevant mass windows for three $m({\mathrm {Z}'})$ hypotheses. The values of the coupling strengths are chosen for the purpose of illustration.
Summary
A search for a Z' gauge boson resulting from an $L_{\mu}-L_{\tau}$ U(1) local gauge symmetry is presented, based on data from proton-proton collisions at $\sqrt{s} = $ 13 TeV corresponding to an integrated luminosity of 77.3 fb$^{-1}$ recorded in 2016 and 2017 by the CMS detector at the LHC. Events with four muons having an invariant mass near the mass of the standard model Z boson are selected, and the search sensitivity is optimized for the presence of $\mathrm{Z} \to \mathrm{Z'}\mu\mu\to4\mu$ decays. The search places strong constraints on theories that attempt to explain various experimental anomalies including the lack of a dark matter signal in direct-detection experiments, tension in the measurement of the anomalous magnetic moment of the muon, and reports of possible lepton flavor universality violation in B meson decays. The event yields are consistent with the standard model expectations. Upper limits of $ 10^{-8} $-$ 10^{-7} $ at 95% confidence level are set on the product of branching fractions $\mathcal{B}(\mathrm{Z} \to \mathrm{Z'}\mu\mu) \mathcal{B}(\mathrm{Z'}\to\mu\mu)$, depending on the Z' mass, which excludes a Z' boson coupling strength to muons above 0.004-0.3. These are the first dedicated limits on $L_{\mu}-L_{\tau}$ models at the LHC and result in a significant increase in the excluded model parameter space.
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Compact Muon Solenoid
LHC, CERN