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| CMS-PAS-BPH-24-010 | ||
| Search for the lepton flavor violating $ \tau^{-}\to\mu^{-}\mu^{+}\mu^{-} $ decay in proton-proton collisions at $ \sqrt{s}= $ 13.6 TeV | ||
| CMS Collaboration | ||
| 2026-03-26 | ||
| Abstract: This work presents a search for lepton flavor violating decay of a tau lepton into three muons ($ \tau^{-}\to\mu^{-}\mu^{+}\mu^{-} $) in proton-proton collisions at a center-of-mass energy of 13.6 TeV collected by the CMS experiment in 2022 and 2023, corresponding to an integrated luminosity of up to 63 fb$ ^{-1} $. Two sources of tau leptons are considered: heavy-flavor hadrons and vector boson decays. No significant excess above the expectation from combinatorial backgrounds is observed in the mass spectrum of three muons. Observed (expected) upper limits on the branching fraction $ \mathcal{B}(\tau^{-} \to \mu^{-}\mu^{+}\mu^{-}) $ at 90% confidence level are 6.7 (4.7)$ \times 10^{-8} $. | ||
| Links: CDS record (PDF) ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Signal and background distributions for the four observables with the highest impact on the V channel BDT performance: the relative tau isolation (upper left), the $ \cos(\alpha_{\text{2D}}) $ (upper right), the transverse mass $ m_T $ (lower left), and the muon triplet total transverse momentum $ p_{\mathrm{T}}(3\mu) $ (lower right). The signal and background distribution are obtained respectively from simulated events in W boson decay and from data in mass sidebands, and normalized to unity. The first and last bins contain the underflow and overflow events, respectively. |
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Figure 1-a:
Signal and background distributions for the four observables with the highest impact on the V channel BDT performance: the relative tau isolation (upper left), the $ \cos(\alpha_{\text{2D}}) $ (upper right), the transverse mass $ m_T $ (lower left), and the muon triplet total transverse momentum $ p_{\mathrm{T}}(3\mu) $ (lower right). The signal and background distribution are obtained respectively from simulated events in W boson decay and from data in mass sidebands, and normalized to unity. The first and last bins contain the underflow and overflow events, respectively. |
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Figure 1-b:
Signal and background distributions for the four observables with the highest impact on the V channel BDT performance: the relative tau isolation (upper left), the $ \cos(\alpha_{\text{2D}}) $ (upper right), the transverse mass $ m_T $ (lower left), and the muon triplet total transverse momentum $ p_{\mathrm{T}}(3\mu) $ (lower right). The signal and background distribution are obtained respectively from simulated events in W boson decay and from data in mass sidebands, and normalized to unity. The first and last bins contain the underflow and overflow events, respectively. |
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Figure 1-c:
Signal and background distributions for the four observables with the highest impact on the V channel BDT performance: the relative tau isolation (upper left), the $ \cos(\alpha_{\text{2D}}) $ (upper right), the transverse mass $ m_T $ (lower left), and the muon triplet total transverse momentum $ p_{\mathrm{T}}(3\mu) $ (lower right). The signal and background distribution are obtained respectively from simulated events in W boson decay and from data in mass sidebands, and normalized to unity. The first and last bins contain the underflow and overflow events, respectively. |
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Figure 1-d:
Signal and background distributions for the four observables with the highest impact on the V channel BDT performance: the relative tau isolation (upper left), the $ \cos(\alpha_{\text{2D}}) $ (upper right), the transverse mass $ m_T $ (lower left), and the muon triplet total transverse momentum $ p_{\mathrm{T}}(3\mu) $ (lower right). The signal and background distribution are obtained respectively from simulated events in W boson decay and from data in mass sidebands, and normalized to unity. The first and last bins contain the underflow and overflow events, respectively. |
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Figure 2:
Trimuon mass distributions of the 2022 (left) and 2023 (right) data events in the three $ |\eta| $ categories A (upper row), B (middle row) and C (lower row) of the V channel analysis. Data are shown with black markers, and the blue line represents the background-only fit to data in the sidebands. Expected signal distribution for $ \mathcal{B}(\tau \!\to\! 3\mu) $ from W (Z) boson decay is shown in red (green). |
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Figure 2-a:
Trimuon mass distributions of the 2022 (left) and 2023 (right) data events in the three $ |\eta| $ categories A (upper row), B (middle row) and C (lower row) of the V channel analysis. Data are shown with black markers, and the blue line represents the background-only fit to data in the sidebands. Expected signal distribution for $ \mathcal{B}(\tau \!\to\! 3\mu) $ from W (Z) boson decay is shown in red (green). |
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Figure 2-b:
Trimuon mass distributions of the 2022 (left) and 2023 (right) data events in the three $ |\eta| $ categories A (upper row), B (middle row) and C (lower row) of the V channel analysis. Data are shown with black markers, and the blue line represents the background-only fit to data in the sidebands. Expected signal distribution for $ \mathcal{B}(\tau \!\to\! 3\mu) $ from W (Z) boson decay is shown in red (green). |
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Figure 2-c:
Trimuon mass distributions of the 2022 (left) and 2023 (right) data events in the three $ |\eta| $ categories A (upper row), B (middle row) and C (lower row) of the V channel analysis. Data are shown with black markers, and the blue line represents the background-only fit to data in the sidebands. Expected signal distribution for $ \mathcal{B}(\tau \!\to\! 3\mu) $ from W (Z) boson decay is shown in red (green). |
png pdf |
Figure 2-d:
Trimuon mass distributions of the 2022 (left) and 2023 (right) data events in the three $ |\eta| $ categories A (upper row), B (middle row) and C (lower row) of the V channel analysis. Data are shown with black markers, and the blue line represents the background-only fit to data in the sidebands. Expected signal distribution for $ \mathcal{B}(\tau \!\to\! 3\mu) $ from W (Z) boson decay is shown in red (green). |
png pdf |
Figure 2-e:
Trimuon mass distributions of the 2022 (left) and 2023 (right) data events in the three $ |\eta| $ categories A (upper row), B (middle row) and C (lower row) of the V channel analysis. Data are shown with black markers, and the blue line represents the background-only fit to data in the sidebands. Expected signal distribution for $ \mathcal{B}(\tau \!\to\! 3\mu) $ from W (Z) boson decay is shown in red (green). |
png pdf |
Figure 2-f:
Trimuon mass distributions of the 2022 (left) and 2023 (right) data events in the three $ |\eta| $ categories A (upper row), B (middle row) and C (lower row) of the V channel analysis. Data are shown with black markers, and the blue line represents the background-only fit to data in the sidebands. Expected signal distribution for $ \mathcal{B}(\tau \!\to\! 3\mu) $ from W (Z) boson decay is shown in red (green). |
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Figure 3:
Fits to the $ \mu^{-}\mu^{+}\pi^{+} $ invariant mass distribution in 2022 (left) and 2023 (right) data. The $ D_{s} $ and $ D^{+} $ peaks are modeled with Crystal Ball functions, while the background is fitted with an exponential function. |
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Figure 3-a:
Fits to the $ \mu^{-}\mu^{+}\pi^{+} $ invariant mass distribution in 2022 (left) and 2023 (right) data. The $ D_{s} $ and $ D^{+} $ peaks are modeled with Crystal Ball functions, while the background is fitted with an exponential function. |
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Figure 3-b:
Fits to the $ \mu^{-}\mu^{+}\pi^{+} $ invariant mass distribution in 2022 (left) and 2023 (right) data. The $ D_{s} $ and $ D^{+} $ peaks are modeled with Crystal Ball functions, while the background is fitted with an exponential function. |
png pdf |
Figure 4:
Normalized signal and background distributions for the four variables with the largest importance in the event-level BDT. Shown are the normalized $ \chi^2 $ of the trimuon vertex fit (upper left), the angle between the $ \tau $ candidate direction and the vector between the trimuon vertex and the beamspot in the transverse plane (upper right), the per-muon BDT score of the lowest $ p_{\mathrm{T}} $ muon (lower left), and a measure of the probability that the muon track is comprised of hits belonging to two independent particle trajectories (lower right). In the latter case, the maximum value out of the three muons is considered. |
png pdf |
Figure 4-a:
Normalized signal and background distributions for the four variables with the largest importance in the event-level BDT. Shown are the normalized $ \chi^2 $ of the trimuon vertex fit (upper left), the angle between the $ \tau $ candidate direction and the vector between the trimuon vertex and the beamspot in the transverse plane (upper right), the per-muon BDT score of the lowest $ p_{\mathrm{T}} $ muon (lower left), and a measure of the probability that the muon track is comprised of hits belonging to two independent particle trajectories (lower right). In the latter case, the maximum value out of the three muons is considered. |
png pdf |
Figure 4-b:
Normalized signal and background distributions for the four variables with the largest importance in the event-level BDT. Shown are the normalized $ \chi^2 $ of the trimuon vertex fit (upper left), the angle between the $ \tau $ candidate direction and the vector between the trimuon vertex and the beamspot in the transverse plane (upper right), the per-muon BDT score of the lowest $ p_{\mathrm{T}} $ muon (lower left), and a measure of the probability that the muon track is comprised of hits belonging to two independent particle trajectories (lower right). In the latter case, the maximum value out of the three muons is considered. |
png pdf |
Figure 4-c:
Normalized signal and background distributions for the four variables with the largest importance in the event-level BDT. Shown are the normalized $ \chi^2 $ of the trimuon vertex fit (upper left), the angle between the $ \tau $ candidate direction and the vector between the trimuon vertex and the beamspot in the transverse plane (upper right), the per-muon BDT score of the lowest $ p_{\mathrm{T}} $ muon (lower left), and a measure of the probability that the muon track is comprised of hits belonging to two independent particle trajectories (lower right). In the latter case, the maximum value out of the three muons is considered. |
png pdf |
Figure 4-d:
Normalized signal and background distributions for the four variables with the largest importance in the event-level BDT. Shown are the normalized $ \chi^2 $ of the trimuon vertex fit (upper left), the angle between the $ \tau $ candidate direction and the vector between the trimuon vertex and the beamspot in the transverse plane (upper right), the per-muon BDT score of the lowest $ p_{\mathrm{T}} $ muon (lower left), and a measure of the probability that the muon track is comprised of hits belonging to two independent particle trajectories (lower right). In the latter case, the maximum value out of the three muons is considered. |
png pdf |
Figure 5:
Trimuon mass distributions for the three subcategories of pseodorapidity category A. Results for 2022 (2023) data are shown on the left (right). Data points in the sidebands are fitted with the lowest $ \chi^2 $ pdf in the envelope (blue line), while the signal for $ \mathcal{B}(\tau\to3\mu)=10^{-7} $ is fitted with a Crystal Ball function plus a Gaussian function (red line). |
png pdf |
Figure 5-a:
Trimuon mass distributions for the three subcategories of pseodorapidity category A. Results for 2022 (2023) data are shown on the left (right). Data points in the sidebands are fitted with the lowest $ \chi^2 $ pdf in the envelope (blue line), while the signal for $ \mathcal{B}(\tau\to3\mu)=10^{-7} $ is fitted with a Crystal Ball function plus a Gaussian function (red line). |
png pdf |
Figure 5-b:
Trimuon mass distributions for the three subcategories of pseodorapidity category A. Results for 2022 (2023) data are shown on the left (right). Data points in the sidebands are fitted with the lowest $ \chi^2 $ pdf in the envelope (blue line), while the signal for $ \mathcal{B}(\tau\to3\mu)=10^{-7} $ is fitted with a Crystal Ball function plus a Gaussian function (red line). |
png pdf |
Figure 5-c:
Trimuon mass distributions for the three subcategories of pseodorapidity category A. Results for 2022 (2023) data are shown on the left (right). Data points in the sidebands are fitted with the lowest $ \chi^2 $ pdf in the envelope (blue line), while the signal for $ \mathcal{B}(\tau\to3\mu)=10^{-7} $ is fitted with a Crystal Ball function plus a Gaussian function (red line). |
png pdf |
Figure 5-d:
Trimuon mass distributions for the three subcategories of pseodorapidity category A. Results for 2022 (2023) data are shown on the left (right). Data points in the sidebands are fitted with the lowest $ \chi^2 $ pdf in the envelope (blue line), while the signal for $ \mathcal{B}(\tau\to3\mu)=10^{-7} $ is fitted with a Crystal Ball function plus a Gaussian function (red line). |
png pdf |
Figure 5-e:
Trimuon mass distributions for the three subcategories of pseodorapidity category A. Results for 2022 (2023) data are shown on the left (right). Data points in the sidebands are fitted with the lowest $ \chi^2 $ pdf in the envelope (blue line), while the signal for $ \mathcal{B}(\tau\to3\mu)=10^{-7} $ is fitted with a Crystal Ball function plus a Gaussian function (red line). |
png pdf |
Figure 5-f:
Trimuon mass distributions for the three subcategories of pseodorapidity category A. Results for 2022 (2023) data are shown on the left (right). Data points in the sidebands are fitted with the lowest $ \chi^2 $ pdf in the envelope (blue line), while the signal for $ \mathcal{B}(\tau\to3\mu)=10^{-7} $ is fitted with a Crystal Ball function plus a Gaussian function (red line). |
png pdf |
Figure 6:
The expected median (dashed line) with its 68% and 95% confidence intervals (green and yellow bands) and observed upper limit for $ \mathcal{B}(\tau \!\to\! 3\mu) $ at 90% CL, obtained with 2022 and 2023 data separately and combined, using a combination of the heavy-flavor and V channels. |
| Tables | |
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Table 1:
Event selection in the V channel. |
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Table 2:
Systematic uncertainties affecting the signal normalization in the V channel and their impacts on the expected signal yield. The last column indicates whether the uncertainties are correlated among the years (Y) or categories (C). |
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Table 3:
Signal event selection in the heavy-flavor channel. |
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Table 4:
Systematic uncertainties and their impact on the expected signal yield in the heavy-flavor channel. The last column indicates whether the uncertainties are correlated among the years (Y) or categories (C). |
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Table 5:
Event yields in the signal region of the muon triplet mass spectrum. Shown are the number of expected signal events for $ \mathcal{B} (\tau \!\to\! 3\mu) = 10^{-7} $, the background expectation from the fit to the $ m(3\mu) $ sidebands, and the number of events observed in data. |
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Table 6:
The expected and observed upper limit for different combinations of the analysis categories. The upper limits are computed at 90% of confidence level and reported in units of 10$ ^{-8} $. |
| Summary |
| A search for the lepton flavor violating decay $ \tau \!\to\! 3\mu $ has been performed in proton-proton collisions at a center-of-mass energy of $ \sqrt{s} = $ 13.6 TeV, recorded with the CMS experiment in 2022 and 2023. The decays of tau leptons produced in heavy-flavor, W, and Z boson decays have been utilized. No evidence for the decay has been observed, and upper limits on the branching fraction $ \mathcal{B}(\tau \!\to\! 3\mu) $ are set, yielding an observed (expected) upper limit of 6.7 $ \:(4.7) \times 10^{-8} $ at 90% confidence level. |
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