CMS-BPH-22-003

CMS-BPH-22-003 ; CERN-EP-2023-071
Observation of the rare decay of the $ \eta $ meson to four muons
CMS Collaboration
8 May 2023
Phys. Rev. Lett. 131 (2023) 091903
Abstract: A search for the rare $ \eta \to \mu^{+} \mu^{-} \mu^{+} \mu^{-} $ double-Dalitz decay is performed using a sample of proton-proton collisions, collected by the CMS experiment at the CERN LHC with high-rate muon triggers in 2017-2018 and corresponding to an integrated luminosity of 101 fb$ ^{-1} $. A signal having a statistical significance well in excess of 5 standard deviations is observed. Using the $ \eta \to \mu^{+} \mu^{-} $ decay as normalization, the branching fraction $ \mathcal{B}(\eta \to \mu^{+} \mu^{-} \mu^{+} \mu^{-}) = $ (5.0 $ \pm $ 0.8 (stat) $ \pm $ 0.7 (syst) $ \pm $ 0.7 ($\mathcal{B}_{2 \mu}$)) $\times $ 10$^{-9} $ is measured, where the last term is the uncertainty in the normalization channel branching fraction. This is the first measurement of this branching fraction and is found to be in agreement with theoretical predictions.
Links: e-print arXiv:2305.04904 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; Physics Briefing ; CADI line (restricted) ;

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: Feynman diagram of pseudoscalar decays into four leptons, known as double-Dalitz decays.
png pdf	Figure 2: Distribution of $ m_{2 \mu} $ obtained with the dimuon selection integrated in dimuon $ p_{\mathrm{T}} $ and in three $ p_{\mathrm{T}} $ ranges as indicated in the legend, with the number of events in the selected $ p_{\mathrm{T}} $ ranges multiplied by five for better visibility.
png pdf	Figure 3: Measured $ m_{4 \mu} $ distribution, with the fit result overlaid. The pull distribution in the lower panel is shown relative to the background component of the fit model and defined as $ (\text{Data} - \text{FitBkg}) /\sqrt{\sigma_{\text{Data}}^2 - \sigma_{\text{FitBkg}}^2} $. Uncertainties are statistical only.
png pdf	Figure 4: Comparison of the four-muon $ p_{\mathrm{T}} $ spectrum observed in data with 0.53 $ < m_{4 \mu} < $ 0.57 GeV (black points) and the signal prediction from simulation assuming the observed branching fraction (orange dashed line). Also shown is the predicted background shape, extracted from the mass sideband, normalized to the background fit yield (dotted blue line) and the sum of signal and background predictions (solid red line).
png pdf	Figure 5: Predicted background contributions to the signal mass window, estimated with simplified MC simulations. The $ \eta \to \mu^{+} \mu^{-} \mu^{+} \mu^{-} $ signal is displayed as a benchmark (red squares), followed by various other decay modes of the $ \eta $ meson. The curves are normalized to an integrated luminosity of 101 fb$ ^{-1} $. For unobserved decay modes, the current experimental upper limits are conservatively taken as the reference branching fractions in the estimations, with the exception of the signal channel, where the branching fraction measured in this work is used.
png pdf	Figure 6: The total efficiencies for the four-muon ($ A_{4 \mu}^{\mathrm{i,j}} $, red and blue points) and two-muon ($ A_{2 \mu}^{\mathrm{i,j}} $, orange and green points) decay channels, as functions of the generated meson's $ p_{\mathrm{T}} $ and $ y $, evaluated through MC simulation.

Tables

png pdf

Table 1:
Set of dimuon L1 requirements applied in the high-rate triggers. The angular separation between muons in the $ \eta$-$\phi $ plane is defined as $ \Delta R \equiv \sqrt{\smash[b]{(\Delta\eta)^2+(\Delta\phi)^2}} $, where $ \phi $ is the azimuthal angle. The first L1 path requires for each muon $ p_{\mathrm{T}} > $ 4.0 (4.5) GeV in 2017 (2018). The third path imposes separate requirements on each muon $ p_{\mathrm{T}} $. The $ m_{2 \mu} $ column denotes a range of allowed dimuon invariant masses. The charge column indicates if an opposite-sign (OS) requirement exists between muons. The last column reports the fraction of selected events accepted by each path.

Summary

In summary, the first observation of the $ \eta $ meson's rare double-Dalitz decay to four muons is reported. This is made possible by the use of CMS data collected with high-rate muon triggers at $ \sqrt{s} = $ 13 TeV in 2017 and 2018, corresponding to an integrated luminosity of 101 fb$ ^{-1} $. The branching fraction of the $ \eta \to 4 \mu $ decay is measured relative to the $ \eta \to 2 \mu $ decay, yielding a ratio of branching fractions of (0.86 $ \pm $ 0.14 (stat) $ \pm $ 0.12 (syst)) $\times$ 10$^{-3} $. Using the world average branching fraction value [1] for the normalization channel, the branching fraction of the four-muon decay channel is $ \mathcal{B}(\eta \to \mu^{+} \mu^{-} \mu^{+} \mu^{-}) = $ (5.0 $ \pm $ 0.8 (stat) $ \pm $ 0.7 (syst) $ \pm $ 0.7 ($\mathcal{B}_{2 \mu}$)) $\times$ 10$^{-9} $, where the last term is the uncertainty in the normalization channel branching fraction. This result is in agreement with theoretical predictions [10].

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