CMS-PAS-BPH-22-003

CMS-PAS-BPH-22-003
First observation of the rare 4 $ \mu $ decay of the $ \eta $ meson
CMS Collaboration
25 February 2023

Abstract: The first observation of the double-Dalitz decay $ \eta \rightarrow \mu^+\mu^-\mu^+\mu^- $ is reported with 2017 and 2018 data by the CMS experiment at the CERN LHC. A signal having a statistical significance well in excess of 5 standard deviations was identified using high-rate muon trigger data collected at a proton-proton collision center of mass energy of 13 TeV corresponding to an integrated luminosity of 101 fb$ ^{-1} $. Using the $ \eta \rightarrow \mu^+\mu^- $ decay as normalization, the branching fraction $ \mathcal{B}(\eta \rightarrow \mu^+\mu^-\mu^+\mu^-) = $(5.0 $ \pm $ 0.8 (stat) $\pm$ 0.7 (syst) $\pm$ 0.7 ($\mathcal{B}$)) $\times$ 10$^{-9} $ is measured, in agreement with theoretical estimates.
Links: CDS record (PDF) ; Physics Briefing ; CADI line (restricted) ; These preliminary results are superseded in this paper, PRL 131 (2023) 091903. The superseded preliminary plots can be found here.

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: Feynman diagrams of pseudoscalar decays into four leptons. The upper graph represents direct contributions to the decay, while the lower graph shows the contributions associated with vector-meson dominance.
png pdf	Figure 1-a: Feynman diagrams of pseudoscalar decays into four leptons. The upper graph represents direct contributions to the decay, while the lower graph shows the contributions associated with vector-meson dominance.
png pdf	Figure 1-b: Feynman diagrams of pseudoscalar decays into four leptons. The upper graph represents direct contributions to the decay, while the lower graph shows the contributions associated with vector-meson dominance.
png pdf	Figure 2: Distributions of $ m_{\mu\mu} $ obtained with the dimuon selection. Black points denote the inclusive $ p_{\mathrm{T}}^{\mu\mu} $ range, blue points denote 10 $ < p_{\mathrm{T}}^{\mu\mu} < $ 11 GeV (with 5x magnification), and red points denote 28 $ < p_{\mathrm{T}}^{\mu\mu} < $ 29 GeV (with 50x magnification).
png pdf	Figure 3: The observed $ m_{4\mu} $ in data with the fit results overlaid. Black points denote the data; the dashed green curve is the background component of the fit, the red dot-dashed curve is the signal component, and the solid blue curve is their sum. The pull on the lower panel is shown relative to the background component of the fit model.
png pdf	Figure 4: CMS $ A{\times}\varepsilon $ of $ \eta \rightarrow 2\mu $ (red) and $ \eta \rightarrow 4\mu $ (blue) decays vs. $ \eta $ candidate $ p_{\mathrm{T}} $, determined in simulation. The $ \eta $ candidate $ p_{\mathrm{T}} $ is the $ p_{\mathrm{T}} $ of the dimuon ($ p_{\mathrm{T}}^{2\mu} $) in the first case and the $ p_{\mathrm{T}} $ of the four-muon combination ($ p_{\mathrm{T}}^{4\mu} $) in the second.
png pdf	Figure 5: Comparison of the four-muon $ p_{\mathrm{T}} $ spectrum observed in data in the window $ m_{4\mu} \in $ [0.53, 0.57] GeV (black points) and the signal prediction from simulation assuming the observed branching fraction (green dashed line). Also shown is the predicted background shape normalized to the background fit yield, whose shape is extracted from the sideband (dotted blue line), and the sum of signal and background predictions (solid red line).
png pdf	Figure 6: Predicted resonant background contributions to the signal mass window, estimated with simplified Monte Carlo 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.

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{(\Delta\phi)^2 + (\Delta\eta)^2} $. The first L1 path requires a muon $ p_{\mathrm{T}} > $ 4 GeV in 2017 and $ > $ 4.5 GeV in 2018. The third path imposes a separate requirement on each muon $ p_{\mathrm{T}} $. The combined efficiency is about 92%.

Summary

In summary, the first observation of the double-Dalitz decay $ \eta \rightarrow \mu^+\mu^-\mu^+\mu^- $ is reported. The observation of such rare decays 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 101fb$^{-1}$. The branching fraction of the $ \eta \rightarrow \mu^+\mu^-\mu^+\mu^- $ decay is measured relative to the decay $ \eta \rightarrow \mu^+\mu^-$, yielding the ratio (0.9 $\pm$ 0.1 (syst) $\pm$ 0.1 (stat)) $\times$ 10$^{-3}$. Using the world average value of the reference channel, the branching fraction of the target channel is measured as $\mathcal{B}(\eta \to \mu^+ \mu^- \mu^+ \mu^-) =$ (5.0 $\pm$ 0.8 (stat) $\pm$ 0.7 (syst) $\pm$ 0.7 ($\mathcal{B}$)) $\times$ 10$^{-9}$, a precision of 26%. The central value is 25% higher than the SM prediction but still in agreement within the quoted uncertainties. A more precise branching fraction measurement of the reference channel will provide a corresponding stimulus to increase the statistics and improve the signal efficiency modeling of the measurement reported in this note.

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