CMS-PAS-BPH-24-001

CMS-PAS-BPH-24-001
Observation of the rare decay $ \eta \to \mu^+\mu^-\mathrm{e^+e^-} $
CMS Collaboration
18 December 2025

Abstract: A first observation of the rare decay $ \eta \to \mu^+\mu^-\mathrm{e^+e^-} $ with significance well in excess of 5 standard deviations is reported by the CMS Collaboration at the CERN LHC. The result is based on a data sample corresponding to an integrated luminosity of 38.0 $ \mathrm{fb^{-1}} $, acquired in 2022 using a special high-rate dimuon trigger. A measurement of the branching fraction of this decay mode, using the decay mode $ \eta \to \mu^+\mu^-\gamma $ as normalization, yields a value $ \mathcal{B}(\eta\to\mu^+\mu^-\mathrm{e^+e^-}) = ( $ 2.1 $ \pm $ 0.7 $) \times 10^{-6} $, including statistical and systematic sources of uncertainty, along with the uncertainty in the branching fraction of the reference mode. This observed branching fraction is close to two orders of magnitude smaller than the existing limit, and is consistent with the latest standard model prediction.
Links: CDS record (PDF) ; CADI line (restricted) ;

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: Summary of expected background contributions to the yield measured in the signal channel based on a simplified MC simulation. Uncertainties are not shown. The equivalent luminosity for the simulation is shown in the top right.
png pdf	Figure 2: Fit of the four-lepton invariant mass spectra in data for the signal (upper) and reference (lower) channels. Black points denote the data, the dashed grey curve is the combinatorial background fit to a threshold function, the cyan dashed curve is the $\eta\to\mu^+\mu^-\gamma$ component of the fit, the red dot-dashed curve (signal channel only) is the $\eta\to\mu^+\mu^-\mathrm{e^+e^-}$ component of the fit, and the solid blue-violet curve is the overall fit including signal and background contributions. The orange distribution is the signal MC simulation (normalized to the BF prediction of $2.4\times10^{-6}$ by Ref.[11]), and the magenta distribution is the $\eta\to\mu^+\mu^-\gamma$ resonant background MC simulation, both normalized using the approximate cross section derived from the $\eta\to\mu^+\mu^-$ channel. Numbers $N$ shown in the legend are the total numbers of events in the signal peak (0.52--0.58 GeV for the signal channel and 0.50--0.62 GeV for the reference channel). Points in the lower panel are pulls relative to the full fit model, (data $-$ fit)/$\sqrt{\smash[b]{\sigma_{\textrm{data}}^2 + \sigma_{\textrm{fit}}^2}}$.
png pdf	Figure 2-a: Fit of the four-lepton invariant mass spectra in data for the signal (upper) and reference (lower) channels. Black points denote the data, the dashed grey curve is the combinatorial background fit to a threshold function, the cyan dashed curve is the $\eta\to\mu^+\mu^-\gamma$ component of the fit, the red dot-dashed curve (signal channel only) is the $\eta\to\mu^+\mu^-\mathrm{e^+e^-}$ component of the fit, and the solid blue-violet curve is the overall fit including signal and background contributions. The orange distribution is the signal MC simulation (normalized to the BF prediction of $2.4\times10^{-6}$ by Ref.[11]), and the magenta distribution is the $\eta\to\mu^+\mu^-\gamma$ resonant background MC simulation, both normalized using the approximate cross section derived from the $\eta\to\mu^+\mu^-$ channel. Numbers $N$ shown in the legend are the total numbers of events in the signal peak (0.52--0.58 GeV for the signal channel and 0.50--0.62 GeV for the reference channel). Points in the lower panel are pulls relative to the full fit model, (data $-$ fit)/$\sqrt{\smash[b]{\sigma_{\textrm{data}}^2 + \sigma_{\textrm{fit}}^2}}$.
png pdf	Figure 2-b: Fit of the four-lepton invariant mass spectra in data for the signal (upper) and reference (lower) channels. Black points denote the data, the dashed grey curve is the combinatorial background fit to a threshold function, the cyan dashed curve is the $\eta\to\mu^+\mu^-\gamma$ component of the fit, the red dot-dashed curve (signal channel only) is the $\eta\to\mu^+\mu^-\mathrm{e^+e^-}$ component of the fit, and the solid blue-violet curve is the overall fit including signal and background contributions. The orange distribution is the signal MC simulation (normalized to the BF prediction of $2.4\times10^{-6}$ by Ref.[11]), and the magenta distribution is the $\eta\to\mu^+\mu^-\gamma$ resonant background MC simulation, both normalized using the approximate cross section derived from the $\eta\to\mu^+\mu^-$ channel. Numbers $N$ shown in the legend are the total numbers of events in the signal peak (0.52--0.58 GeV for the signal channel and 0.50--0.62 GeV for the reference channel). Points in the lower panel are pulls relative to the full fit model, (data $-$ fit)/$\sqrt{\smash[b]{\sigma_{\textrm{data}}^2 + \sigma_{\textrm{fit}}^2}}$.

Tables
png pdf	Table 1: Contributions to the uncertainty in the measurement. Details are provided in the text.

Summary

In summary, the decay $\eta\to\mu^+\mu^-\mathrm{e^+e^-}$ has been observed for the first time, with a significance much greater than $5 \sigma$, with data collected by the CMS experiment at the CERN LHC in 2022. The branching fraction of this decay is measured using a ratio with the $\eta\to\mu^+\mu^-\gamma$ decay mode as normalization: $\mathcal{B}_{2\mu\mathrm{2e}}/\mathcal{B}_{2\mu\gamma} = (6.9 \pm 2.0)\times10^{-3}$. Incorporating the world-average value of $B(\eta\to\mu^+\mu^-\gamma)$ results in an $\eta\to\mu^+\mu^-\mathrm{e^+e^-}$ branching fraction of $(2.1 \pm 0.7) \times 10^{-6}$, which is close to two orders of magnitude below the previous upper limit and is consistent with the latest standard model prediction. This measurement will provide useful information for the determination of transition form factors that are used for theoretical calculations, such as the muon anomalous magnetic moment.

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