CMS-BPH-24-001

CMS-BPH-24-001 ; CERN-EP-2026-023
Observation of the rare decay $ \eta\to\mu^{+}\mu^{-}\mathrm{e}^+\mathrm{e}^- $
CMS Collaboration
1 May 2026
Submitted to Physical Review Letters
Abstract: A first observation of the rare decay $ \eta\to\mu^{+}\mu^{-}\mathrm{e}^+\mathrm{e}^- $ is reported by the CMS Collaboration at the CERN LHC. The result is based on a proton-proton collision data sample at $ \sqrt{s} = $ 13.6 TeV corresponding to an integrated luminosity of 38.0 fb$ ^{-1} $, acquired in 2022 using a high-rate dimuon trigger. Using the $ \eta\to\mu^{+}\mu^{-}\gamma $ decay channel for normalization, the branching fraction is measured to be $ \mathcal{B}(\eta\to\mu^{+}\mu^{-}\mathrm{e}^+\mathrm{e}^-) = ( $ 2.4 $ \pm $ 0.8 $)\times 10^{-6} $, with the uncertainty including statistical and systematic sources as well as the $ \mathcal{B}(\eta\to\mu^{+}\mu^{-}\gamma) $ uncertainty. This result is close to two orders of magnitude smaller than the existing limit, and is consistent with recent theoretical predictions.
Links: e-print arXiv:2605.00615 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ;

Figures	Summary	References	CMS Publications

Figures
png pdf	Figure 1: Leading order standard model Feynman diagram for the decay $ \eta\to\mu^{+}\mu^{-}\mathrm{e}^+\mathrm{e}^- $.
png pdf	Figure 2: Summary of expected background contributions to the yield measured in the signal channel based on a simplified MC simulation. The signal channel is shown in red squares, and is closely mimicked by the $ \eta\to\mu^{+}\mu^{-}\gamma $ channel, shown in blue stars. Uncertainties are not shown. The equivalent luminosity for the simulation is 38.0 fb$ ^{-1} $.
png pdf	Figure 3: 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}^+\mathrm{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^{-}\mathrm{e}^+\mathrm{e}^- $ resonant background MC simulation (normalized to the world average BF measurement of 3.1 $ \times 10^{-4} $ [1]), both also normalized using the approximate cross section derived from the $ \eta\to\mu^{+}\mu^{-} $ 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 3-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}^+\mathrm{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^{-}\mathrm{e}^+\mathrm{e}^- $ resonant background MC simulation (normalized to the world average BF measurement of 3.1 $ \times 10^{-4} $ [1]), both also normalized using the approximate cross section derived from the $ \eta\to\mu^{+}\mu^{-} $ 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 3-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}^+\mathrm{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^{-}\mathrm{e}^+\mathrm{e}^- $ resonant background MC simulation (normalized to the world average BF measurement of 3.1 $ \times 10^{-4} $ [1]), both also normalized using the approximate cross section derived from the $ \eta\to\mu^{+}\mu^{-} $ 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}} $.

Summary

In summary, the decay $ \eta\to\mu^{+}\mu^{-}\mathrm{e}^+\mathrm{e}^- $ has been observed for the first time, with a significance much larger than 5 standard deviations, with data collected by the CMS experiment at the LHC in 2022. The branching fraction of this decay is measured with respect to the $ \eta\to\mu^{+}\mu^{-}\gamma $ decay mode: $ \mathcal{B}(\eta\to\mu^{+}\mu^{-}\mathrm{e}^+\mathrm{e}^-) = (7.3 \pm 2.2)\times 10^{-3}$.Incorporating the world-average value of $ \eta\to\mu^{+}\mu^{-}\gamma $ results in an $ \eta\to\mu^{+}\mu^{-}\mathrm{e}^+\mathrm{e}^- $ branching fraction of $(2.4 \pm 0.8) \times 10^{-6}$, which is close to two orders of magnitude below the previous upper limit and is consistent with the latest standard model predictions.This measurement provides useful information for the determination of transition form factors that are used for theoretical calculations, such as the muon anomalous magnetic moment.

References
1	Particle Data Group , S. Navas et al.	Review of particle physics	PRD 110 (2024) 030001
2	M. Knecht, S. Narison, A. Rabemananjara, and D. Rabetiarivony	Scalar meson contributions to $ a_\mu $ from hadronic light-by-light scattering	PLB 787 (2018) 111	1808.03848
3	CMS Collaboration	Observation of the rare decay of the $ \eta $ meson to four muons	PRL 131 (2023) 31	CMS-BPH-22-003 2305.04904
4	L. Gan, B. Kubis, E. Passemar, and S. Tulin	Precision tests of fundamental physics with $ \eta $ and $ \eta^\prime $ mesons	Phys. Rept. 945 (2022) 1	2007.00664
5	E. Goudzovski et al.	New physics searches at kaon and hyperon factories	Rept. Prog. Phys. 86 (2023) 016201	2201.07805
6	J. Bijnens and J. Gasser	Eta decays at and beyond $ p^4 $ in chiral perturbation theory	Phys. Scripta T 99 (2002) 34	hep-ph/0202242
7	T. Fujiwara et al.	Non-Abelian anomaly and vector mesons as dynamical gauge bosons of hidden local symmetries	Prog. Theor. Phys. 73 (1985) 926
8	M. Bando, T. Kugo, and K. Yamawaki	On the vector mesons as dynamical gauge bosons of hidden local symmetries	NPB 259 (1985) 493
9	T. Petri	Anomalous decays of pseudoscalar mesons	Masters thesis, University of Bonn, Germany, 2010
10	C.-C. Lih	Study of $ \pi^0 $ and $ \eta $ decays containing dilepton	J. Phys. G: Nucl. Part. Phys 38 (2011) 065001	0912.2147
11	R. Escribano and S. Gonz \`a lez-Sol \'i s	A data-driven approach to $ \pi^0 $, $ \eta $ and $ \eta^\prime $ single and double Dalitz decays	Chin. Phys. C 42 (2018) 023109	1511.04916
12	K. Kampf, J. Novotn \'y , and P. Sanchez-Puertas	Radiative corrections to double-Dalitz decays revisited	PRD 97 (2018) 056010	1801.06067
13	T. Aoyama et al.	The anomalous magnetic moment of the muon in the Standard Model	Phys. Rept. 887 (2020) 1	2006.04822
14	R. Aliberti et al.	The anomalous magnetic moment of the muon in the Standard Model: an update	Phys. Rept. 1143 (2025) 1	2505.21476
15	R. Abegg et al.	Measurement of the branching ratio for the decay $ \eta\rightarrow\mu^{+}\mu^{-} $	PRD 50 (1994) 92
16	BESIII Collaboration	Measurement of the branching fraction of $ \eta \to \mu^+\mu^- $ and search for $ \eta \to e^+e^- $	PRD 113 (2026) 072002	2512.07144
17	KLOE, KLOE-2 Collaboration	Observation of the rare $ \eta\to e^+e^-e^+e^- $ decay with the KLOE experiment	PLB 702 (2011) 324	1105.6067
18	BESIII Collaboration	Observation of the double Dalitz decay $ {\eta}^{'}\rightarrow{e}^{+}{e}^{-}{e}^{+}{e}^{-} $	PRD 105 (2022) 11	2203.12229
19	CELSIUS/WASA Collaboration	Measurement of $ \eta $ meson decays into lepton-antilepton pairs	PRD 77 (2008) 032004	0711.3531
20	CMS Collaboration	HEPData record for this analysis	link
21	CMS Collaboration	The CMS experiment at the CERN LHC	JINST 3 (2008) S08004
22	CMS Collaboration	Development of the CMS detector for the CERN LHC Run 3	JINST 19 (2024) P05064	CMS-PRF-21-001 2309.05466
23	CMS Collaboration	Performance of the CMS Level-1 trigger in proton-proton collisions at $ \sqrt{s} = $ 13 TeV	JINST 15 (2020) P10017	CMS-TRG-17-001 2006.10165
24	CMS Collaboration	The CMS trigger system	JINST 12 (2017) P01020	CMS-TRG-12-001 1609.02366
25	CMS Collaboration	Performance of the CMS high-level trigger during LHC Run 2	JINST 19 (2024) P11021	CMS-TRG-19-001 2410.17038
26	CMS Collaboration	Electron and photon reconstruction and identification with the CMS experiment at the CERN LHC	JINST 16 (2021) P05014	CMS-EGM-17-001 2012.06888
27	CMS Collaboration	Performance of the CMS muon detector and muon reconstruction with proton-proton collisions at $ \sqrt{s}= $ 13 TeV	JINST 13 (2018) P06015	CMS-MUO-16-001 1804.04528
28	CMS Collaboration	Description and performance of track and primary-vertex reconstruction with the CMS tracker	JINST 9 (2014) P10009	CMS-TRK-11-001 1405.6569
29	CMS Collaboration	Performance of photon reconstruction and identification with the CMS detector in proton-proton collisions at $ \sqrt{s} = $ 8 TeV	JINST 10 (2015) P08010	CMS-EGM-14-001 1502.02702
30	CMS Collaboration	Enriching the physics program of the CMS experiment via data scouting and data parking	Phys. Rept. 1115 (2025) 678	CMS-EXO-23-007 2403.16134
31	R. Fr \"u hwirth	Application of Kalman filtering to track and vertex fitting	NIM A 262 (1987) 444
32	C. Bierlich et al	A comprehensive guide to the physics and usage of PYTHIA 8.3	SciPost Phys. Codebases 8 (2022)	2203.11601
33	CMS Collaboration	Extraction and validation of a new set of CMS PYTHIA8 tunes from underlying-event measurements	EPJC 80 (2020) 4	CMS-GEN-17-001 1903.12179
34	R. I. Djhelyadin et al.	Investigation of the electromagnetic structure of the $ \eta $ meson in the decay $ \eta \rightarrow \mu^+\mu^-\gamma $	PLB 94 (1980) 548
35	R. H. Dalitz	On higher Born approximations in potential scattering	Proc. R. Soc. A 206 (1951) 509
36	N. M. Kroll and W. Wada	Internal pair production associated with the emission of high-energy gamma rays	PR 98 (1955) 1355
37	GEANT4 Collaboration	GEANT 4---a simulation toolkit	NIM A 506 (2003) 250
38	I. Fröhlich et al.	Pluto: A Monte Carlo simulation tool for hadronic physics	PoS ACAT 07 (2007) 6	0708.2382
39	M. J. Oreglia	A study of the reactions $ \psi^\prime \to \gamma \gamma \psi $	PhD thesis, Stanford University, SLAC Report SLAC-R-236, 1980 link
40	CMS Collaboration	Search for long-lived heavy neutral leptons with displaced vertices in proton-proton collisions at $ \sqrt{s}=13 $TeV	JHEP 07 (2022) 81	CMS-EXO-20-009 2201.05578