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| CMS-PAS-BPH-26-004 | ||
| Observation of $ \eta \to \mu^+\mu^-\pi^+\pi^- $ and improved measurement of the branching fraction for $ \eta \to 2\mu^+2\mu^- $ | ||
| CMS Collaboration | ||
| 2026-07-23 | ||
| Abstract: A search for the rare decay $ \eta\to\mu^{+}\mu^{-}\pi^{+}\pi^{-} $ is performed using proton-proton collision data collected by the CMS experiment at the CERN LHC, corresponding to an integrated luminosity of 62.6 fb$ ^{-1} $ recorded in 2022 and 2023. In addition, the branching fraction ratio of $ \eta\to\mu^{+}\mu^{-}\mu^{+}\mu^{-} $ relative to $ \eta\to\mu^{+}\mu^{-} $ is measured with a precision improved by 60% compared with the previous CMS measurement. Using $ \eta\to\mu^{+}\mu^{-} $ as the normalization channel, the branching fraction ratios are measured to be $ \mathcal{B}(\eta\to\mu^{+}\mu^{-}\pi^{+}\pi^{-})/\mathcal{B}(\eta\to\mu^{+}\mu^{-}) = ( $ 2.89 $ \pm $ 0.48 $ \mathrm{(stat)}^{+0.42}_{-0.29} \mathrm{(syst)})\times10^{-3} $ and $ \mathcal{B}(\eta\to\mu^{+}\mu^{-}\mu^{+}\mu^{-})/\mathcal{B}(\eta\to\mu^{+}\mu^{-}) = ( $ 0.86 $ \pm $ 0.06 $ \mathrm{(stat)}^{+0.09}_{-0.08} \mathrm{(syst)})\times10^{-3} $. | ||
| Links: CDS record (PDF) ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Total reconstruction and selection efficiencies versus $ p_{\mathrm{T}} $ for the $ \eta\to\mu^{+}\mu^{-} $, $ \eta\to\mu^{+}\mu^{-}\pi^{+}\pi^{-} $, and $ \eta\to\mu^{+}\mu^{-}\mu^{+}\mu^{-} $ channels in different $ |\eta| $ ranges. Circles (triangles, squares) denote $ \eta\to\mu^{+}\mu^{-} $ ($ \eta\to\mu^{+}\mu^{-}\pi^{+}\pi^{-} $, $ \eta\to\mu^{+}\mu^{-}\mu^{+}\mu^{-} $). Colors indicate $ |\eta| $ intervals: blue ($ |\eta| < $ 0.9), orange (0.9 $ \leq|\eta| < $ 1.2), red (1.2 $ \leq|\eta| < $ 2.4). |
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Figure 2:
Observed $ \eta\to\mu^{+}\mu^{-} $ yields, $ N_{2\mu}^{i,j} $, in bins of $ p_{\mathrm{T}} $ and $ \eta $, divided by the bin width in $ p_{\mathrm{T}} $. Colors indicate $ |\eta| $ intervals: blue ($ |\eta| < $ 0.9), orange (0.9 $ \leq|\eta| < $ 1.2), red (1.2 $ \leq|\eta| < $ 2.4). |
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Figure 3:
Fits to the invariant mass of the $ \eta\to\mu^{+}\mu^{-}\pi^{+}\pi^{-} $ (left) and $ \eta\to\mu^{+}\mu^{-}\mu^{+}\mu^{-} $ (right) systems using the nominal background model $ (m_\eta - m_0)^{p_0} $. The inset in the left plot shows the same fit in an expanded region around the eta mass, with a linear vertical scale. Black points denote data; the gray curve represents the background component, the red curve the signal component, and the blue curve the total fit (signal + background). The yellow fit-uncertainty band includes both statistical and systematic effects. The lower panel shows the pulls with respect to the full fit model, defined as (data}-\text{fit) $ /\sqrt{\sigma_{\text{data}}^{2}-\sigma_{\text{fit}}^{2}} $. |
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Figure 3-a:
Fits to the invariant mass of the $ \eta\to\mu^{+}\mu^{-}\pi^{+}\pi^{-} $ (left) and $ \eta\to\mu^{+}\mu^{-}\mu^{+}\mu^{-} $ (right) systems using the nominal background model $ (m_\eta - m_0)^{p_0} $. The inset in the left plot shows the same fit in an expanded region around the eta mass, with a linear vertical scale. Black points denote data; the gray curve represents the background component, the red curve the signal component, and the blue curve the total fit (signal + background). The yellow fit-uncertainty band includes both statistical and systematic effects. The lower panel shows the pulls with respect to the full fit model, defined as (data}-\text{fit) $ /\sqrt{\sigma_{\text{data}}^{2}-\sigma_{\text{fit}}^{2}} $. |
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Figure 3-b:
Fits to the invariant mass of the $ \eta\to\mu^{+}\mu^{-}\pi^{+}\pi^{-} $ (left) and $ \eta\to\mu^{+}\mu^{-}\mu^{+}\mu^{-} $ (right) systems using the nominal background model $ (m_\eta - m_0)^{p_0} $. The inset in the left plot shows the same fit in an expanded region around the eta mass, with a linear vertical scale. Black points denote data; the gray curve represents the background component, the red curve the signal component, and the blue curve the total fit (signal + background). The yellow fit-uncertainty band includes both statistical and systematic effects. The lower panel shows the pulls with respect to the full fit model, defined as (data}-\text{fit) $ /\sqrt{\sigma_{\text{data}}^{2}-\sigma_{\text{fit}}^{2}} $. |
| Tables | |
png pdf |
Table 1:
Summary of relative systematic uncertainties in the $ \eta\to\mu^{+}\mu^{-}\pi^{+}\pi^{-} $ and $ \eta\to\mu^{+}\mu^{-}\mu^{+}\mu^{-} $ signal yields. |
| Summary |
| In summary, the first observation of $ \eta\to\mu^{+}\mu^{-}\pi^{+}\pi^{-} $ decays and an improved measurement of $\eta\to\mu^{+}\mu^{-}\mu^{+}\mu^{-}$ are presented using proton-proton collision data collected by the CMS experiment at $\sqrt{s}=13.6$ TeV. The measured branching fraction ratios are the most precise to date, with the $\eta\to\mu^{+}\mu^{-}\mu^{+}\mu^{-}$ result improving upon the previous CMS measurement. These results provide new experimental constraints on pseudoscalar transition form factors and precision studies of hadronic effects relevant to the anomalous magnetic moment of the muon. They also establish benchmarks for future studies of rare $\eta$ decays and for searches for low-mass mediators that could modify these decay rates. |
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