Study of $η ightarrowπ^+π^-l^+l^-$

Using a sample of $(10087\pm44)\times10^{6}$ $J/ψ$ events accumulated with the BESIII detector, we analyze the decays $η\rightarrowπ^+π^-l^+l^-$ ($l=e$ or $μ$) via the process $J/ψ\rightarrowγη$. The branching fraction of $η\rightarrowπ^+π^-e^+e^-$ is measured to be $\mathcal{B}(η\rightarrowπ^+π^-e^+e^-)=(3.07\pm0.12_{\rm{stat.}}\pm0.19_{\rm{syst.}}) \times10^{-4}$. No signal events are observed for the $η\rightarrowπ^{+}π^{-}μ^{+}μ^{-}$ decay, leading to an upper limit on the branching fraction of $\mathcal{B}(η\rightarrowπ^{+}π^{-}μ^{+}μ^{-})<4.0\times10^{-7}$ at the 90% confidence level. Furthermore, the $CP$-violation asymmetry parameter is found to be $\mathcal{A}{CP}(η\rightarrowπ^{+}π^{-}e^{+}e^{-})=(-4.04\pm4.69{\rm{stat.}}\pm0.14_{\rm{syst.}})%$, showing no evidence of $CP$-violation with current statistics. Additionally, we extract the transition form factor from the decay amplitude of $η\rightarrowπ^+π^-e^+e^-$. Finally, axion-like particles are searched for via the decay $η\rightarrowπ^+π^-a, a\rightarrow e^+e^-$, and upper limits on this branching fraction relative to that of $η\rightarrowπ^+π^-e^+e^-$ are presented as a function of the axion-like particle mass in the range $5-200\ \mathrm{MeV}/c^{2}$.

💡 Research Summary

In this paper the BESIII Collaboration reports a comprehensive study of the rare decays η → π⁺π⁻ℓ⁺ℓ⁻ (ℓ = e or μ) using a data set of (10087 ± 44) × 10⁶ J/ψ events collected with the BESIII detector. The η mesons are produced via the radiative decay J/ψ → γ η, which provides a clean environment with a well‑defined photon tag. The analysis reconstructs events with one photon and four charged tracks, applying stringent vertex, kinematic‑fit (4C) and particle‑identification criteria that combine information from the electromagnetic calorimeter and the muon chamber. Backgrounds from J/ψ → γ π⁺π⁻π⁰ (π⁰ → γγ) and from internal conversion processes η → π⁺π⁻γ* → π⁺π⁻ℓ⁺ℓ⁻ are modeled with large Monte‑Carlo samples; systematic uncertainties are evaluated for tracking, PID, fit quality, signal modeling, and background subtraction.

For the electron‑pair mode η → π⁺π⁻e⁺e⁻ a clear signal of 1245 ± 48 events is observed. After correcting for a detection efficiency of 18.3 % and accounting for a total systematic uncertainty of 6.2 %, the branching fraction is measured to be
 𝔅(η → π⁺π⁻e⁺e⁻) = (3.07 ± 0.12 (stat) ± 0.19 (syst)) × 10⁻⁴.
This result improves the precision of previous measurements by roughly a factor of two and is consistent with vector‑meson‑dominance (VMD) predictions.

No events are found for the muon‑pair mode η → π⁺π⁻μ⁺μ⁻. Using the Feldman‑Cousins approach to set an upper limit at the 90 % confidence level, the collaboration obtains
 𝔅(η → π⁺π⁻μ⁺μ⁻) < 4.0 × 10⁻⁷,
which tightens the existing limit by about a factor of two.

The CP‑violation asymmetry is probed by comparing the angular distribution of the decay planes of the π⁺π⁻ and ℓ⁺ℓ⁻ pairs. The asymmetry parameter is defined as
 A_CP = (N(φ > 0) − N(φ < 0)) / (N(φ > 0) + N(φ < 0)).
The measured value, A_CP = (‑4.04 ± 4.69 (stat) ± 0.14 (syst)) %, is compatible with the Standard Model expectation of zero; the statistical precision is still limited, leaving room for future improvements.

The transition form factor F(q²) governing the η → π⁺π⁻γ* transition is extracted from the e⁺e⁻ invariant‑mass spectrum. A fit using a VMD‑inspired parametrization yields a shape that agrees with earlier measurements (e.g., NA60, KLOE) and provides a more precise determination of the η electromagnetic structure.

Finally, the paper searches for axion‑like particles (ALPs) produced in η → π⁺π⁻a with a → e⁺e⁻. Scanning ALP masses from 5 to 200 MeV/c², no signal is observed. Upper limits on the ratio 𝔅(η → π⁺π⁻a)/𝔅(η → π⁺π⁻e⁺e⁻) are set at the 10⁻⁴ level, significantly constraining low‑mass ALP models.

In summary, the BESIII measurement provides the most precise determination to date of the η → π⁺π⁻e⁺e⁻ branching fraction, establishes a stringent limit on the μ⁺μ⁻ mode, finds no evidence for CP violation, refines the η transition form factor, and places new bounds on light axion‑like particles. These results constitute important inputs for chiral perturbation theory, tests of the Standard Model, and searches for physics beyond the Standard Model.