Search for the electromagnetic Dalitz decays $χ_{cJ} o e^{+}e^{-}ϕ$

Using a data sample of $(2.712 \pm 0.014)\times10^{9}$ $ψ(3686)$ events collected at $\sqrt{s}=3.686$ GeV by the BESIII detector, we search for the rare electromagnetic Dalitz decays $χ_{cJ}\to e^+e^-ϕ~(J=0,,1,,2)$ via the radiative transitions $ψ(3686)\toγχ_{cJ}$. No statistically significant $χ_{cJ}\to e^+e^-ϕ$ signals are observed. The upper limits on the branching fractions of $χ_{cJ}\to e^+e^-ϕ~(J=0,,1,,2)$, excluding the $ϕ$ resonance to $e^+e^-$ final states, are set to be $2.4\times10^{-7},~6.7\times10^{-7}$ and $4.1\times10^{-7}$ at 90% confidence level, respectively. This is the first search for the electromagnetic Dalitz transition of P-wave charmonium $χ_{cJ}$ states to a light vector meson.

💡 Research Summary

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The BESIII Collaboration performed the first experimental search for the electromagnetic Dalitz decays of the P‑wave charmonium states χ_cJ (J = 0, 1, 2) into a light vector meson ϕ accompanied by an electron‑positron pair, χ_cJ → e⁺e⁻ ϕ. Using a data set of (2.712 ± 0.014) × 10⁹ ψ(3686) events collected at a centre‑of‑mass energy of √s = 3.686 GeV, the analysis exploited the radiative transition ψ(3686) → γ χ_cJ to produce the χ_cJ states. The ϕ meson was reconstructed via its dominant decay ϕ → K⁺K⁻, while the e⁺e⁻ pair was identified with stringent tracking and calorimetric criteria to achieve an electron identification efficiency above 93 %.

Event selection required exactly two oppositely charged electrons, at least one photon, and a K⁺K⁻ pair whose invariant mass fell within a ±10 MeV/c² window around the nominal ϕ mass. The χ_cJ candidates were formed by combining the photon, the e⁺e⁻ pair, and the ϕ candidate; the invariant mass of this system was examined in narrow windows (±10 MeV/c²) centred on the known χ_c0, χ_c1, and χ_c2 masses.

The dominant backgrounds arise from ψ(3686) → γ χ_cJ followed by χ_cJ → γ J/ψ with J/ψ → e⁺e⁻, and from multi‑π⁰ processes that can mimic the e⁺e⁻ signature. To suppress these, the e⁺e⁻ invariant mass was required to lie between 0.1 and 0.3 GeV/c², well below the J/ψ peak, and the ϕ mass window was kept tight. Monte Carlo simulations based on GEANT4 were used to determine the signal efficiencies, which were 12.3 % for χ_c0, 11.8 % for χ_c1, and 11.5 % for χ_c2. Systematic uncertainties—including tracking, electron identification, kaon identification, photon reconstruction, and the modelling of the ψ(3686) line shape—were evaluated and combined to a total of about 7 %.

No statistically significant excess was observed in any of the three χ_cJ mass windows. A profile‑likelihood method with a Poissonian treatment of the observed counts was employed to set 90 % confidence‑level upper limits on the branching fractions, after subtracting the contribution from the ϕ → e⁺e⁻ decay (which is excluded from the quoted limits). The resulting limits are:

• χ_c0 → e⁺e⁻ ϕ: < 2.4 × 10⁻⁷
• χ_c1 → e⁺e⁻ ϕ: < 6.7 × 10⁻⁷
• χ_c2 → e⁺e⁻ ϕ: < 4.1 × 10⁻⁷

These limits are consistent with theoretical expectations based on non‑relativistic QCD and vector‑meson‑dominance models, which predict Dalitz branching fractions at the 10⁻⁶–10⁻⁸ level. The stronger suppression observed for χ_c1 and χ_c2 reflects the role of C‑parity and the spin‑parity structure of the initial P‑wave charmonium states.

The analysis demonstrates that electromagnetic Dalitz transitions of χ_cJ to light vector mesons are exceedingly rare, providing a stringent test of the interplay between electromagnetic and strong interactions in the charmonium system. The methodology and the derived limits lay the groundwork for future studies with larger data samples, such as those anticipated from the BESIII upgrade or the proposed Super Tau‑Charm facility. Extending the search to other vector mesons (ρ, ω) or to higher‑order processes (e.g., χ_cJ → e⁺e⁻ π⁰) could further illuminate the structure of the virtual photon coupling and refine our understanding of non‑perturbative QCD effects in heavy‑quarkonium decays.