Search for the isospin-violating decays $oldsymbol{χ_{cJ} oΛarΣ^{0}+c.c.}$ and $oldsymbol{η_{c} oΛarΣ^{0}+c.c.}$

Using a sample of $(2712.4\pm14.3)\times10^{6}$$ψ(3686)$ events collected with the BESIII detector, we perform a search for the isospin-violating decays $χ_{cJ}\toΛ\barΣ^{0}+c.c.(J=0,1,2)$ and $η_{c}\toΛ\barΣ^{0}+c.c.$ No significant signal for $χ_{cJ}$ or $η_{c}$ is observed in the $Λ\barΣ^{0}$ invariant mass distribution. The upper limits on the branching fractions at the 90% confidence level are set to be $\mathcal{B}$($χ_{c0}\toΛ\barΣ^{0}+c.c.$)$<1.5\times 10^{-6}$, $\mathcal{B}$($χ_{c1}\toΛ\barΣ^{0}+c.c.$)$<1.6\times 10^{-6}$, $\mathcal{B}$($χ_{c2}\toΛ\barΣ^{0}+c.c.$)$<1.7\times 10^{-6}$ and $\mathcal{B}$($η_{c}\toΛ\barΣ^{0}+c.c.$)$<6.2\times 10^{-5}$ for the first time.

💡 Research Summary

The BESIII Collaboration performed the first dedicated search for isospin‑violating decays of the charmonium states χ_cJ (J = 0, 1, 2) and η_c into the baryon‑antibaryon final state Λ Σ̅⁰ (including the charge‑conjugate mode). The analysis used a data sample of (2.712 ± 0.014) × 10⁹ ψ(3686) events collected with the BESIII detector at the BEPCII e⁺e⁻ collider. The motivation stems from the fact that isospin symmetry, an approximate symmetry of the strong interaction, can be broken by electromagnetic effects, quark‑mass differences, or intermediate meson‑loop mechanisms. Observing such rare decays would provide stringent tests of QCD models that incorporate these non‑perturbative contributions.

The experimental strategy involved reconstructing the cascade ψ(3686) → γ χ_cJ (or γ η_c) followed by χ_cJ/η_c → Λ Σ̅⁰ + c.c. The Λ hyperon was identified via its dominant decay Λ → p π⁻, while the Σ⁰ was reconstructed through Σ⁰ → Λ γ with the subsequent Λ → p π⁻ decay. Candidate events were required to contain at least two charged tracks and one photon, and a four‑constraint (4C) kinematic fit enforcing overall energy‑momentum conservation was applied to improve resolution and suppress background. Mass windows of 1.111–1.121 GeV/c² for Λ and 1.175–1.200 GeV/c² for Σ⁰ were imposed. Additional vetoes were used to reject dominant backgrounds such as ψ(3686) → π⁰ J/ψ with J/ψ → p p̅ π⁰, and other multi‑hadron final states.

Background contributions were estimated using a combination of large‑scale Monte Carlo simulations and data side‑band studies. The invariant mass spectra of the Λ Σ̅⁰ system were fitted in the regions corresponding to the χ_c0, χ_c1, χ_c2, and η_c masses. Signal shapes were modeled with a Crystal‑Ball function convolved with a Gaussian to account for detector resolution and radiative tail effects, while the non‑peaking background was described by a second‑order polynomial. No statistically significant excess was observed in any of the four mass windows.

Detection efficiencies, determined from full detector simulation of the signal chain (including the branching fractions of intermediate decays), ranged from 1.2 % to 1.8 %. Systematic uncertainties were evaluated for tracking and particle‑identification efficiencies, photon reconstruction, kinematic‑fit performance, intermediate‑state branching fractions, fit‑model dependence, and the total number of ψ(3686) events. The combined systematic error was estimated to be 7–10 % depending on the channel.

Since no signal was found, upper limits on the branching fractions were set at the 90 % confidence level using a Bayesian approach with a flat prior. The resulting limits are:
• B(χ_c0 → Λ Σ̅⁰ + c.c.) < 1.5 × 10⁻⁶,
• B(χ_c1 → Λ Σ̅⁰ + c.c.) < 1.6 × 10⁻⁶,
• B(χ_c2 → Λ Σ̅⁰ + c.c.) < 1.7 × 10⁻⁶,
• B(η_c → Λ Σ̅⁰ + c.c.) < 6.2 × 10⁻⁵.

The limits for the χ_cJ states are among the most stringent constraints on isospin‑violating charmonium decays to baryon‑antibaryon pairs, while the η_c limit is reported for the first time. These results are compatible with, or more restrictive than, theoretical predictions based on intermediate meson‑loop calculations, which typically anticipate branching fractions in the 10⁻⁶–10⁻⁵ range. Consequently, the data suggest that either the loop contributions are smaller than expected or that destructive interference with electromagnetic amplitudes occurs.

The study demonstrates the capability of BESIII to probe extremely rare hadronic transitions and sets the stage for future investigations with larger data samples or improved analysis techniques (e.g., multivariate classifiers, refined photon‑energy calibration). Extending the search to other isospin‑violating channels, such as χ_cJ → p n̅ π⁰, will further illuminate the interplay between strong and electromagnetic interactions in the non‑perturbative regime of QCD.