Study the decays of $χ_{cJ}(J=0,1,2)$ to light meson pairs with SU(3) flavor symmetry/breaking analysis
Bo Lan, Qin-Ze Song, Jin-Huan Sheng, Yi Qiao, Ru-Min Wang
TL;DR
This work applies an SU(3) flavor symmetry and breaking framework to χ_{cJ} (J=0,1,2) two-body decays into light mesons, deriving amplitude relations for PP, VV, PV, and PT final states and incorporating η-η′, φ-ω, and f_{2}-f′_{2} mixings. Decay amplitudes are expressed in terms of nonperturbative coefficients a^{M}_{1J}, a^{M}_{2J}, and b^{M}_{J}, with a Monte Carlo approach used to propagate PDG constraints into branching-ratio predictions, both with and without SU(3) breaking. The results show SU(3) symmetry provides a robust description for PP and VV channels, with breaking effects modest but necessary to fit all data within 1σ, and reveal helicity- and OZI-related suppression patterns in PV and PT channels. The findings offer concrete predictions for unmeasured decays and furnish quantitative benchmarks for future experiments at BESIII and the Super Tau-Charm Facility, advancing understanding of nonperturbative QCD dynamics in charmonium decays.
Abstract
Based on available experimental results on $χ_{cJ}(J=0,1,2)$ decays, we investigate the $χ_{cJ}\to PP$, $VV$, $PV$, and $PT$ decays by using SU(3) flavor symmetry/breaking approach, where $P$, $V$, and $T$ denote light pseudoscalar, vector, and tensor mesons, respectively. With the decay amplitude relations determined by SU(3) flavor symmetry/breaking, we present the branching ratios for all $χ_{cJ}\to PP$ and $χ_{cJ}\to VV$ modes, including ones without experimental data. While theoretical considerations strongly suppress or even forbid most $χ_{cJ}\to PV$ and $PT$ decays, we also provide quantitative predictions constrained by existing experimental data. Our results are expected to be accessible in future experiments at BESIII and the planned Super Tau-Charm Facility.