Probing ${\chi }_{cJ}(J=0,1,2)$ decay into baryon and anti-baryon with SU(3) flavor analysis

With the accurate measurements of ${\chi }_{cJ}(J=0,1,2)$ charmonium decays, we explore ${\chi }_{cJ}\to {\mathcal{B}}_8{\bar{\mathcal{B}}}_8$ and ${\mathcal{B}}_{10}{\bar{\mathcal{B}}}_{10}$ decays based on the SU(3) flavor symmetry model, where ${\mathcal{B}}_8$ and ${\mathcal{B}}_{10}$ are light octet and decuplet baryons, respectively. The decay amplitude relations are determined by an effective interaction Hamiltonian. Then using experimental data and the amplitude relations of ${\chi }_{cJ}\to {\mathcal{B}}_8{\bar{\mathcal{B}}}_8$, ${\mathcal{B}}_{10}{\bar{\mathcal{B}}}_{10}$ decays, relative nonperturbative coefficients are constrained, and the branching ratios of unmeasured ${\chi }_{cJ}\to {\mathcal{B}}_8{\bar{\mathcal{B}}}_8,{\mathcal{B}}_{10}{\bar{\mathcal{B}}}_{10}$, for examples, ${\chi }_{cJ}\to n\bar{n}$ and ${\chi }_{cJ}\to \mathrm{\Lambda }{\bar{\mathrm{\Sigma }}}^0+\bar{\mathrm{\Lambda }}{\mathrm{\Sigma }}^0$ channels, are predicted. Moreover, we discuss the case of adding a mixing angle between $\mathrm{\Lambda }$ and ${\mathrm{\Sigma }}^0$, which is determined by the quark mass differences. Our results provide valuable insights that will aid in advancing our understanding of the mechanisms and characteristics of ${\chi }_{cJ}$ decays.