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

TL;DR

This paper uses SU(3) flavor symmetry to analyze and predict decay rates of $oldsymbol{ ext{chi}_cJ}$ charmonium states into baryon-antibaryon pairs, based on experimental data and effective Hamiltonian relations.

Contribution

It introduces a method to relate decay amplitudes using SU(3) symmetry and constrains nonperturbative coefficients to predict unmeasured decay branching ratios.

Findings

Predicted branching ratios for unmeasured $oldsymbol{ ext{chi}_cJ}$ decays.

Constrained nonperturbative coefficients using experimental decay data.

Analyzed effects of $oldsymbol{ ext{Lambda}}$-$oldsymbol{ extSigma^0}$ mixing angle.

Abstract

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 $\chi _{cJ}\to\Lambda \bar{\Sigma}^{0}+\bar{\Lambda} \Sigma^{0}$ channels, are predicted. Moreover, we discuss the case of adding a mixing angle between $\Lambda $ and $\Sigma ^{0}$, 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.