The Negative-$\Sigma\bar{\Sigma}$ Angular-Parameter Puzzle in $J/\psi$ and $\psi(2S)$ Decays

Abstract

Experimental measurements of $J/\psi$ and $\psi(2S)$ decays to octet baryon pairs reveal a negative-$\Sigma\bar{\Sigma}$ puzzle in the angular distributions: $\alpha_\Sigma^{J/\psi}<0$, whereas the other measured $J/\psi$ octet channels and the corresponding $\psi(2S)$ channels have positive angular parameters. We show that an $\mathrm{SU}(3)_F$-exact singlet description is strongly disfavored in a $\chi^2$ fit, giving $\chi^2\simeq 10^5$. By contrast, a reduced scenario in which a common final-state interaction mixes the $\mathrm{S}$- and $\mathrm{D}$-wave amplitudes, with an antisymmetric direct octet and a full diagonal $\mathrm{S}$-$\mathrm{D}$ rescattering block, gives $\chi^2=4.21$ for two nominal degrees of freedom. The negative $\Sigma\bar{\Sigma}$ angular parameter is traced to the pattern of the rescattered $\mathrm{S}$- and $\mathrm{D}$-wave amplitudes. The apparent large $\mathrm{SU}(3)_F$-breaking effect is decomposed into three ingredients: the fitted $\mathrm{D}$-wave source is much larger than the $\mathrm{S}$-wave source, the breaking remains modest when normalized to the $\mathrm{D}$ wave, and $\mathrm{D}\to\mathrm{S}$ rescattering transfers the $\mathrm{SU}(3)_F$-breaking effect from the $\mathrm{D}$ wave into the small $\mathrm{S}$-wave baseline, where it appears large. The largest remaining pull comes from the $\psi(2S)\to N\bar{N}$ angular input, motivating a renewed experimental check of $\psi(2S)\to n\bar{n}$.