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 $\psi (2S)\to n\bar{n}$.

Comments: References update, 9 pages, 2 figures