The Negative-$\hat{I}\pounds \bar{\hat{I}}\pounds$ Angular-Parameter Puzzle in $J/\ddot{I}ˆ$ and $\ddot{I}ˆ(2S)$ Decays

Abstract

Experimental measurements of $J/\ddot{I}ˆ$ and $\ddot{I}ˆ(2S)$ decays to octet baryon pairs reveal a negative-$\hat{I}\pounds \bar{\hat{I}}\pounds$ puzzle in the angular distributions: $\hat{I}{\pm }_{\hat{I}}{\pounds }^{J/\ddot{I}ˆ}<0$, whereas the other measured $J/\ddot{I}ˆ$ octet channels and the corresponding $\ddot{I}ˆ(2S)$ channels have positive angular parameters. We show that an $\mathrm{SU}(3{)}_F$-exact singlet description is strongly disfavored in a $\ddot{I}{‡}^2$ fit, giving $\ddot{I}{‡}^2\simeq 10^5$. 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 $\ddot{I}{‡}^2=4.21$ for two nominal degrees of freedom. The negative $\hat{I}\pounds \bar{\hat{I}}\pounds$ 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 $\ddot{I}ˆ(2S)\to N\bar{N}$ angular input, motivating a renewed experimental check of $\ddot{I}ˆ(2S)\to n\bar{n}$.

References update, 9 pages, 2 figures