Modeling Charmonium-$\eta$ Decays of $J^{PC}=1^{--}$ Higher Charmonia

TL;DR

This paper introduces a new NJL-inspired model to study $ ext{eta}$ meson emissions in heavy quarkonium transitions, successfully reproducing observed decay widths and predicting unobserved channels to aid experimental searches.

Contribution

The paper presents a novel model for light meson creation in heavy quarkonium decays, providing predictions for decay widths and branching fractions of higher charmonia states.

Findings

Predicted decay width for $ ext{Psi} o J/ ext{psi} ext{eta}$

Predicted branching fraction for $ ext{psi}(4415) o h_c(1P) ext{eta}$

Support for assigning $Y(4360)$ and $Y(4660)$ as specific $car{c}$ states

Abstract

We propose a new model to create a light meson in the heavy quarkonium transition, which is inspired by the Nambu$-$Jona-Lasinio (NJL) model. Hadronic transitions of $J^{PC}=1^{--}$ higher charmonia with the emission of an $\eta$ meson are studied in the framework of the proposed model. The model shows its potential to reproduce the observed decay widths and make predictions for the unobserved channels. We present our predictions for the decay width of $\Psi \to J/\psi \eta$ and $\Psi \to h_{c}(1P)\eta$, where $\Psi$ are higher $S$ and $D$ wave vector charmonia, which provide useful references to search for higher charmonia and determine their properties in forthcoming experiments. The predicted branching fraction $\mathcal B(\psi(4415)\to h_{c}(1P)\eta)=4.62\times 10^{-4}$ is one order of magnitude smaller than the $J/\psi \eta$ channel. Estimates of partial decay width $\Gamma(Y \to J/\psi \eta)$ are given for $Y(4360)$, $Y(4390)$ and $Y(4660)$ by assuming them as $c\bar{c}$ bound states with quantum numbers $3 ^3D_1$, $3 ^3D_1$ and $5 ^3S_1$, respectively. Our results are in favor of these assignments for $Y(4360)$ and $Y(4660)$. The corresponding experimental data for these $Y$ states has large statistical errors which do not provide any constraint on the mixing angle if we introduce $S-D$ mixing. To identify $Y(4390)$, precise measurements on its hadronic branching fraction are required which are eagerly awaited from BESIII.