Radially Excited States of $\eta_c$

TL;DR

This study investigates the mass spectrum and decay properties of radially excited η_c states using a chiral quark model and Gaussian expansion method, providing insights into their experimental identification.

Contribution

It offers a detailed theoretical analysis of η_c(ns) states up to n=6, including mass predictions and decay widths, and discusses their possible experimental counterparts.

Findings

Masses of η_c(1S) and η_c(2S) match experimental data.

X(3940) is unlikely to be η_c(3S) due to decay width discrepancies.

X(4160) could be η_c(4S) based on decay widths and branching ratios.

Abstract

In the framework of chiral quark model, the mass spectrum of $\eta_c(ns) (n=1,...,6)$ is studied with Gaussian expansion method. With the wave functions obtained in the study of mass spectrum, the open flavor two-body strong decay widths are calculated by using $^3P_0$ model. The results show that the masses of $\eta_c(1S)$ and $\eta_c(2S)$ are consistent with the experimental data. The explanation of X(3940) as $\eta_c(3S)$ is disfavored for X(3940) is a narrow state, $\Gamma=37^{+26}_{-15} \pm 8 $ MeV, while the open flavor two-body strong decay width of $\eta_c(3S)$ is about 200 MeV in our calculation. Although the mass of X(4160) is about 100 MeV less than that of $\eta_c(4S)$, the assignment of X(4160) as $\eta_c(4S)$ can not be excluded because the open flavor two-body strong decay width of $\eta_c(4S)$ is consistent with the experimental value of X(4160) and the branching ratios of $\eta_c(4S)$ are compatible with that of X(4160), and the mass of $\eta_c(4S)$ can be shifted downwards by taking into account the coupling effect of the open charm channels. There are still no good candidates to $\eta_c(5S)$ and $\eta_c(6S)$.