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 $\eta_c(6S)$.
Highlights
In recent years, a lot of charmonium-like states, the so-called “X Y Z ” states [1], have been observed by Belle, BaBar, BESIII, and other collaborations
The spectrum of these ηc(nS) (n = 1, . . . , 6) mesons is obtained by using a high-precision fewbody method, the Gaussian expansion method (GEM) [15], in the framework of chiral quark model [16]
The hadron decay occurs via quark–antiquark pair production from the hadronic vacuum, so the quantum numbers of the created quark pair are of the hadronic vacuum, J PC = 0++. This model has given a rather good description of the open flavor two-body strong decay width of hadrons [19–24], which are allowed by the Okubo– Zweig–Iizuka (OZI) rule
Summary
A lot of charmonium-like states, the so-called “X Y Z ” states [1], have been observed by Belle, BaBar, BESIII, and other collaborations. Most of them cannot be accommodated in the quark models as conventional mesons because of their exotic properties. In the present work we study the open charm two-body strong decay widths of all the ηc(nS) 6) mesons systematically in a constituent quark model In the numerical evaluation of the transition matrix elements of decay widths, the wavefunctions obtained in the study of the meson spectrum, rather than the simple harmonic oscillator (SHO) ones, are used. 2, the chiral quark model and wavefunctions of meson are presented; the 3 P0 decay model is briefly reviewed in Sect.
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