Charmonium J^PC = 1^–– Decay in the C³P₀ Model

Abstract

Widely applied to both light and heavy meson decay and standing as one of the most successful strong decay models is the $^{3}P_{0}$ model, in which $q\bar{q}$ pair production is the dominant mechanism. In the present, we use the bound-state corrected version of the $^{3}P_{0}$, called the C$^{3}P_{0}$ model, to calculate the decay widths of the charmonium $J^{PC}=1^{--}$ states, nominally $J/\psi$, $\psi (2S)$, $\psi (3770)$, $\psi (4040)$, $\psi (4160)$, $\psi (4415)$ and $\psi (4660)$ to several common channels.

Appendix. Parameters

After the simulation the best $J/\psi$ fit to the experimental data is achieved with $\gamma =0.33$, $\beta _{J/\psi }= 0.182$ GeV, $\beta _\rho =0.55$ GeV, $\beta _\pi = 0.55$ GeV, $\beta _\omega = 0.328$ GeV, $\beta _{\eta }= 0.348$ GeV, $\beta _{\eta ^\prime }= 0.170$ GeV, $\beta _K= 0.4$ GeV, $\beta _{K^*}=0.315$ GeV, $\beta _{\phi }=0.340$ GeV, $\beta _{\phi _\Delta }=0.3$ GeV, $\beta _{\omega _\Delta }=0.6$ GeV and $\beta _{J/\psi _\Delta }=0.3$ GeV. These results and the experimental values are shown in the left part of Table 2.

The best $\psi (2S)$ fit to the experimental data is achieved with $\gamma =0.33$, $\beta _{\psi }= 0.042$ GeV, $\beta _\rho =0.55$ GeV, $\beta _\pi = 0.55$ GeV, $\beta _\omega = 0.7$ GeV, $\beta _{\eta }= 0.7$ GeV, $\beta _{\eta ^\prime }= 0.8$ GeV, $\beta _K= 0.47$ GeV, $\beta _{K^*}=0.8$ GeV, $\beta _{\phi }=0.7$ GeV, $\beta _{\phi _\Delta }=0.9$ GeV, $\beta _{\omega _\Delta }=0.6$ GeV and $\beta _{\psi _\Delta }=0.042$ GeV. These results and the experimental values are shown in the right part of Table 2.

The best $\psi (3770)$ is $\beta _{\psi (3770)} = 0.9$ GeV, $\gamma =0.33$, $\beta _\rho =0.105$ GeV, $\beta _\pi = 0.86$ GeV, $\beta _\omega = 0.22$ GeV, $\beta _{\eta }= 0.7$ GeV, $\beta _{\eta ^\prime }= 0.9$ GeV, $\beta _K= 0.8$ GeV, $\beta _{K^*}=0.175$ GeV, $\beta _{\phi }=0.65$ GeV, $\beta _{\phi _\Delta }=0.9$ GeV, $\beta _{\omega _\Delta }=0.6$ GeV and $\beta _{\psi _\Delta }=0.2$ GeV.

For the D channels a minor modification is observed in the parameters $\beta _{\psi (3770)} = \beta _{\psi (4040)} = \beta _{\psi (4160)} = \beta _{\psi (4415)} = \beta _{\psi (4660)} = 0.5$ GeV and $\beta _{D^*}=0.2$ GeV, $\beta _D=0.6$ GeV, $\beta _{D^{0\,*}}=\beta _{D^0}= 0.51$ GeV, $\beta _{D_s} = \beta _{D^*_s} =0.53$ GeV ; $\beta _{\phi _\Delta }=0.9$ GeV, $\beta _{\omega _\Delta }=0.6$ GeV and $\beta _{\psi _\Delta }=0.2$ GeV.