The Strong Decays of X(3940) and X(4160)

Abstract

The new mesons $X(3940)$ and $X(4160)$ have been found by Belle Collaboration in the processes $e^{+}{e}^{-}\to J/\psi D^{(\ast )}{\bar{D}}^{(\ast )}$. Considering $X(3940)$ and $X(4160)$ as ${\eta }_c(3S)$ and ${\eta }_c(4S)$ states, the two-body open charm OZI-allowed strong decay of ${\eta }_c(3S)$ and ${\eta }_c(4S)$ are studied by the improved Bethe-Salpeter method combine with the ${}^3{P}_0$ model. The strong decay width of ${\eta }_c(3S)$ is ${\Gamma }_{{\eta }_c(3S)}=(33.5_{-15.3}^{+18.4})$ MeV, which is closed to the result of $X(3940)$, therefore, ${\eta }_c(3S)$ is a good candidate of $X(3940)$. The strong decay width of ${\eta }_c(4S)$ is ${\Gamma }_{{\eta }_c(4S)}=(69.9_{-21.1}^{+22.4})$ MeV, considering the errors of the results, it's closed to the lower limit of $X(4160)$. But the ratio of the decay width $\frac{\Gamma (D{\bar{D}}^{\ast })}{\Gamma (D^{\ast }{\bar{D}}^{\ast })}$ of ${\eta }_c(4S)$ is larger than the experimental data of $X(4160)$. According to the above analysis, ${\eta }_c(4S)$ is not the candidate of $X(4160)$, and more investigations of $X(4160)$ is needed.

Comments: 14 pages, 4 figures. arXiv admin note: text overlap with arXiv:1605.09091