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

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