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

TL;DR

This paper investigates the nature of the mesons X(3940) and X(4160) by modeling them as excited states of eta_c and calculating their decay widths, finding strong evidence for X(3940) being eta_c(3S).

Contribution

The study applies an improved Bethe-Salpeter method combined with the $^3P_0$ model to analyze the decay properties of eta_c(3S) and eta_c(4S), providing insights into their identification with X(3940) and X(4160).

Findings

The decay width of eta_c(3S) matches X(3940) data.

The decay width of eta_c(4S) is consistent with X(4160) lower limit.

The decay ratio of eta_c(4S) does not match X(4160) experimental data.

Abstract

The new mesons $X(3940)$ and $X(4160)$ have been found by Belle Collaboration in the processes $e^+e^-\to J/\psi D^{(*)}\bar D^{(*)}$. 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 $^3P_0$ model. The strong decay width of $\eta_c(3S)$ is $\Gamma_{\eta_c(3S)}=(33.5^{+18.4}_{-15.3})$ 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 $\Gamma_{\eta_c(4S)}=(69.9^{+22.4}_{-21.1})$ MeV, considering the errors of the results, it's closed to the lower limit of $X(4160)$. But the ratio of the decay width $\frac{\Gamma(D\bar D^*)}{\Gamma (D^*\bar D^*)}$ 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.