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^-rightarrow 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 combined 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 close 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 is close 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.