The strong decays of X(3940) and X(4160)

The new mesons X(3940) and X(4160) have been found by Belle Collaboration in the processes e⁺e⁻→ J/ψ D(*)D̄(*) . Considering X(3940) and X(4160) as η c(3S) and η c(4S) states, the two-body open charm OZI-allowed strong decay of η c(3S) and η c(4S) are studied by the improved Bethe–Salpeter method combined with the ³P₀ model. The strong decay width of η c(3S) is Γ η c(3S)=(33.5+18.4-15.3) MeV, which is close to the result of X(3940); therefore, η c(3S) is a good candidate of X(3940). The strong decay width of η c(4S) is Γ η 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 Γ (DD̄^*)Γ (D^*D̄^*) of η c(4S) is larger than the experimental data of X(4160). According to the above analysis, η c(4S) is not the candidate of X(4160), and more investigations of X(4160) is needed.