Are the $X$(4160) and $X$(3915) charmonium states?

Abstract

Inspired by the newly observed $X$(4160) and $X$(3915) states, we analyze the mass spectrum of these states in different quark models and calculate their strong decay widths by the ${}^3{P}_0$ model. According to the mass spectrum of charmonium states predicted by the potential model, the states ${\chi }_0(3^3{P}_0),{\chi }_1(3^3{P}_1),{\eta }_{c2}(2^1{D}_2),{\eta }_c(4^1{S}_0)$ all can be candidates for the $X$(4160). However, only the decay width of the state ${\eta }_{c2}(2^1{D}_2)$ in our calculation is in good agreement with the data reported by Belle and the decay of ${\eta }_{c2}(2^1{D}_2)\to D\bar{D}$, which is not seen in experiment, is also forbidden. Therefore, it is reasonable to interpret the charmonium state ${\eta }_{c2}(2^1{D}_2)$ as the state X(4160). For the state X(3915), although the mass of ${\chi }_0(2^3{P}_0)$ is compatible with the experimental value, the calculated strong decay width is much larger than experimental data. Hence, the assignment of X(3915) to charmonium state ${\chi }_0(2^3{P}_0)$ is disfavored in our calculation.

Comments: 9 pages, 8 figures