Interpretations for the X(4160) observed in the double charm production at B factories

Abstract

Belle Collaboration has recently observed a new state, the X(4160), in the process of double charm production $e^{+}{e}^{-}\to J/\psi +X(4160)$ followed by $X(4160)\to D^{\ast }\overline{D^{\ast }}$. We discuss possible interpretations for the X(4160) based on the NRQCD calculations and the potential model estimates for the charmonium spectrum. We first focus on the D-wave spin-singlet $2^{-+}$ charmonium ${}^1{D}_2(2D)$, which is estimated to have a small production rate of about 5% of that for $e^{+}{e}^{-}\to J/\psi +{\eta }_c(1S)$, and therefore is incompatible with the observed data for X(4160). We then discuss the possibility that the X(4160) is the known $J^{PC}=1^{--}$ charmonium state $\psi (4160)$, which can be produced via two photon fragmentation, but the production rate is much smaller than observed for $e^{+}{e}^{-}\to J/\psi +X(4160)$. In contrast to above two possibilities, the ${\eta }_c(4S)$ assignment is a likely one, which is supported by the observed relatively large production rate and non-observation of $D\bar{D}$ decay of X(4160), but we have to understand why ${\eta }_c(4S)$ has such a low mass, which deserves further studies. The P-wave excited state ${\chi }_{c0}(3P)$ is also an interesting candidate, if the observed broad peak around 3.8-3.9 GeV in the recoil mass of $D\bar{D}$ against $J/\psi$ in $e^{+}+e^{-}\to J/\psi +D\bar{D}$ is due to the ${\chi }_{c0}(2P)$ state. Measurements of production angular distributions will be helpful to distinguish between ${\eta }_c(4S)$ and ${\chi }_{c0}(3P)$ assignments. Production mechanisms in nonrelativistic QCD are emphasized.

Comments: version to appear in Phys. Lette. B, discussions and references added