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

Belle Collaboration has recently observed a new state, the X(4160), in the process of double charm production e(+)e(-) -> J/Psi + X(4160) followed by X (4160) -> D* (D) over bar*. 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 D-1(2)(2D), which is estimated to have a small production rate of about 5% of that for e(+)e(-) -> 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(-) -> 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 (D) over bar 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 (D) over bar against J/Psi in e(+) + e(-) -> J/Psi in + D (D) over bar 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. (C) 2008 Elsevier B.V. All rights reserved.