X(3915) and X(4350) as new members in the P-wave charmonium family.

The analysis of the mass spectrum and the calculation of the strong decay of P-wave charmonium states strongly purport to explain the newly observed X(3915) and X(4350) as new members in the P-wave charmonium family, i.e., chi{c0}{'} for X(3915) and chi{c2}{''} for X(4350). Under the P-wave charmonium assignment to X(3915) and X(4350), the J{PC} quantum numbers of X(3915) and X(4350) must be 0{++} and 2{++} respectively, which provide important criteria to test the P-wave charmonium explanation for X(3915) and X(4350) proposed by this Letter. The decay behavior of the remaining two P-wave charmonium states with the second radial excitation is predicted, and an experimental search for them is suggested.