Molecular charmonium andC-exotic mesons?

Recently De Rújula et al. and Okun and Voloshin suggested that several peaks in $e^{-}{e}^{+}$ annihilation cross section into hadrons are due to resonances between two charmed mesons in a relative $P$ wave. Such a picture raises at once the question whether $C$-exotic mesons formed also from two charmed mesons (or four-quark molecules) in a relative $P$ wave may not coexist at comparable mass. We examine briefly here the spectroscopy for $C$-exotic mesons with $J^P=0^{-}$, $I^G=0^{-}, 1^{+}$, and $J^P=1^{-}$, $I^G=0^{+}, 1^{-}$.