Charmonium levels near threshold and the narrow stateX(3872)→π+π−J/ψ

We explore the influence of open-charm channels on charmonium properties and profile the $1^3{D}_2,$ $1^3{D}_3,$ and $2^1{P}_1$ charmonium candidates for $X\left(3872\right).$ The favored candidates, the $1^3{D}_2$ and $1^3{D}_3$ levels, both have prominent radiative decays. The $1^3{D}_2$ might be visible in the $D^0{D}^{*0}$ channel, while the dominant decay of the $1^3{D}_3$ state should be into $D\overline{D}.$ We propose that additional discrete charmonium levels can be discovered as narrow resonances of charmed and anticharmed mesons.