Heavy quark spin selection rules in meson-antimeson states

In the heavy quark limit, we discuss the spin of the charm-anticharm pair $J_{c\bar{c}}$ in an S-wave meson-antimeson molecule or resonance. One finds two cases that $J_{c\bar{c}}$ cannot be 0: (a) $J=\mathrm{\mid }{j}_2-j_4\mathrm{\mid }-1$ or $J=j_2+j_4+1$ where $J$ is the total spin of the system and $j_2$ ($j_4$) is the total angular momentum of the light degree of freedom in a charmed meson (antimeson); (b) $J^C=1^{+},2^{-},3^{+},\mathrm{.}\mathrm{.}\mathrm{.}$, if the two different mesons belong to the same doublet. The decays to spin-singlet charmonium states are suppressed when one of the two conditions is satisfied. We discuss constrained decay properties for selected systems.