A Phenomenological Estimate of the Binding Energy of Heavy Dimesons

A phenomenological estimate is derived such that the binding energies of dimesons are expressed as combinations of masses of different mesons and baryons. The estimate is almost model-independent, the only major assumptions being that the wave functions of the two light quarks in $\Lambda_c$, $\Lambda_b$ and in the $\bar{c}\bar{c}qq$ and $\bar{b}\bar{b}qq$ dimesons are very similar, and that for heavy quarks the $QQ$ interaction is half as strong as the $Q\bar{Q}$ interaction. We get $\bar{b}\bar{b}qq$ (I=0, J=1) bound by about 100 MeV and $\bar{c}\bar{c}qq$ unbound.