Hadronic corrections to the annihilation rate of heavy vector mesons to lepton pairs

Hadronic corrections to the annihilation rate of heavy vector mesons to lepton pairs are considered to leading nontrivial order in gluon exchange and in the quark-confining potential. It is shown that, to an excellent approximation, the rate is $\Gamma (V\to l^{+}{l}^{-})\simeq \left(\frac{16\pi {\alpha }^2{e_Q}^2}{M^2}\right){\left|{\phi }_0\right(r=\frac{1}{m}\left)\right|}^2$, where $M\simeq 2m$ is the vector-meson mass and ${\phi }_0\mathrm{}\left(r\right)\mathrm{}$ is the solution of the zeroth-order nonrelativistic quark-antiquark bound-state problem. This has the effect of reducing the Van Royen-Weisskopf prediction for the rate.