Scaling law for the $\Upsilon(4S) \to B \bar B$ and $\psi(3770) \to D \bar D$ decay constants from effective sum rules

Abstract

Sum rules for exclusive production of heavy meson pairs in $e^+e^-$ annihilation are used to evaluate the $\Upsilon(4S) \to B \bar B$ and $\psi(3770) \to D \bar D$ decay widths. Infinitely heavy quark limit is discussed, so that scaling law for the quarkonium-meson coupling constant is derived. A value of the $B\bar B$ pair contribution into the leptonic constant $f_{\Upsilon(4S)}$ is estimated.