Universal Scaling Relations for Coupling Constants of Mesons Containing Heavy Quarks

The formulation of quasi-local sum rules for the S-wave levels in a heavy quarkonium and the region of their applicability are discussed. The sum rules allow one to use the regularity in the mass spectrum and derive scaling relations for the leptonic decay constants that are in close agreement with the available experimental data for the vector states in the systems of charmonium and bottomonium. The proposed method is generalized to heavy mesons with a single heavy quark for which the scaling relation, consistent with the heavyquark effective theory, is derived. Numerical estimates are presented for the QCD parameters in the heavyquark sector: quark masses, coupling constant a,., binding energy, and the average square of heavy-quark momentum in a heavy meson. The sum rules for mesonic currents that determine the decay constant of a heavyvector quarkonium into the pair of heavy pseudoscalar mesons are considered for obtaining the scaling relation connecting the decay constants of quarkonia with different quark contents. The comparison with experimental data shows a good agreement with theoretical estimates. Some properties of the (bc) quarkonium are predicted on the basis of the derived scaling relations.