On hyperfine splitting of s levels heavy quarkonium

An expression is obtained for the hyperfine splitting of the s levels in heavy quarkonium with account of nonperturbative effects. These effects arise from the quark interactions with large-scale fluctuations of the gluonic field in the physical vacuum of QCD, which are not described by the perturbation theory. An estimate is presented for the mass splitting of the γ resonance and etasub(b): M(γ)-M(etasub(b)) < or approximately 30 MeV. Estimates are also obtained for similar splittings in the t anti t quarkonium