Wave Functions and S Factor for a Composite System of Two Arbitrary-Mass Relativistic Spinor Quarks

Exact solutions of relativistic quasipotential equations in the configuration representation are found for the s-state wave function for a composite system of two arbitrary-mass relativistic spinor quarks interacting via a Coulomb-like chromodynamic potential. Composite systems whose spinor structure corresponds to the pseudoscalar, pseudovector, and vector cases are considered. Quantization conditions for the energy levels of the meson s-wave state are determined in the pseudoscalar, pseudovector, and vector cases. Expressions for the relativistic threshold resummation S factor corresponding to a Coulomb-like chromodynamic potential are obtained for these spinor meson structures, and the properties of this factor are studied. New regularities in the behavior of the threshold S factor are revealed. The present analysis is performed within the relativistic quasipotential approach based on the covariant Hamiltonian formulation of quantum field theory by means of the transition from the momentum representation in Lobachevsky space to the three-dimensional relativistic configuration representation for the case of a composite system of two arbitrary-mass relativistic spinor particles.