Leptonic Decay Widths for a Compound System of Two Relativistic Equal-Mass Fermions

A new relativistic semiclassical expression is derived for leptonic decay widths of vector mesons as a composite system of two quarks having equal masses and interacting via a funnel-like potential. This new expression is compared with its nonrelativistic spinless and relativistic spin and spinless analogs. The effect of the spins of equal-mass quarks forming vector mesons on the behavior of the leptonic decay widths of these mesons is analyzed. This analysis is performed within the relativistic quasipotential approach based on the covariant Hamiltonian formulation of quantum field theory by means of a transition from the momentum representation in Lobachevsky space to the three-dimensional relativistic configuration representation for the case of a composite system of two relativistic spin equal-mass particles.