The Spinless Salpeter Equation and Meson Dynamics

Applying the variational method, the spinless reduced Bethe-Salpeter (RBS) equation is solved for the mesonic systems, and the mass spectra are obtained. The method is applied to the Hamiltonian with the Gaussian and hydrogen-type trial wave functions, and different potential models are examined. The results for the different potentials are in challenge in light mesons, while they are consistent in heavy mass region. In spite of this, the consistency for all mesons occurs in Power-law (Rosner, …), Logarithmic (Quigg and Rosner), )4.0(GevKMS=Λ and )5.0(GevGMS=Λ potentials and the theoretical results are in general in agreement with the experimental data. The inconsistency in light mesons has the origin in the nonrelativistic treatment of the potential derivations and the reduced form of the Bethe-Salpeter equation. The consistent and non-consistent interquark potentials show a distinct behaviour at both short and long distances.