Relativistic bound states of fermions and antifermions. III

This paper reports on further progress made on the new approach to hadrons proposed in our earlier papers. One major achievement concerns the application of the Bethe-Salpeter (BS) formalism to find the eigenstates (or hadrons) of the proposed bound-state Hamiltonian. We show that it is entirely reasonable to apply the Taylor expansion to the irreducible BS kernel with respect to the four-dimensional relative momenta. With this expansion, the BS equation reduces to the eigenvalue equations for the bound states without any additional assumption. Furthermore, the resulting eigenvalue equations determine the dominant BS amplitudes for these bound states. The other major achievement is the study of the strong decays of hadrons based upon these dominant BS amplitudes. We show that the agreement between this theory and the experiments on the S- and P-wave mesons is entirely satisfactory. It is also concluded that the axial-vector gluon couples much more strongly than the vector gluon in this theory