Relativistic Composite Model Consistent with the Bethe-Salpeter Equation, Approximate SU(6) Symmetry and Duality. I

Abstract

Dual composite theory of many-meson amplitudes is applied to investigation of the Bethe-Salpeter (BS) equation for one-meson states. The interaction kernel is the direct extension to this case of those which were determined by duality for many-meson amplitudes. The BS equation is shown to have solutions with the following properties: i) There are no second-kind exotic states in the leading Regge trajectories. ii) Mesons form approximate irreducible representations of SU(6) ⊗O(3)L and SU(6)W ⊗O(2)Lz symmetry at rest and for linearly moving states respectively. iii) These states may be made exact irreducible representations if one takes an appropriate form of an arbitrary function of total momentum which remains in the BS amplitudes. iv) Mesons form linearly rising Regge trajectories with respect to the total orbital angular momentum of urbaryons inside the meson. v) Dependence on relative space-time coordinates of the BS amplitudes is given by the factorized residue functions at the poles of the dual function in the interaction kernel. vi) BS amplitudes on the leading trajectory have positive norm, whereas there appear negative norm states also on the daughter trajectories when the Veneziano function is chosen as the space-time part of the interaction kernel. Discussion is given on the relations among the constructive and interactive forces and on the duality in the composite theory of hadrons.