Veneziano's Model for Pseudoscalar-Pseudoscalar Scattering, Factorization and the Nonet Ansatz

Abstract

Crossing-symmetric, Regge behaved amplitudes of the Veneziano type are constructed for P₈-P₈ scattering, where P₈ denotes the pseudoscalar meson octet. Factorization of the parent and the first (odd) daughter Regge trajectories is investigated in detail. Several relations for the V₉P₈P₈ and the T₉P₈P₈ coupling constants which are equivalent to or consistent with the SU(3) symmetry and Okubo's nonet ansatz are obtained, where V₉ and T₉ denote the vector and the tensor meson nonets, respectively. Positive definiteness of the square of the first daughter-P₈-P₈ coupling constant leads to inequalities for the trajectories or the masses which are well satisfied by experiment. Factorization condition for the first daughter trajectories leads to trajectory or mass relations which are well satisfied experimentally. In particular the requirement of the universality for the parent and the first daughter ρ couplings leads to the broken SU(6) mass relations which have been obtained by Kawarabayashi, Kitakado and Yabuki using Adler's PCAC consistency conditions applied to the Veneziano model. Consequences from the requirement of the PCAC conditions on the η-meson processes are discussed briefly.