Veneziano Duality inSU(3)-Symmetric Meson-Baryon Scattering

Abstract

An SU(3) symmetric Veneziano model for pseudoscalar meson-baryon scattering is con­ structed. The model incorporates the full content of the exchange degeneracy pattern of baryon spectrum. A hypothesis is made that the leading trajectories bootstrap themselves as long as it is consistent with the crossing relation, no ghosts on the leading trajectories and certain physical requirements. If we further adopt a subsidiary hypothesis on the SU (3) structures of the daughter states, the A amplitude (we use CGLN's notation) is completely determined to within a scale factor. Possible SU (3) splitting of the trajectories is considered. Theoretical prediction for threshold values of A amplitudes agrees quantitatively with ex­ perimental values (which are given in terms of the s-wave and p-wave scattering lengths) for rrN and KN scattering. It is shown that in the limit of quantized intercepts, the present model satisfies Adler's condition approximately. When applied to high-energy forward scat­ tering, the model predicts the t-dependence of the F/ D ratios of vector and tensor meson couplings. The theoretical value of the A amplitude associated with the nonstrange vector and tensor Regge pole exchange agrees with the empirical value within a factor of two. § I. Introduction In vanous dynamical schemes ever proposed to describe hadron scattering processes, exchanges play a primary role. In the early days, particle exchanges in the s-, t- and u-channels were treated separately and added up to give the whole amplitude. The results, however, are sensitive to the choice of types of couplings and the way of extrapolating resonance formula to the off-mass shell region. Even if the particle exchange is Reggeized, the t-dependence of residue functions remains undetermined. Furthermore, it has become evident from the study of finite energy sum rules applied to pion-nucleon scattering that the extrapolation of Regge pole terms down to the intermediate energy region gives the average of the contributions of the direct channel resonances. 1 ),Z) The problem of double counting would occur m general if one simply sums resonance terms in all three channels. Veneziano has proposed a new model as a solution to this problem. 3 ) The