Crossing Invariant Solution of Baryon Exchange Degeneracy and Reggeon F/D Ratios in SU(4)

Abstract

Crossing matrices are derived for meson-baryon scattering in SU(4). Using the ClebshGordan coefficients and crossing matrices, a crossing invariant solution of baryon exchange degeneracy is found within the framework of SU(4) and no exotics in all channels. §I. IntroductionIn the past decade, hadron physics seems to have confirmed an SU(3) symmetry, which could be based on a fundamental triplet as sub-hadronic particles. However, there is no a priori reason to believe that the triplet model retains its validity far above several Ge V in hadron spectrum.In an experiment of jet shovvers in cosmic ray reactions, Niu et al.n have got a clue to a new charged particle with a large mass. Recently, in the experiments of electron-positron colliding beams, new narrow boson resonances J(3.1) j1Jf (3.1) and 1Jf (3.7) have been discovered. 2 J These heavy particles could be super hadrons with a new quantum number, for instance, charm 3 l and/or color. 4 l In trying to understand the structure of strong interactions (including the interactions of newly discovered particles), several higher symmetry schemes have been proposed. Introducing the fourth quark (charm quark), Glashow, Iliopoulos and Maiani,') and many other authors') have proposed an SU( 4) symmetry scheme.Another model, conventionally called color model, has been proposed by Nambu and Han. 4 l In this model the new particles are the candidates for states of higher multiplets SU (3) Q9SU(3).Another important aspect to understand strong interactions is in an approach of duality. In the requirement of no exotics in all channels supplemented by crossing invariance (i.e., the baryon spectrum must close under s-u crossing), the t-channel F / D ratios of the reggeon BE coupling have been given consistently with SU(3) or SU(6) . 5 ) Following Glashow, Iliopoulos and Maiani, we have introduced the fourth (charm) quark and have derived a number of basic relations 6 l emerging from an SU ( 4) symmetry, which will be useful for a future analysis of the quartet model.For completeness and to demonstrate how to handle some relations, \Ve derive in this paper crossing matrices for meson-baryon scattering amplitudes in §