Boson Levels and Composite Model

Abstract

Boson levels are investigated dynamically from the viewpoint of the symmetrical Sakata model. It is assumed that almost all the observed bosons are the bound states of baryonanti-baryon pair. We formulate the problem by the NfD method in a modified form suitable for our purpose. The consequences about the mass spectrum which are derived irrespectively of the mass difference Jm between nucleon and A, are that, i) there exist no other octet bosons than n-octet and p-octet bosons, ii) there are bound states in unitary singlet SP 0 state (ABC-particle) and in 3S 1 state (~-particle), iii) the existence of unitary singlet IS 0 (o-+) composite particle is probable. Our theory can reproduce almost correctly the observed mass spectrum, when we take account of the mass difference between N and A. Relations of our theory to the usual Yukawa coupling theory about the interaction of bosons and baryons are also investigated. We obtain a right order of magnitude of the effective coupling constant. Especially it is shown that the coupling constant of pion to nucleon is correctly given independent of the details of our method. Finally, comments on the properties of nuclear forces in the inner region are given. § 1. IntroductionAs the development of experimental techniques, new excited levels of bosons and fermions have been found for these several years. The increase of the number of these levels forces us to understand all of them in a unified manner.Since Sakata proposed a model in which only p, n and A particles are considered to be fundamental and other particles are composed of these particles and their anti-particles,ll the study along the above line has been accelerat~d.In fact, there are many attempts to find a correct mass level formula, grouptheoretical investigations of the symmetry property of three-dimensional unitary space, 2 ),s), 4 J and attempts to establish the spin-mass relation by analyticity conat NERL on May 31, 2015 http://ptp.oxfordjournals.org/ Downloaded from

Chapter 4. Dispersion Theoretic Approach

“…In his treatment, the deuteron is defined as the zero of the D-function on the negative real axis of v. This definition of bound state is the same as that in the treatment of the composite particle by the N/1) method. 50 ) He considered the coupled N/D equation for the 3 Sr 3 D 1 coupled state, and approximated the left-hand-cut by the contribution from single n, p and w-meson exchanges. T'he subtraction constant was fixed from the experimental value of the 3 81 scattering length.…”