“Ur-citon”: An Attempt for Unified Theory of Hadrons*

Abstract

A theoretical scheme for unified treatment of the world of all hadrons is presented, which includes heuristically the successes of the quark model without the well-known difficulties regarding spin-statistics connection and binding problem. Our essential idea exists in the following: Introducing the operator ψA(p,ξ), called “ur-citon” which transforms similarly to the quark, depends on the internal Lorentz variables ξ, and is quantized through Bose-type commutation relations; we consider the “inner Fock expansion” of the general “inner state vector”. Then the expansion coefficients, which satisfy the “generalized Bargmann-Wigner equations,” are considered to represent our hadron fields, and are “second-quantized” following the prescription of the usual quantum field theory. In our theory the level scheme of mesons and baryons is given through the system of two and three three-dimensional harmonic oscillators, respectively, contrasting with one and two oscillators in the quark model. For the baryons this difference makes no detectable results at present, so our scheme shares the success with the usual quark model. For the mesons a degree of success seems to be much reinforced in our theory, providing an explanation of the “anomalous fine structure” and a possible solution for the A2-splitting problem. A general scheme for getting various kinds of effective vertices among hadrons is investigated also from the same unified view-point. Then it is useful to use a diagram, called “ur-citon diagram,” which is written by lines with an arrow representing a flow of ur-citons. A tentative application to the electromagnetic form factors of nucleons is shown to lead to a satisfactory result which reproduces the famous experimental behavior, the scaling law and the dipole-like behavior. Weak interactions among hadrons and leptons are, similarly to the usual theory, assumed to be given by a “current-current” like interaction in our scheme, where its parts relevant to hadrons are treated by our ur-citon scheme. Then we can derive rigorously the phenomenological rule “octet dominance” for the non-leptonic interaction. Moreover, as a result of detailed application to the non-leptonic hyperon decay it is shown that our theory with only one parameter reproduces the characteristic experimental behavior of both the S-wave and P-wave decays.