Three-Field Model and Higher Symmetry GroupW3with Parity Interchange

Abstract

A theory of hadrons (strongly interacting particles) based on the higher symmetry group ${W}_{3}={U}_{3}\ensuremath{\bigotimes}{U}_{3}$ (or $S{W}_{3}=S{U}_{3}\ensuremath{\bigotimes}S{U}_{3}$) with parity interchange between the two ${U}_{3}$ (or $S{U}_{3}$) groups has been developed. The four-fermion vector model with three massless Dirac fields has been used to guide the construction of the meson and baryon particles. A parity doublet structure in the ${W}_{3}$ (or $S{W}_{3}$) limit is found for the mesons but not for the baryons. Mass relations between scalar (axial vector) and pseudoscalar (vector) octets or nonets of mesons are derived under various assumptions concerning the underlying group, the tensorial behavior of the symmetry-breaking terms, and the particle representations. Some experimental tests of these mass relations are noted. The possibility of incorporating the leptons into the theory is discussed.