Finite isospin groups and their experimental consequences

Abstract

Under the assumption that the observed isospin symmetry is a manifestation of the group structures of hadrons and their interactions, it is attempted to determine the order of the symmetry group, if finite, and to clarify the physical meaning of each group element. Our scheme is based on the observations that (1) classifications of particles according to irreducible representations of both the finite and the continuous groups are possible under certain restrictions, and (2) the transformation law of particles under continuous rotations in isospin space cannot be established directly by experiments. In particular, we consider the polyhedral kaleidoscope groups. The consistent formulation by finite groups needs a selection rule to exclude unobserved exotic states, which turns out to be a requirement of charge conservation. Several experiments are suggested to test our assumptions in strong-interaction processes.