Unified Weak-Electromagnetic Gauge Schemes Based on the Three-Dimensional Unitary Group

Abstract

SU(3)\ifmmode\times\else\texttimes\fi{}U(1) and chiral SU(3)\ifmmode\times\else\texttimes\fi{}SU(3)\ifmmode\times\else\texttimes\fi{}U(1)\ifmmode\times\else\texttimes\fi{}U(1) models for the weak and electromagnetic interactions of leptons and hadrons are proposed. The usual quark model for hadrons as well as the usual Cabibbo rotation scheme is assumed. Symmetry-breaking effects due to inequalities in the masses of the gauge bosons are considered. By making a simple choice of the gauge boson masses based on the $U$-spin subgroup of SU(3), the undesired $|\ensuremath{\Delta}S|=2$ weak nonleptonic transitions can be completely eliminated and the undesired $|\ensuremath{\Delta}S|=1$ neutral current semileptonic transitions drastically suppressed. These models can reproduce the ordinary phenomenological weak interaction but are sufficiently flexible to give the possibility of interesting new effects for neutral leptonic and semileptonic processes, as well as to allow the possibility of an over-all arbitrariness in normalization for the effective nonleptonic interaction. Another consequence of the present scheme is the existence of very heavy leptons. A brief discussion of including the strong interactions in a grand unification is also presented.