A Unitary Symmetric Spurion Formalism of Weak Interaction

Abstract

Roles played by the unitary symmetry in the weak interactions are investigated in the framework of a spurion formalism. By making use of spurions, currents of strongly interacting particles are constructed formally in octet form, and the interaction Hamiltonian is written in a form of current-current interaction, which is apparently invariant under the three-dimensional unitary group. Lepton current can be introduced in such a way that the transitions with IL1SI=2 do not occur. Isotopic spin selection rule, IL1II=1/2, holds for nonleptonic decays of baryons, but in leptonic processes (I .JII = 3/2) -transitions also occur, which lead to LIS/ LJQ = -1. If one assumes that the vector current is conserved in the unitary-symmetry limit, only terms corresponding to (LIS/ LJQ = 1) -transitions are included in the vector current, and thus transitions with LlS/LlQ= -1 occur mainly through the axial-vector interaction. Further, if we assume that the weak interaction Hamiltonian is invariant under R-reflection, we can fix the relative strength among the most of weak coupling constants by comparing our results with the experimental values of leptonic decays of baryons and the decay ratio of K->,uv-process to n~,uv-one. Using these coupling constants, we have derived the following conclusions which are consistent with experiments; (i) the leptonic decay probabilities of hyperons CIL1SI=1) are about one-tenth of the probability of ordinary beta decay, (ii) _l'+--> n,u+v decay probability (L1SjL1Q= --1) is about one-tenth of that of leptonic decays of hyperons, and (iii) relative decay probabilities and asymmetric coefficients of nonleptonic decays of baryons are all consistent with experimental facts.