Superconductivity Model with Chiral S U (3) × S U (3) Symmetry Properties and Weak Decays of Elementary Particles

Abstract

The dynamical model of the pion-nucleon system, originally proposed by Nambu and Jona-Lasinio on the basis of an analogy with superconductivity, is extended to a Sakata triplet system. The Lagrangian with four-fermion interactions is assumed to be invariant under the chiral SU(3) × SU(3) group except for the small bare masses (MN(0) ≠ MΛ(0)) of the nucleons and the lamda. Characteristic features of the physical masses and the strong interactions, in particular the large mass splittings of the octet mesons, are explained as results from the superconductivity mechanism working among bare baryons. Introducing in addition the weak four-fermion interactions among bare baryons and leptons, the weak decays of the physical baryons and mesons: π → µν, K → µν and Λ → Nπ, are investigated. It is shown in an explicit way that the bare Cabibbo angle is unaffected by renormalization of the strong interactions in contrast to the large shifts among the masses. The amplitudes for the nonleptonic decay Λ → Nπ are derived in a form similar to the results from a meson-pole dominance model and are in agreement with the experimental data.