Nonleptonic Decays ofKMesons in Chiral Dynamics and the Proof of the ΔI=1/2 Rule

Abstract

We construct weak interactions from the nonlinear chiral invariant Lagrangian, and dis­ cuss the nonleptonic decays of K mesons in the chiral vector meson model. Correction to this model due to the current-current interact jon and the K*- and KA-poles violates the AI=1/2 rule, but the violation is quite small and consistent with experiment. Moreover we assume the intermediate boson mass to be 12 Be V in the model to explain the K 1°-'>2rr: decay rate. 1 ) has derived an effective Lagrangian for soft-pion interac­ tion, which reproduces the results of current algebra in a simple way. On the basis of the (J model, he has employed an SU(2) chiral transformation. Schwinger2) has also derived an effective Lagrangian, and has introduced the vector and axial-vector mesons as gauge fields. The concept of chiral invariance plays ail important role in understanding the low energy phenomena. The purpose of this paper is to show that chiral invariance is also useful for the problem in weak interactions. Moreover we discuss the nonleptonic decays of K mesons, and prove the validity of the LJI = 1/2 rule on the basis of the chiral invariant Lagrangian. In§ 2 a generalization of the SU (2) chiral dynamics to SU (3) is formulated ll1 the quark model. S ) The vector and axial-vector mesons are introduced as gauge fields. The Lagrangian written by actual fields is invariant under the nonlinear chiral transformation. In § 3 the Lagrangian for the weak interaction is constructed from the Lagrangian for the strong interaction obtained in § 2. In § 4 the nonleptonic decays of K mesons and the LJI = 1/2 rule are discussed. It can be shown that the LJI = 1/2 rule holds, though at first sight the weak Lagrangian (17) seems to violate the 111=1/2 rule. In a previous paper 4 ) we considered the K-72n decay and proved the 111=1/2 rule for this process on the basis of the quark model. In this paper we consider the K1D decay by the self­ energy type diagram due to the vector mesons, the axial-vector mesons and the intermediate boson without introduction of quark. We find that this model (chiral vector meson model) also explains the 111=1/2 rule, and that the result of this model is the same as current algebra with a slight difference in coefficient. The contributions of the current-current interaction and the K* -pole and KA-pole;· 1402