Three-Body Leptonic Decays of K-Mesons and Hyperons

TLDR: In this paper, a method of treating weak interaction processes involving composite particles is formulated on the basis of the theory of bound states of quantum field theory, which is applied to the analysis of the decay K+__,no+ft.v.

Abstract: A method of treating weak interaction processes involving composite particles is for­ mulated on the basis of the theory of bound states of quantum field theory. The method is applied to the analysis of the decay K+__,no+ft.v. And it is shown that under a possible set of assumptions ~-value of this decay must lie between -1 and + 1 irrespective of the structure of n and K-meson. Then the method is applied to the leptonic decays of hyperons and it is shown that if we take K-baryon model for hyperons there is a possibility of understanding the smallness of the decay rates compared to the ones expected from the universal coupling theory. ~ l. · Introduction At the time of the proposal of composite model of elementary particles by S. Sakata, it was pointed out that present status of the theory of elementary particles should be compared to the early days of the theory of atomic nuclei.l) After that, many investigations have been done along this line of thought. In 1956, K. Matumotdl proposed the mass formula of composite particles, which corresponds to Weizsacker's empirical mass formula for nucleus, and Z. Maki 3 l examined the possibility of the formation of n-meson with a nucleon and an anti­ nucleon from field theoretical viewpoints, which corresponds to the deuteron problem in the nuclear theory. In 1959, Ikeda, Ogawa and Ohnuki 4 l have deve­ loped group theoretical investigations based on the assumption of the symmetry among a proton, a neutron and a A-particle in the strong interaction, 5 l which corresponds to the group theoretical investigations of nucleus. Furthermore, the analysis of various weak processes have been done from the viewpoints of composite particles by Z. Maki, Y. Ohnuki, M. Nakagawa and other authors. 6 l Some of these investigations, especially the search for mass formula and group theoretical investigations based on some symmetries were inherited by a great many authors, 7 l although from somewhat different viewpoints. But if we take more seriously the above mentioned analogy between present status of the theory of elementary particles and early days of the nuclear theory, we should remember the various aspects of the developments of the nuclear theory. When we review the developments of the nuclear theory, we will im­ mediately be aware of the roles played by quantum mechanics as the dynamics