Sakata Model Research Articles

The Non-leptonic Decays of Hyperons

The non-leptonic decays of hyperons are investigated based on the Sakata model and the V-A theory of weak interactions. The Λ-decay and the Σ-decay are treated in a unified way. In the latter case, a possibility of interpreting the experimental evidenes is given provided that the structure of Σ-hyperon satisfies some suitable conditions.

Symmetry in Sakata's Model and Weak Interactions. II

A scheme is studied for non-leptonic decays of hyperons and K-mesons, in the full symmetry theory of Sakata's composite model. It is shown that the relations between various decay amplitudes are independent of particular configurations assigned to the particles which participate in the reactions. The K-3 pi decay is studied to show that the decay scheme is workable. Anomalous decay modes are discussed in which there appear one or more pi /sup 0/' or pi / sup 0/' in place of pi /sup 0/. (auth)

Chapter 5. Weak Interaction in the Sakata Model

In the Sakata model it wili be natural to consider that all the weak processes are caused by the primary weak interactions which exist only among the assumed basic baryons (p,n, lambda ) and the leptons ( omega ,e, mu ). A search is made for the possible schemes of such primary weak interactions from the standpoint of the Sakata model through analysis of experimental data. A brief summary is presented of the general kinematical consequences which are obtained to the lowest order of the charge-exchange weak four-fermion interaction, independently of the complicated effects of the strong interactions. The problem of the dynamics of strong interactions in the Sakata model is considered. (W.D.M.)

Chapter 3. Mass Formula in the Sakata Model

A mass formula is introduced in the Sakata model and its implications are discussed. The revised form of the mass formula is developed and the energies of full symmetry quantum states, which are represented by the basis vectors of irreducible representations of U, are evaluated in order to compare the theoretical predictions thus obtained with experimental indications. Another approach is suggested to find the masses of particle states of the full symmetry theory.

Single Pion Production Process in Pion-Nucleon Collision and the Sakata Model

Based on the Sakata model, we propose a model for the single pion production process in n-N collision which is essentially an extension of the Lindenbaum-Sternheimer model. It is pointed out that the analyses of sub-Bev single pion production phenomena will give us useful information about the level scheme of the Sakata Model. As a first step of the inves­ tigation of this model an analysis of the single pion production process in n+-p collision at 500 Mev is made. Our model predicts the contribution of the 1=2 boson isobar as well as the 1=3/2 fermion isobar (Lindenbaum-Sternheimer model) for this process. Such a prediction is consistent with the present experimental branching ratio (n++p~n++no+p)/( n++p~n++n++n)=1. 5. We calculate the energy and angular distribution of the pion and nucleon which will be useful for obtaining information about the 1=2 boson isobar and 1=3/2 fermion isobar from this process.

Chapter 2. The Full Symmetry Theory of the Sakata Model

A possible symmetry among the basic particles in the Sakata model is studied. A theory is developed which incorporates such a symmetry in a satisfactory way. Theoretical predictions are compared with experimental information. Some speculations are also made for further progress.

Chapter 4. Quantum Mechanical Approach to the Composite Model of Elementary Particles

The structure of composite particles seem to be intimately connected with the nature of more fundamental dynamical laws which will reveal themselves beyond the limit of applicability of the point model. A general formulism for treating the Sakata model by means of quantum field theory is constructed and several consequences are derived, bearing in mind that the theory applied to the present model would have a physical reliability only in the corresponding- theoretical sense. (W.D.M.)

Chapter 1. The Sakata Model

General remarks and underlying ideas concerning the composite model approach to the theory of elementary particles are given. Classification of elementary particles and the Nakano-Nishijima-Gell-Mann rule are reviewed. The Sakata model for baryon-meson systems is discussed in some detail and comparison is made with other models.

Chapter 2. A New Stage of Elementary Particle Theory

1. The number of elementary particles has increased very rapidly smce World War II. It is said that many theoretically uninvited guests have appeared. At present moment, there are photons (r), neutrinos (v), electrons (e) and muons (p) as leptons, and pions (rc) and strange K-mesons as mesons. There are also protons (p) and neutrons (n) as heavy particles, and lamda-particles (A), sigma-particles (.S) and xi-particles (8) as strange particles. It seems to be one of the present-day central problems how to understand these particles in a unified way. 2. Japanese elementary particle physicists first paid attention to the strange properties of a series of new particles very soon after they had been discovered. The most typical feature seen in the case of strange particle production is that they are always produced in pairs. Later, in 1953, the strangeness quantum number was introduced by Nakano-Nishijima and inde­ pendently by Gell-Mann, so that a rule of the elementary particle world was obtained. 3. As to the structure or the property of elementary particles the research work has been done from several directions. At the two meetings, which were held at the Research Institute for Fundamental Physics (Kyoto) in November and in December, 1959, separately, some possibility to connect these directions was disclosed and a further outlook of the future development was pointed out. Namely, the following directions might be unified in an orgamc way: (a) To attack the problem from the outside region by making use of the meson theory of nuclear forces and nucleon structures; (b) To clarify the electromagnetic structures of elementary particles, and to investigate the effects of weak interactions on the structure of elementary particles; (c) To study the Sakata model, which is a composite model of mesons and heavy particles, and to develop the Nagoya model, which is a

Symmetry in Sakata's Model and Weak Interactions. I

Symmetry in Sakata's Model and Weak Interactions. I

Composite Model and the Nature of Vector Interactions in Strangeness-Violating Decays

In this paper we discuss decay interactions based on Sakata's composite model in which neutron, n, proton, p, and Λ-particle are supposed to be “elementary”. Symmetry with respect to n, p, and Λ is also assumed. Then it is shown that (πK) currents are necessarily added to the usual strangeness violating (|ΔS|=1) baryon vector currents in the conventional Yukawa type interaction. This is analogous to the situation that (ππ) and (KK) currents necessarily appear in the |ΔS|=0 leptonic decay interaction in the Sakata model. By taking the (πK) currents into account, the transition probabilities for Ke3, Kµ3, and beta- and muon-decays of Λ are shown to be consistently described with the same coupling constant as that obtained from Kµ2+ decay. Thus the coupling constant for strangeness-violating leptonic decays seems to be smaller than that for strangeness conserving ones. For non-leptonic decays, the Hamiltonian which guarantees the |ΔI|=1/2 selection rule is easily found by virtue of the additional neutral terms withe the universal coupling constant. The lifetimes and branching ratios of non-leptonic decays of Λ and K are in good agreement with experiment in terms of the normal beta-decay coupling constant. The situation is a little complicated for Kπ3. Admixture of |ΔI|=3/2 transitions are also briefly discussed. Some comments are made on the observability of π0', a neutral meson having an isotopic spin 0.

A Unified Model for Elementary Particles

By extending the Sakata model, a unified model for elementary particles is proposed, the basic particles in the Sakata model are assumed to be constructed of the lepton and B+, which is regarded as a new kind of matter. The full symmetry among three basic particles and the symmetrical property of the weak interactions which was recently pointed out by Gamba, Marshak and Okubo come automatically of this model. The nature of B+ and the new mechanics which accounts for the binding of B+ to the lepton will be the central problem to be studied in the future. very interesting results which are in good agreement with experimental data. In spite of these successes, the Sakata model has been concerned only with the strongly interacting particles, and nothing has been done with the lepton. TvIoreover, even in the case of strong interactions, the charge independence or the full symmetry (which -we shall call the 1.0.0. symmetry) among the three basic particles was introduced in a formal \vay, and it has not yet been clear why the strong interaction should have such invariance properties. In order to describe both baryon and lepton in a unified way, and to find out a profound meaning hid­ den behind the charge independence or the 1.0.0. symmetry, we must go further from the Sakata model. For this purpose let us turn our attention to the weak interaction. The theory of yveak interaction has now come to a very definite point after the great success of the current-current interaction theory proposed by· Feynman and Cell-Mann. 8 ) Furthermore, it has recently become clear that the Feynman-Gell-Mann current derived from the Sakata model is quite suf--ficient to account for the experimental facts concerning the weak processes. 9 ),10) Especially, it should be noted that the terms which obeyed the conditions J S/ LiQ = - 1 and I LlS/ LlO I > 1 automatically dropped out of the current. Thus, by adopting the Feynman and Cell-Mann theory and

On the Structure of the Elementary Particles

Recently a unified model for the elementary particles (called “the Nagoya Model”) has been proposed in which the basic baryons in the Sakata model are assumed to be composed of the leptons and a new kind of matter, B. Through the investigation of the mass formula for the compound particles in the Sakata model, it is shown that B-matter has a charge-like character similar to the electric charge (ε=-ε). On the basis of this character of the B-matter, i) the mass formula (the bound character and the mass-bond relation) is reproduced, ii) the physical ground is given to Taketani's idea, and his idea is developed. A dynamical law of the basic baryons within the compound particle is discussed. Remarks on new boson-baryon family and photon are given.

On the Model of Elementary Particles

A model of elementary particles is constructed on the basis of continuous rather than discontinuous (abrupt creation and annihilation) particle reactions. The various decay modes of particles examined in the above way yield only p, e, , and as the stable (fundamental) particles; all the others are sums of these stable particles plus an energy term G. Then, the particle reactions can be explained by the separation and addition of these stable particles. The charge distributions of p and n derived from e-p scattering appear to be favorable to the above model: the neutron can be visualized as an electron rotating around a proton. If the B/sup +/ in Sakata's model is considered to be a composite particle constructed of p, -bar, and G, then this model is similar to the abcve one. Possible questions to be taken up in this model are discussed. (D.L.C.)

Classification of Composite Bosons in the Sakata Model

Assuming the Sakata model (p, n, Λ are basic, all other strongly interacting particles are composite particles) and neglecting moderately strong interactions which contribute to N-Λ mass splitting, we find the complete symmetry between three fundamental fields (referred to as global symmetry). Under this global approximation, classification of two baryon pair states–which are supposed to represent physical mesons–is described.

A Note on the Leptonic Decay of Hyperons

The leptonic decay modes of pions and K-mesons are studied from the viewpoint of compound model (Sakata model). By comparing these processes (π→µ+ν and K→µ+ν), a conjecture for the leptonic decay of hyperons (e.g. Λ→p+µ-+ν) is given which suggests that the (squared) bare coupling constant of this process is smaller than that of ordinary β-decay or µ-capture process of nucleons by a factor ∼10.

A Possibile Symmetry in Sakata's Model for Bosons-Baryons System

In the full symmetry theory a physical system can be characterized by six quantum numbers. Following the original intention of the composite model, an attempt is made to replace these quantum numbers by others that are easier to understand by intuition. This study leads to a new picture of the particle, which contrasts with the usual picture in the perturbation theoretical treatment. The realistic aspects developed not only promote a deeper understanding of the full symmetry theory of the composite model, but also throw a new light on the structure of elementary particles. (auth)

A Possible Symmetry in Sakata's Composite Model

In Sakata's model of strongly interacting particles, it is assumed that the proton, neutron, and LAMBDA -particles are the basic particles which combine in various manners to make up mesons and other baryons. A certain quality which exists among these three particles is investigated. The view is taken that there exists a certain origin of the mass of the particle which can never be redueed to the self-action of the usual interactions. The symmetry of the interaction among the three basic particles is of primary importance and charge independence has a secondary meaning. (A.C)