Shoichi Hori

An approach to a relativistic strong coupling theory

Abstract As is well known, the vacuum expectation value of the S-matrix provides us with the knowledge of all Feynman amplitudes and is equivalent to the S-matrix itself, if we introduce appropriate source functions. As the vacuum expectation value, which we call SVAC, is a c-number quantity, it is often more convenient to treat Svac than the S-matrix itself. Here we treat three cases: (i) two neutral scalar fields, ψ and φ, interacting through the interaction gψφ; (ii) the charged scalar field interacting with an external neutral scalar field φ through gψ ∗ ψφ ; (iii) interacting charged and neutral scalar fields ψ and φ through the interaction gψ ∗ ψφ . We derive several functional differential equations which Svac should satisfy and in which the coupling constant g and the source functions are variables. Then we obtain the solution in the form of an inverse power expansion of the coupling constant by solving the functional differential equations. In case (i), we can sum up the inverse power series and the result agrees with the exact solution. In case (ii), the only relevant Feynman amplitude is the modified propagator for the ψ-field, which is also expanded into an inverse power series of the coupling constant. In case (iii), Svac is expressed in a form involving only functional differentiations, but no more path integrals. If we carry out the functional differentiations, the result will also be an inverse power series of the coupling constant. Extension to other cases is also discussed.

A sextet model with modified left-handed current

Abstract A sextet model is proposed, in which left-handed weak doublets contain mixed states of charmed and ordinary quarks. It is shown that the model gives satisfactory explanations for high energy neutrino phenomena.

The Fundamental Triplet and Its New Degree of Freedom

The urbaryons which form a triplet state with respect to the usual SU3 group are assumed also to belong to the three-dimensional representation of the new su3 group introduced in this paper. We assume further that the forces between urbaryons and/or anti-urbaryons are mediated by a vector meson which is a singlet with respect to the . usual SU3 and an octet with respect to the new SU3 group. Under these simple assumptions we can understand the essential features of the urbaryon dynamics at least in the non-relativistic approximation which seems to be valid for bound states of massive urbaryons and/or anti-urbaryons. For example we can show that the potential energy between an urbaryon and an anti-urbaryon is twice as attractive as the potential between two urbaryons, and stable bound states are confined to the states which belong to the regular representations (1, 8, 10, ... ) of the usual SU3 group and are singlets with respect to the new SU3 group. Thus the meson states and baryon states are understood on the same footing. No para-statistics is necessary. These urbaryons may be quarks, but it is shown that there is the possibility of assigning integral charges to the urbaryons.

On the interaction Hamiltonian for the decay of Σ-hyperons

Abstract The interaction Hamiltonian for the decay of Σ-hyperons is phenomenologically constructed under the assumptions that: 1) the spin of the Σ-hyperon is 1 2 , 2) the CP-invariance holds, 3) the effects of the final state interactions are negligible, 4) τ(Σ−) = 2τ(Σ+), 5) the branching ratio w(Σ+ → p+π0)/w(Σ+ → n+π+) = 1, 6) the ΔI = 1 2 rule is valid, 7) α+ = α− = 0. These assumptions are sufficient to determine the interaction Hamiltonian uniquely if the coupling type (derivative or direct) of the Hamiltonian is prescribed, and from the Hamiltonian we obtain the result α0 = ±1 not inconsistent with the experiment. Conversely, when we replace the assumption 6) by α0 = ±1, we cannot conclude that the ΔI = 1 2 rule holds. If we assume α0 = ±1, α+ = 0, and leave α− arbitrary, taking into account the fact that the polarization of the Σ−-hyperon may be small, we obtain two kinds of solutions, one of which coincides with the result under the assumption α− = 0; the other yields |α−| = 0.8.

On the Longitudinal and Transverse Polarization of Positrons in µ+-Meson Decay

The density matrix which characterizes the polarization state of positrons emitted from mu /sup +/-meson decays at rest was calculated, using general parity non-conserving interactions, the mass of the electron being neglected. From the density matrix, the degree and direction of pclarization of the positrons are determined. Detection of transverse polarization perpendicular to the plane spannsd by the polarization vector of the initial mu /sup +/-meson and the propagation vector of the positron, wlll provide a test for whether invariance under Wigners time reversal is valid. (auth)

A Solution of the Einstein Equation in a Stationary Gravitational Field Due to a Rotating Source

The stationary and axially symmetric gravitational field due to a rotating deformed source can be treated by the Ernst equation. We prove analytically the validity of the solution of the Ernst equation that was presented as a possible solution in a previous paper for arbitrary real values of the deformation parameter δ. By means of analytic continuations of the solution we obtain a new solution in oblate spheroidal coordinates. This leads to a metric different from the Tomimatsu-Sato metric. From these solutions for real δ we determine the metric functions both in prolate and oblate spheroidal coordinates.

On the Generating Functional and Sum Rules for Correlation Functions in Inclusive Reactions

The second step in the study of inclusive reactions will be the investigation of the two-particle correlation function. In this connection it will be useful to consider sum rules which relate different correlation functions to each other. It is desirable that the sum rules should be independent of particular models or assumptions. The most important ones are the constraints imposed by the law of energy-momentum conservation. Such sum rules will be referred to as CFSRs in the following. So far a set of sum rules (ICSRs) has been derived among inclusive cross-sections based on the law of energy-momentum conservation and later it has been reexpressed in terms of the correlation functions. In § 2 we shall briefly recapitulate the generating functional formalism which the present authors introduced in a previous paper.1> In § 3 we shall derive directly a full set of CFSRs with the aid of the generating functional. There remains a question how many independent CFSRs are derived from a single law of energy-momentum conservation. As for ICSRs, Tye2> proved that one of Predazzi-V eneziano sum rules3> (Eq. (8) below) which seems at a glance to contain infinitely many CFSRs, is actually equivalent to a single Chow-Yang sum rule4> (Eq. (10) below). In § 4, we shall select independent ones out of numerous CFSRs obtained in § 3.

E-meson decay in the Veneziano model

Abstract It is shown that the pseudo-scalar assignment for the E-meson is preferable in the Veneziano model.

K-π resonance and the strangeness violating weak interactions

Abstract It is pointed out that for the p-wave K-π resonance M, comparison of the rates of K + →e+ ν + π 0 and M + →K + + π 0 decays could provide us with useful information with respect to the value of the coupling constant of strangeness violating weak interactions and also to that of strong interaction of M. The results are consistent with the experimentally found low rate of Λ →p+e − + ν decay and also with the sharp backward peaking of the Λ° in the reaction π − + p→ Λ °+K 0 with high incident pion energy. The effects of the K-π resonances on the K → e+ ν + π decay are discussed and it is inferred that these effects are not important. The status of the strangeness violating weak interaction is discussed.

On the Wave Functions of Higher Spin Particles

The 2s + 1 mutually orthogonal wave functions of a particle with spin s are explicitly worked out in the tensor formalism for a boson and in the RaritaSchwinger formalism for a fermion, respectively. As an example of application, a method is described according to which an angular correlation function is calculated relativistically, in the case of an associated production of a hyperon and a kaon and their ensuing decays, assuming that they have higher spins. (auth)