Showing papers in "Progress of Theoretical Physics in 1981"

Effects of Superheavy Quarks and Leptons in Low-Energy Weak Processes K_L{to}{μ}bar{μ}, K^+{to}{π}^+{ν}bar{ν} and K^0{leftrightarrow}bar{K^0}

Abstract: We investigate potentially important effects due to the existence of superheavy quarks and leptons of the sequential type in higher·order weak processes at low energies. The second-order LlS * 0 neutral-current processes Kl. ~ I'ii, K~ 1[+ vi) and KL-Ks mass difference are analysed allowing for fermions of masses comparable to or larger than the weak-boson mass in the Kobayashi-Maskawa scheme and in the general sequential scheme with an arbitrary number of generations. Possible connection between heavy·quark masses and light-heavy quark mixing are also examined. The requirement that the rare decay processes such as KL ~ l1ii and K+ ~ 1[+ vi) be absent up to order aGF yields a rather stringent bound on the magnitude of light-heavy Quark mixing: Such mixing has to be less than mW/mQuack times a factor much smaller than unity.

Short Range Part of Baryon-Baryon Interaction in a Quark Model. I —Formulation—

Abstract: The short range part of the interaction between non-strange baryons (N and Δ) is studied in a nonrelativistic quark model. The mass of a quark is assumed to be about one-third of the nucleon mass and the quark-quark interaction consists of a confinement term and the one gluon exchange potential. Baryons are described as clusters of three quarks and the resonating group method, which has been extensively developed in the nuclear cluster model, is used to treat the bound state and scattering problems of two baryons. This paper discusses the formal aspects of the present approach, while the numerical results will be given in the subsequent paper.

The Lie Algebra Structure of Nonlinear Evolution Equations Admitting Infinite Dimensional Abelian Symmetry Groups

Abstract: Hereditary operators in Lie algebras are investigated. These are operators which are characterized by a special algebraic equation and their main property is that they generate abelian subalgebras of the given Lie algebra. These abelian subalgebras are infinite dimensional if the hereditary operator is not cyclic. As a consequence hereditary operators generate on a systematic level nonlinear dynamical systems which possess infinite dimensional abelian groups of symmetry transformations. We show that hereditary operators can be understood as special Lie algebra deformations with a linear interpolation property. In order to construct new hereditary operators out of given ones we study the permanence properties of these operators; this study of permanence properties leads in a natural way to a notion of compatibility. For local hereditary operators it is shown that eigenvector decompositions are time invariant (such an eigenvector decomposition is known" to characterize pure multisoliton solutions). Apart from the well-known equations (KdV, sine-Gordon, etc.), we give-as examples-many new nonlinear equations with infinite dimensional groups of symmetry transformations. A detailed analysis of the celebrated Korteweg-de Vries equation reveals that this nonlinear evolution equation possesses an infinite dimensional abelian group of symmetry transformations. This group of symmetry transformations is given by the resolvents of the so-called generalized KdV equations. And this striking property is shared by many other nonlinear evolution equations; Only to name a few: Burgers equation, sine-Gordon equation, Zakharov-Shabat equations, Gardner equation etc. Furthermore one discovers that for these equations (except Burgers equation) the structure of this abelian symmetry group is intimately connected with the existence (and description) of multisoliton solutions, and in addition connected to the existence of infinitely many conservation laws (via Noether's theorem or rather a suitable generalization thereof).

On the Partical Conservation of the U(1) Current

Abstract: Recently proposed partial conservation of the UO) current (PCU,C) is applied to estimate the decay rates of various OZI forbidden processes. The results obtained are in good agreement with experiments and thus indicate the important role played by the UO) axial-vector anomaly in these decay processes. Octet jP = } + baryons are next introduced into this scheme and low energy theorems related to the B dependence of the matrix elements are investigated. Physical consequences of non-zero B (strong CP-violation) are also discussed with the help of the PCU,c. The results are used to give the bound on B.

Nuclear Binding Mechanism and Structure of Neutron-Rich Be and B Isotopes by Molecular-Orbital Model

Abstract: The neutron-rich (n-rich) Be and B isotopes are investigated by a molecular-orbital model, which is constructed on the (l-(l cluster structure of 8Be. Total energies of the ground states and some excited states are calculated with a densityand starting-energy-dependent effective interaction, including rearrangement effects. The absolute values of the binding energies and the general trend of their isotope dependence are well reproduced for nuclei up to l6Be and 17B. I t is found that not only the densityand starting-energy-dependence of the effective interaction, but also the spin-orbit potential has important effects on the particle stability of n-rich nuclei, especially, extremely n-rich nuclei. It is also found that the (l-(l cluster structure as a core persists in these isotopes, especially in non-normal parity states. The spin-orbit potential reduces clustering in nuclei up to the neutron-closed shell nucleus and, on the other hand, it enhances clustering in extremely n-rich nuclei. Our model easily reproduces the non-normal parity states of 'Be 0/21+: 1.68 MeV) and ilBe (l/2": ground state) in very low energy regions and is useful for explanation of low-lying level structure of Be and B isotopes.

Neutorino Mass, the Right-Handed Interaction and the Double Beta Decay. I ---Formalism---

Abstract: In order to shed light on the important question whether neutrinos are Dirac of Majorana particles, the double β decay is investigated within a general form of weak interaction Hamiltonian. The systematic study is made on the 0^+ →J^+ nuclear transitions for the tow-neutrino and neutrinoless modes both in the two-nucleon- and N^*-mechanism. It is shown that for the neutrinoless mode, only the 0^+ →0^+ transition in the two-nucleon mechanism is allowed if there is no right-handed interaction. When the right-handed interaction gives a sizable contribution, the role of the 0^+ →2^+ transition becomes as important as the 0^+ →0^+ transition. The comparison of our results with the previous ones is also presented.

Classical Planar Heisenberg Ferromagnet, Complex Scalar Field and Nonlinear Excitations

Abstract: Nonlinear excitations in a classical planar Heisenberg ferromagnet in an external field (CPHFF) are studied. Taking a classical counterpart of the spin-raising operator as a relevant field variable, we establish a close correspondence between the CPHFF and a complex scalar field (CSF) in which each atom in a complex lattice field, while coupled with its neighbours, sits on \D'-like on-site potential with saturable nonlinearity; In their static form CPHFF equations and CSF equations are identical to each other. In the continuum limit the CSF takes a semi-classical form of a Bose liquid with nonlinearity, however, characteristic of classical spin system. Solutions to the field equations are studied by using the continuum approximation. In one-dimensional case moving domain-wall solutions associated with symmetry-breaking states are obtained for the CPHFF and the CSF. In two- and three-dimensional cases static solutions to the field equations are obtained in the form of vortex solutions in close analogy to the case of the Ginzburg-Pitaevskii equation in the theory of superfluidity.

Turbulized Rotating Chemical Waves

Abstract: From the numerical study of a simple nonlinear kinetics with scalar diffusion, it is shown that rotating waves easily transform to turbulence. The turbulence here is triggered by a single phaseless point, and spreads over the entire system through the endless production of phaseless points in pairs. A possible turbulence· inducing mechanism is interpreted. Rotating spiral waves are an intriguing mode of spatio-temporal organization in non­ linear dissipative media with oscillatory or excitable local kinetics. The existence of such waves has most clearly been demon­ strated ' ) for the Belousov-Zhabotinskii reac­ tion, where even the geometrical structure of their three-dimensional version, viz. scroll waves, has been analyzed in detaiL 2 ) Similar wave phenomena are also met in life pro­ cesses.") For instance, the circus movement of electrical activities was shown to occur in rabbit heart tissue:) and this kind of circulat­ ing activity has long been speculated to have a connection with some forms of high fre­ quency irregularity of heart beat. 5) Another well-studied biological system associated with the spiral wave pattern is the aggrega­ tion of slime mold amoebae. 6

The Group Theoretical Structure of Fermion Many-Body Systems Arising from the Canonical Anticommutation Relation I : Lie Algebras of Fermion Operators and Exact Generator Coordinate Representations of State Vectors

Abstract: We study in this series the group theoretical structure of Fermion many-body systems arising from the canonical anticommutation relation of the annihilation-creation operators. Owing to the canonical anticommutation relation, a Fermion system with N single particle states has at least six Lie algebras of Fermion operators, a U(N), an SO(2N), an SO(2N + I), an SO(2N +2) and two U(N + 1) Lie algebras. There are also two Clifford algebras of 2N and 2N + 1 dimensions. The Fermion space is shown to belong to the spinor representations of the SO(2N), SO(2N + 1) and SO(2N +2) groups. The canonical transformations generated by the U(N), SO(2N) and SO(2N + 1) Lie algebras are characterized as the transformations to induce the linear U( N), SO(2N) and SO(2N + 1) transformations for the Clifford algebras. The independent (quasi-) particle type wave functions of three kinds including the Hartree-Fock and Hartree-Bogoliubov wave functions are constructed by means of the canonical transformations and their relationship is studied. We derive three exact generator coordinate representations for state vectors in which the generator coordinates are the U(N), SO(2N) or SO(2N + 1) group and the generating functions are the independent (quasi-) particle type wave functions. We characterize the structures of state vectors in the generator coordinate representations and study the relationship of the three representations.

On a Semi-Relativistic Treatment of the Gravitational Radiation from a Mass Thrusted into a Black Hole

Abstract: •A semi·relativistic treatment estimating the gravitational radiation emitted by a particle thrusted into a Schwarzschild black hole with a finite kinetic energy at infinity is presented on the two extreme assumptions: (a) The particle moves along a geodesic in a curved space and (b) the particle radiates as if it were in flat space-time. The structure of the burst and beaming process of gravitational radiation are studied. The merit of this approach lies in its simplicity and in providing a direct and complemen­ tary understanding of the results obtained by a fully relativistic treatment. The recent progress in the development of a new family of gravitational wave antennae!) and the possibility of achieving the accuracy required to observe predicted levels of gravitational wave signals coming from galactic sources,2) have made a new analysis of the detailed structure of bursts of gravitational waves necessary. In this paper we propose a semi-relativistic treatment for the estimation of the gravitational radiation emitted by a particle thrusted into a Schwarzschild black hole with a finite kinetic energy at infinity. Following the approach used in Ref. 3) we have made two extreme assumptions: (a) the particle moves along a geodesic in the Schwarzschild geometry, and (b) the particle radiates as if it were in flat space-time. However, contrary to Ref. 3), in which the stress is mainly on the energy spectrum of the radiation, here we are interested in the temporal structure of the burst. Therefore, we introduce an approximation technique by which the details of the radiating process can be readily studied and easily compared with the results obtained by using a fully relativistic treat­ ment. The fully relativistic treatment of this same process is presented in Ref. 4). § 2. Perturbations induced by a particle thrusted into a black hole in the semi-relativistic treatment

Phase Transition and Slowing Down in Non-Equilibrium Stochastic Processes

Abstract: A general criterion of appearance of slowing down in non·equilibrium stochastic processes is proposed. Many examples for this general criterion are shown, in which a phenomenon of slowing down occurs at a certain value of the relevant parameter. In particular, a generalized scaling treatment of transient phenomena is effectively applied to deriving the relaxation spectra of some multiplicative stochastic processes. The concept of asymptotic slowing down for finite systems is also proposed.