Showing papers in "Progress of Theoretical Physics in 1997"

Strong gravitational lensing and velocity function as tools to probe cosmological parameters : current constraints and future predictions

Abstract: Constraints on cosmological models from strong gravitational lensing statistics are in­ vestigated We pay particular attention to the role of the velocity function in the calculation of the lensing probability The velocity function derived from the observed galaxy luminos­ ity function, which is used in most previous work, is unable to predict the large separation lensing events In this paper, we also use the Press-Schechter theory to construct a velocity function theoretically Model predictions are compared with the observed velocity function and the HST snapshot survey Comparison with the latter observation shows that the pre­ dictions based on the theoretical velocity function are consistent with the observed large separation events in COBE normalized low-density models, especially with a non-vanishing cosmological constant Adopting the COBE normalization, however, we have not been able to find a model which simultaneously satisfies both the observed velocity function and the HST snapshot survey We systematically investigate various uncertainties in the gravita­ tionallensing statistics including finite core radius, the distance formula, magnification bias, and dust obscuration The results are very sensitive to these effects as well as theoretical models for the velocity function, implying that current limits on the cosmological parameters should be interpreted with caution Predictions for future surveys are also presented

Stability analysis of spherically symmetric star in scalar - tensor theories of gravity

Abstract: A stability analysis of a spherically symmetric star in scalar-tensor theories of gravity is given in terms of the frequencies of quasi-normal modes. The scalar-tensor theories have a scalar field which is related .to gravitation. There is an arbitrary function, the so-called coupling function, which determines the strength of the coupling between the gravitational scalar field and matter. Instability is induced by the scalar field for some ranges of the value of the first derivative of the coupling function. This instability leads to significant discrepancies with the results of binary-pulsar-timing experiments and hence, by the stability analysis, we can exclude the ranges of the lirst derivative of the coupling function in which the instability sets in. In this article, the constraint on the first derivative of the coupling function from the stability of relativistic stars is found. Analysis in terms of the quasi­ normal mode frequencies accounts for the parameter dependence of the wave form of the scalar gravitational waves emitted from the Oppenheimer-Snyder collapse. The spontaneous scalarization is also discussed.

Analysis of a Kπ-Scattering Phase Shift and Evidence for the κ(900) Meson

Abstract: Recently we have shown an evidence for existence of \sigma-particle in the previous works/ where the \pi\pi S-wave phase shift is reanalyzed, by introducing a repulsive background suggested by the chiral symmetry, and by applying a new method of Interfering Breit-Wigner Amplitudes. In this work we also show, reanalyzing the K\pi S-wave phase shift from a similar standpoint, an evidence for existence of \kappa(900), possibly to be a member of \sigma-nonet.

Analytic Solutions of the Teukolsky Equation and Their Properties

Abstract: The analytical solutions reported in our previous paper are given as series of hypergeometric or Coulomb wave functions. Using them, we can get the Teukolsky functions analytically in a desired accuracy. For the computation, the deep understanding of their properties is necessary. We sum· marize the main result: The relative normalization between the solutions with a spin weight sand - s is given analytically using the Teukolsky·Starobinsky (T·S) identities. By examining the asymptotic behavior of our solution and combined with the T·S identities and the Wronskian, we found nontrivial identities between the sums of coefficients of the series. These identities will serve to make various expression in simpler forms and also become a powerful tool to test the accuracy of the computation. As an application, we investigated the absorption rate and the evaporation rate of black hole and obtain interesting analytic results. In our previous paper,I) we reported the analytic solutions of the Teukolsky equation 2 ) which consist of two types of series; one is given in the form of series of hypergeometric functions (hereafter we call it the hypergeometric type solution) and the other is given in the form of series of Coulomb wave functions (hereafter we call it the Coulomb type solution which was first given by Leaver3». The hypergeometric type solutions are shown to be convergent in the region except infinity with all finite E=2 Mw, M being the mass of black hole and wan angular frequency. The Coulomb type solutions are convergent in the region above the outer horizon for all finite E. We showed that the matching of these two types of solutions is perfect in the interme­ diate region where both solutions are convergent. In this way, we found the solutions which are convergent in the entire region of r for all finite E. In addition, we showed that our solutions are suitable to obtain the Teukolsky functions in the E expansion or the numerical computation. We also presented analytical solutions of the Regge­ Wheeler equation. 4 ) We showed!) that the solution can be written in various forms so that we have to choose some special ones. Furthermore, it is necessary to investigate further the properties of solutions to calculate the Teukolsky functions, because the solutions are given as series. For this purpose, we examined the asymptotic behaviors of the solutions and compared with the general result derived before. We made a system­ atic study on the incoming solution on the outer horizon. As for the incoming solution on the horizon, we take the same hypergeometric

Schild action and space-time uncertainty principle in string theory

Abstract: We show that the path-integral quantization of relativistic strings with the Schild action is essentially equivalent to the usual Polyakov quantization at critical space-time dimensions. We then present an interpretation of the Schild action which points towards a derivation of superstring theory as a theory of quantized space-time where the squared string scale plays the role of the minimum quantum for space-time areas. A tentative approach towards such a goal is proposed, based on a microcanonical formulation of large N supersymmetric matrix model.

The Renormalization-Group Method Applied to Asymptotic Analysis,of Vector Fields

Abstract: The renormalization group method of Goldenfeld, Oono and their collaborators is applied to asymptotic analysis of vector fields. The method is formulated on the basis of the theory of envelopes, as was done for scalar fields. This formulation actually completes the discussion of the previous work for scalar equations. It is shown in a generic way that the method applied to equations with a bifurcation leads to the Landau-Stuart and the (time-dependent) Ginzburg-Landau equations. It is confirmed that this method is actually a powerful theory for the reduction of the dynamics as the reductive perturbation method is. Some examples for ordinar diferential equations, such as the forced Duffing, the Lotka-Volterra and the Lorenz equations, are worked out in this method: The time evolution of the solution of the Lotka-Volterra equation is explicitly given, while the center manifolds of the Lorenz equation are constructed in a simple way in the RG method.

R-Invariant Natural Unification

Abstract: A nonvanishing superpotential gives a negative cosmological constant in super­ gravity. R symmetry is a unique symmetry that forbids a constant term in the su­ perpotential, and thus it may play a fundamental role in understanding a vanishing cosmological constant in supergravity. The R symmetry has been widely considered in phenomenology of supersymmetric (SUSY) gauge theories or supergravity, since it (or its discrete subgroup) allows for the avoidance of too rapid proton decay 1), 2) and provides a candidate for cold dark matter in our universe. 3) In a recent article 4) it has been pointed out that the spontaneous breakdown of the R symmetry U(I)R to its discrete subgroup Z2nR 5) produces a flat potential for a new inflation model. Motivated by the above theoretical and phenomenological considerations, we construct in this paper, R-invariant unification models. In the next section, we show that the minimal SUSY grand unified theory (GUT) is easily extended to an R-invariant one. However, we stress that this model has a serious dOUblet-triplet splitting problem, as do all the SUSY-GUTs. In §3, we construct an R-invariant extension of recently proposed natural unification theo­ ries, 6),7) where the doublet-triplet splitting problem is solved. Namely, masslessness of the Higgs doublets is guaranteed by the R symmetry, while the Higgs triplets have R-invariant masses at the unification scale. In this model, however, a pair of Higgs doublets is completely massless as long as the R symmetry is unbroken. In §4, we discuss how to generate a mass for the Higgs doublets at the electroweak scale by modifying the above model. The final section is devoted to a discussion on low-energy predictions of the R-invariant natural unification model. A possible connection to superstring theory is also briefly noted.

Evolution of Cosmological Perturbation in Reheating Phase of the Universe

Abstract: The evolution of the cosmological perturbation during the oscillatory stage of the scalar field is investigated. For the power law potential of the inflaton field, the evolution equation of the Mukhanov's gauge invariant variable is reduced to the Mathieu equation and the density perturbation grows by the parametric resonance.

Post-Newtonian Expansion of Gravitational Waves from a Particle in Circular Orbits around a Rotating Black Hole: Effects of Black Hole Absorption

Abstract: When a particle moves around a Kerr black hole, it radiates gravitational waves.Some of these waves are absorbed by the black hole. We calculate such absorption of gravitational waves induced by a particle of mass mu in a circular orbit on an equatorial plane around a Kerr black hole of mass M. We assume that the velocity of the particle v is much smaller than the speed of light c and calculate the energy absorption rate analytically. We adopt an analytic technique for the Teukolsky equation developed by Mano, Suzuki and Takasugi. We obtain the energy absorption rate to O((v/c)^8) compared to the lowest order. We find that the black hole absorption occurs at O((v/c)^5) beyond the Newtonian-quadrapole luminosity at infinity in the case when the black hole is rotating, which is O((v/c)^3) lower than the non-rotating case. Using the energy absorption rate, we investigate its effects on the orbital evolution of coalescing compact binaries.

The Ruijsenaars-Schneider Model

Abstract: We seek to clarify some of the physical aspects of the Ruijsenaars-Schneider models. This important class of models was presented as a relativistic generalisation of the Calogero-Moser models but, as we shall argue, this description is misleading. It is far better to simply view the models as a one-parameter generalisation of CalogeroMoser models. By viewing the models as describing certain eigenvalue motions we can appreciate the generic nature of the models.

QCD Sum Rules for ρ, ω, ϕ Meson-Nucleon Scattering Lengths and the Mass Shifts in Nuclear Medium

Abstract: A new QeD sum rule analysis on the spin-isospin averaged· p, wand tjJ meson-nucleon scattering lengths is presented. By introducing the constraint relation on the low energy limit of the vector-current nucleon forward scattering amplitude (low energy theorem), we obtain ap = -0.47±O.05 fm, aw = -0.41±O.05 fm and a¢ = -O.15±O.02 fm, which suggests that these V-N interactions are attractive. It is also proved that previous studies on the mass shift of these vector mesons in the nuclear medium are essentially those obtained from these scattering lengths in the linear density approximation.

Low Energy Reactions of Halo Nuclei in a Three-Body Model

Abstract: Low energy nuclear reactions of nuclei with halo structure are theoretically studied in a three· body model in which the projectile is described as the weakly bound state of the halo neutron and core nucleus A time·dependent wave packet method is employed to solve the three·body Schrodinger equation and to calculate reaction probabilities Numerical results with various internal Hamiltonians reveal that the reaction mechanisms depend strongly on the single particle structures of the core and target nuclei The adiabatic dynamics is found to be important when the neutron is bound tightly in the projectile For a weakly bound projectile with halo structure, the fusion probability is found to decrease due to the addition of a neutron

Non-Perturbative Renormalization Group Analysis of the Chiral Critical Behavior in QED

Abstract: We study the chiral critical behavior of QED using non-perturbative renormalization group (NPRG). Taking account of the non· ladder contributions, our flow equations are free from the gauge parameter a dependence. We clarify the chiral phase structure and calculate the anomalous dimen· sion of ¢t/J, which is enhanced compared to the ladder approximation. We find that the cutoff scheme dependence of the physical results is very small.

Nucleon Superfluidity in Neutron Star Core with Direct URCA Cooling

Abstract: Nucleon superftuidity in a neutron star core with abundant protons making possible the direct URCA cooling is investigated using a realistic approach. It is found that the existence of both nand p-superftuids is unlikely when the realistic effective mass of nucleons is taken into account. This leads to the conclusion that the direct URCA cooling would be excluded from the candidates of rapid cooling scenario of neutron stars and thereby constrain their masses.

Topological Matrix Model

Abstract: Starting from the primal principle based on the noncommutative nature of (9+1)-dimensional spacetime, we construct a topologically twisted version of the supersymmetric reduced model with a certain modification. Our formulation automatically provides extra 1+1 dimensions, thereby the dimensions of spacetime are promoted to 10+2. With a suitable gauge choice, we can reduce the model with (10+2)-dimensional spacetime to the one with (9+1)-dimensions and thus we regard this gauge as the light-cone gauge. It is suggested that the model so obtained would describe the light-cone F-theory. From this viewpoint we argue the relation of the reduced model to the matrix model of M-theory and the SL(2,Z) symmetry of type IIB string theory. We also discuss the general covariance of the matrix model in a broken phase, and make some comments on the background independence.

The Breakup Condition of Shearless KAM Curves in the Quadratic Map

Abstract: We determined the exact location of the shearless KAM curve in the quadratic map and numerically investigate the breakup thresholds of those curves in the entire parameter space. The breakup diagram reveals many sharp singularities like fractals on the reconnection thresholds of the twin-chains with rational rotation numbers.

Effective Interactions for Mesons and Baryons in Nuclei

Abstract: A new method is proposed to construct the effective nuclear interactions which describe nuclear systems even beyond the pion threshold. The method is based on the unitary trans­ formation, which assures Hermiticity of the effective interactions. The effective interactions are defined to be regular and include a meson-nucleon potential, an isobar transition poten­ tial, pion-production/annihilation operators, electromagnetic exchange current, and so on. The nucleon-nucleon potentials defined here are very similar to those in the formalism of Fukuda-Sawada-Taketani, that of Okubo, and that of Nishijima. The theory is a natural and sound extension of conventional nuclear theory and covers nuclear physics in low- and intermediate-energy regions.

The Spectrum of gravitational wave perturbations in the one bubble open inflationary universe

Abstract: We give the initial spectrum of quantized gravitational waves in the context of the one­ bubble open inHationary universe scenario. In determining the quantum state after the bubble nucleation, we adopt the prescription to require the analyticity of positive frequency functions in half of the Euclidian extension of the background 0(3, I)-symmetric spacetime. We find the spectrum is well behaved at the infrared limit and there appears no supercurva­ ture mode. In the thin wall approximation, the explicit form of the spectrum of gravitational wave perturbations is calculated.

Lorentz Symmetry of Supermembrane in Light Cone Gauge Formulation

Abstract: We prove the Lorentz symmetry of supermembrane theory in the light cone gauge to complete the program initiated by de Wit, Marquard and Nicolai We give some comments on extending the formulation to the M(atrix) theory After the discovery of string duality, our perception of string theory was dras­ tically changed What used to be the obscure inhabitants of the string theory, the p-branes, turned out to be the key ingredients of the non-perturbative physics M­ theory is believed to be one of the most symmetric forms of the "string" theory However, because of our ignorance of the quantization of the p-branes, the very definition of the theory has been unknown By critical use of the simplification due to the infinite momentum frame, BFSS 1) proposed a constructive definition of the M-theory The momentum along the eleventh dimension is identified with the zero-brane charge The infinite boost kills the degree of freedom which has zero (fundamental string) and negative (anti-zero brane) charges The resulting Lagrangian is made up of only the zero-branes de­ scribed by the large N limit of the SU(N) Yang-Mills theory BFSS have indicated two major pieces of evidence which support their idea 1 The matrix theory Lagrangian coincides with that of supermembrane proposed by de Wit, Hoppe and Nicolai (dWHN) 2) if one replaces the gauge group from SU(N) to the area preserving diffeomorphism (APD) in two dimensions 2 The scattering of the zero-branes coincides with the prediction of eleven­ dimensional supergravity As usual, the subtlety in the infinite momentum frame is the Lorentz symmetry This problem is very difficult to analyze in the matrix theory since the momentum exchange in the eleventh dimension implies the exchange of zero-brane charge We need to treat the quantum process which changes the size of matrices**) On the other hand, the analysis of a similar problem in the dWHN model is

Distributional Energy-Momentum Densities of Schwarzschild Space-Time

Abstract: For Schwarzschild space-time, distributional expressions of energy-momentum densities and of scalar concomitants of the curvature tensors are examined for a class of coordinate systems which includes those of the Schwarzschild and of Kerr-Schild types as special cases. The energy-momentum density $\tilde T_\mu^{ u}(x)$ of the gravitational source and the gravitational energy-momentum pseudo-tensor density $\tilde t_\mu^{ u}$ have the expressions $\tilde T_\mu^{ u}(x) =-Mc^2\delta_\mu^0\delta_0^{ u} \delta^{(3)}x)$ and $\tilde t_\mu^{ u}=0$, respectively. In expressions of the curvature squares for this class of coordinate systems, there are terms like $\delta^{(3)}(x)/r^3$ and $[\delta^{(3)}(x)}]^2$, as well as other terms, which are singular at $x=0$. It is pointed out that the well-known expression $R^{\rho\sigma\mu u}({}) R_{\rho\sigma\mu u}({})$ $=48G^{2}M^{2}/c^{4}r^{6}$ is not correct, if we define $1/r^6 = \lim_{\epsilon\to 0}1/(r^2+\epsilon^2)^3$.}

Explicit CP Violation in the Higgs Sector of the Next-to-Minimal Supersymmetric Standard Model

Abstract: We analyze explicit CP violation in the Higgs sector of the next-to-minimal supersymmetric standard model which contains an additional gauge singlet field N. It is shown that there is no mixing among scalar and pseudoscalar Higgs fields in the two Higgs doublets, and scalar-pseudoscalar mixings could exist between two Higgs doublets and the singlet N, and between N itself. CP symmetry is conserved in the extreme limits of >> v, > 1. In the region of = O(v) and tan beta = O(1), large scalar-pseudoscalar mixings are realized, and this effect can reduce the lightest Higgs mass. The mass difference between no mixing and mixing case is about 10 - 30 GeV. The neutron electric dipole moment in this model is consistent with the present experimental upper limit provided that squark and gaugino masses are heavy enough of O(1) TeV.

Getting at the Quark Mass Matrices

Abstract: We present a class of Ansatze for the up and down quark mass matrices which leads approximately to: |V_{us}| \sim \sqrt{m_d / m_s}, |V_{cb}| \sim m_s / m_b, and |V_{ub} / V_{cb}| \sim \sqrt{m_u / m_c}. Sizes of the Kobayashi-Maskawa matrix elements are controlled solely by quark mass ratios. In particular, we introduce no other small parameter and our results do not rely on delicate cancellation.

Quantum nucleation of two flavor quark matter in neutron stars

Abstract: Rates for nucleation of two-flavor quark matter in a neutron star core, originally composed of nuclear matter in $\beta$ equilibrium, are calculated at zero temperature by a quantum tunneling analysis incorporating the electrostatic energy. We find that a nucleated droplet would develop into bulk matter due to electron screening effects.

Quark Recombination Model for Spin Polarization in High Energy Inclusive Hadron Reactions

Abstract: We study the polarizations and the analyzing powers in high energy inclusive hadron reactions based on the quark recombination (QRC) mechanism. The QRC model repro­ duces the empirical rule of DeGrand and Miettinen with a relativistic description for the parton-parton interaction. We apply the QRC model to the polarizations of various hadron production processes and demonstrate its success by comparing with experiment. We discuss the importance of relativistic effects in the formulation of the quark recombination process and their significance with regard to spin polarization phenomena in hadron reactions to­ gether with quark momentum distributions in hadrons.

Implications of baryon asymmetry for the electric dipole moment of the neutron

Abstract: The supersymmetric standard model (SSM) contains a new source of CP violation in the mass-squared matrices for squarks, which could imply the t squark mediation of the charge transport mechanism producing the baryon asymmetry of the universe. This CP-violating source also induces the electric dipole moment (EDM) of the neutron. We show that this t-squark transport can lead to a baryon asymmetry consistent with its observed value within reasonable ranges of SSM parameters, where the neutron EDM has a magnitude slightly smaller than its experimental upper bound.