Showing papers in "Progress of Theoretical Physics in 2005"

Low energy hadron physics in holographic QCD

Abstract: We present a holographic dual of four-dimensional, large N_c QCD with massless flavors. This model is constructed by placing N_f probe D8-branes into a D4 background, where supersymmetry is completely broken. The chiral symmetry breaking in QCD is manifested as a smooth interpolation of D8 - anti-D8 pairs in the supergravity background. The meson spectrum is examined by analyzing a five-dimensional Yang-Mills theory that originates from the non-Abelian DBI action of the probe D8-brane. It is found that our model yields massless pions, which are identified with Nambu-Goldstone bosons associated with the chiral symmetry breaking. We obtain the low-energy effective action of the pion field and show that it contains the usual kinetic term of the chiral Lagrangian and the Skyrme term. A brane configuration that defines a dynamical baryon is identified with the Skyrmion. We also derive the effective action including the lightest vector meson. Our model is closely related to that in the hidden local symmetry approach, and we obtain a Kawarabayashi-Suzuki-Riazuddin-Fayyazuddin-type relation among the couplings. Furthermore, we investigate the Chern-Simons term on the probe brane and show that it leads to the Wess-Zumino-Witten term. The mass of the \eta' meson is also considered, and we formulate a simple derivation of the \eta' mass term satisfying the Witten-Veneziano formula from supergravity.

More on a holographic dual of QCD

Abstract: We investigate the interactions among the pion, vector mesons and external gauge fields in the holographic dual of massless QCD proposed in a previous paper [T. Sakai and S. Sugi-moto, Prog. Theor. Phys. 113 (2005), 843; hep-th/0412141] on the basis of probe D8-branes embedded in a D4-brane background in type IIA string theory. We obtain the coupling constants by performing both analytic and numerical calculations, and compare them with experimental data. It is found that the vector meson dominance in the pion form factor as well as in the Wess-Zumino-Witten term holds in an intriguing manner. We also study the ω → πγ and ω → 3π decay amplitudes. It is shown that the interactions relevant to these decay amplitudes have the same structure as that proposed by Fujiwara et al. [T. Fujiwara, T. Kugo, H. Terao, S. Uehara and K. Yamawaki, Prog. Theor. Phys. 73 (1985), 926]. Various relations among the masses and the coupling constants of an infinite tower of mesons are derived. These relations play crucial roles in the analysis. We find that most of the results are consistent with experiments.

Nuclidic Mass Formula on a Spherical Basis with an Improved Even-Odd Term

Abstract: 1Advanced Science Research Center, Japan Atomic Energy Research Institute (JAERI), Ibaraki 319-1195, Japan 2Senior High School of Waseda University, Tokyo 177-0044, Japan 3Advanced Research Institute for Science and Engineering, Waseda University, Tokyo 169-8555, Japan 4Ministry of Education, Culture, Sports, Science and Technology, Tokyo 100-8959, Japan 5The Institute of Physical and Chemical Research (RIKEN), Saitama 351-0198, Japan

Masses, deformations and charge radii: Nuclear ground-state properties in the relativistic mean field model

Abstract: We perform a systematic study of the ground-state properties of all the nuclei from the proton drip line to the neutron drip line throughout the periodic table employing the relativistic mean field model. The TMA parameter set is used for the mean-field Lagrangian density, and a state-dependent BCS method is adopted to describe the pairing correlation. The ground-state properties of a total of 6969 nuclei with Z, N ≥ 8a ndZ ≤ 100 from the proton drip line to the neutron drip line, including the binding energies, the separation energies, the deformations, and the rms charge radii, are calculated and compared with existing experimental data and those of the FRDM and HFB-2 mass formulae. This study provides the first complete picture of the current status of the descriptions of nuclear ground-state properties in the relativistic mean field model. The deviations from existing experimental data indicate either that new degrees of freedom are needed, such as triaxial deformations, or that serious effort is needed to improve the current formulation of the relativistic mean field model.

Describing Curved Spaces by Matrices

Abstract: It is shown that a covariant derivative on any d-dimensional manifold M can be mapped to a set of d operators acting on the space of functions defined on the principal Spin(d)-bundle over M. In other words, any d-dimensional manifold can be described in terms of d operators acting on an infinite-dimensional space. Therefore it is natural to introduce a new interpretation of matrix models in which matrices represent such operators. In this interpretation, the diffeomorphism, local Lorentz symmetry and their higher-spin analogues are included in the unitary symmetry of the matrix model. Furthermore, the Einstein equation is obtained from the equation of motion, if we take the standard form of the action, S = −tr [Aa, Ab][A a , A b ] � .

Gravitational Collapse and Black Hole Evolution — Do Holographic Black Holes Eventually “Anti-Evaporate”? —

Abstract: We study the gravitational collapse of compact objects in the Brane-World. We begin by arguing that the regularity of the five-dimensional geodesics does not allow the energymomentum tensor of matter on the brane to have (step-like) discontinuities, which are instead admitted in the four-dimensional General Relativistic case, and compact sources must therefore have an atmosphere. Under the simplifying assumption that matter is a spherically symmetric cloud of dust without dissipation, we can find the conditions for which the collapsing star generically “evaporates” and approaches the Hawking behavior as the (apparent) horizon is being formed. Subsequently, the apparent horizon evolves into the atmosphere and the back-reaction on the brane metric reduces the evaporation, which continues until the effective energy of the star vanishes. This occurs at a finite radius, and the star afterwards re-expands and “anti-evaporates”. We clarify that the Israel junction conditions across the brane (holographically related to the matter trace anomaly) and the projection of the Weyl tensor on the brane (holographically interpreted as the quantum back-reaction on the brane metric) contribute to the total energy as, respectively, an “anti-evaporation” and an “evaporation” term. Concluding, we comment on the possible effects of dissipation and obtain a new stringent bound for the brane tension.

Tensor Correlation in 4He and Its Effect on the Doublet Splitting in 5He

Abstract: the characteristics of the tensor correlation, which is represented by an admixture of the 0s1/2 configuration with a spatially modified 0p1/2 orbit. For 5 He, we solve a coupled OCM equation for an extended 4 He+n model, while taking into account the tensor correlation in the 4 He cluster. It is shown that the tensor correlation produces the Pauli blocking, in particular, for the J π =1 /2 − state, and its effect causes about half of the p-wave doublet splitting in 5 He. This indicates that the strength of the effective spin-orbit interaction should be reduced by about half from the conventional one. We obtain a reliable 4 He-n interaction, including the tensor correlation, which further improves the behavior of the d -a ndf -wave phase shifts in the 4 He+n system.

Local Energy Gap in Deformed Carbon Nanotubes

Abstract: The effects of graphite surface geometrical deformation on the dynamics of conducting electrons are investigated theoretically. The analysis is performed within the framework of a deformation-induced gauge field and corresponding deformation-induced magnetic field. It is shown that the latter gives a local energy gap along the axis of a deformed nanotube. We compare our energy gap results with experimental data on energy gaps in nanotubes and peapods. We also discuss the mixing of two Fermi points and construct a general model of low energy dynamics, including a short-range deformation of the graphite sheet. This model is equivalent to the Weyl equation in U(1) Abelian and SU(2) non-Abelian deformation-induced gauge fields.

Adiabatic Radiation Reaction to Orbits in Kerr Spacetime

Abstract: The geodesic motion of a point particle in Kerr geometry has three constants of motion, the energy E, the azimuthal angular momentum L, and the Carter constant Q. Under the adiabatic approximation, the radiation reaction effect is characterized by the time evolution of these constants. In this paper, we show that the scheme for evaluating them can be greatly simplified.

Nonlinear Second Order Ode's: Factorizations and Particular Solutions

Abstract: We present particular solutions for the following important nonlinear second order differential equations: modified Emden, generalized Lienard, convective Fisher and generalized Burgers-Huxley. For the latter two equations these solutions are obtained in the travelling frame. All these particular solutions are the result of extending a simple and efficient factorization method that we developed in Phys. Rev. E 71 (2005), 046607.

Phase Transitions in the NMSSM

Abstract: We study phase transitions in the Next-to-Minimal Supersymmetric Standard Model (NMSSM) with the weak scale vacuum expectation values of the singlet scalar, constrained by Higgs spectrum and vacuum stability. We find four different types of phase transitions, three of which have two-stage nature. In particular, one of the two-stage transitions admits strongly first order electroweak phase transition, even with heavy squarks. We introduce a tree-level explicit CP violation in the Higgs sector, which does not affect the neutron electric dipole moment. In contrast to the MSSM with the CP violation in the squark sector, a strongly first order phase transition is not so weakened by this CP violation.

On the Stability of Naked Singularities with Negative Mass

Abstract: We study the linearised stability of the nakedly singular negative mass Schwarzschild solution against gravitational perturbations. There is a one parameter family of possible boundary conditions at the singularity. We give a precise criterion for stability depending on the boundary condition. We show that only one particular boundary condition gives perturbations of finite energy and show that the spacetime is stable with this boundary condition.

Constraining cosmological parameters by the cosmic inversion method

Abstract: We investigate the question of how tightly we can constrain the cosmological parameters by using the cosmic inversion method in which we directly reconstruct the power spectrum of primordial curvature perturbations, P(k), from the temperature and polarization spectra of the cosmic microwave background (CMB). In a previous paper, we suggested that it may be possible to constrain the cosmological parameters using the fact that the reconstructed P(k) does not depend on how many polarization data we incorporate in our inversion procedure if and only if the correct values of the cosmological parameters are used. The advantage of this approach is that we need no assumption regarding the functional form of P(k). In this paper, we estimate typical errors in the determination of the cosmological parameters when our method is applied to the PLANCK observation. We investigate constraints on h, Ω b , Ω m , and Ω A through Monte Carlo simulations.

Level Density in the Complex Scaling Method

Abstract: It is shown that the continuum level density (OLD) at unbound energies can be calculated with the complex scaling method (CSM), in which the energy spectra of bound states resonances and continuum states are obtained in terms of L 2 basis functions. In this method, the extended completeness relation is applied to the calculation of the Green functions, and the continuum-state part is approximately expressed in terms of discretized complex scaled continuum solutions. The obtained result is compared with the CLD calculated exactly from the scattering phase shift. The discretization in the CSM is shown to give a very good description of continuum states. We discuss how the scattering phase shifts can inversely be calculated from the discretized CLD using a basis function technique in the CSM.

Structures of Metastable States in Phase Transitions with a High-Spin Low-Spin Degree of Freedom

Abstract: The difference in the degeneracy of low-spin (LS) and high-spin (HS) states causes interesting entropy effects on spin-crossover phase transitions and charge transfer phase transitions in materials composed of spin-crossover atoms. Mechanisms of the spin-crossover (SC) phase transitions have been studied using the Wajnflasz model, where the degeneracy of the spin states (HS or LS) is taken into account, and the cooperative nature of the spin-crossover phase transitions has been well described. Recently, a charge transfer (CT) phase transition due to electron hopping between LS and HS sites has been studied using a generalized Wajnflasz model. Systems with SC and CT both have a high temperature structure (HT) and a low temperature structure (LT), and the transition between them can be a smooth crossover or a discontinuous first-order phase transition, depending on the parameter values of the systems. Although, apparently, the standard SC system and the CT system are very different, it lias been shown that the two models are equivalent under a certain transformation of variables. In both systems, the structure of the metastable state at low temperatures is a matter of interest. We study the temperature dependence of the fraction of HT systematically in a, unified model and find several structures of equilibrium and metastable states of the model as functions of the system parameters. In particular, we find a reentrant-type metastable branch of HT in a low temperature region, which sould play an important role in the study of the photo-irradiated processes of related materials.

Second-Order Gauge Invariant Perturbation Theory --- Perturbative Curvatures in the Two-Parameter Case

Abstract: Based on the gauge invariant variables proposed in our previous paper [K. Nakamura, Prog. Theor. Phys. 110 (2003), 723], some formulae for the perturbative curvatures of each order are derived. We follow the general framework of the second-order gauge invariant perturbation theory on an arbitrary background spacetime to derive these formulae. It is found that these perturbative curvatures have the same form as those given in the definitions of gauge invariant variables for arbitrary perturbative fields, which were proposed in the above paper. As a result, we explicitly see that any perturbative Einstein equation can be given in terms of a gauge invariant form. We briefly discuss physical situations to which this framework should be applied.

Vacua of Massive Hyper-Kähler Sigma Models with Non-Abelian Quotient

Abstract: The Higgs branch of N = 2 supersymmetric gauge theories with non-Abelian gauge groups is described by hyper-Kahler (HK) nonlinear sigma models with potential terms. Using the non-Abelian HK quotient with respect to U (M )a ndSU(M ) gauge groups, we derive the massive HK sigma models that are not toric in the N = 1 superfield formalism and the harmonic superspace formalism. The U (M ) quotient gives N !/(M !(N − M )!) discrete vacua that may allow various types of domain walls, whereas the SU(M ) quotient gives no discrete vacua.

The higgs sector in the next-to-MSSM

Abstract: We study the Higgs sector in the next-to-minimal supersymmetric standard model both with and without explicit CP violation, focusing on the case of a weak-scale expectation value of the singlet field. We scan a wide range of the parameter space to determine allowed regions by requiring that the electroweak vacuum be the global minimum of the effective potential and that the neutral Higgs bosons with moderate gauge coupling be heavier than the lower bound on the Higgs boson in the standard model. Among the allowed sets of parameter values, some sets yield the situation in which the light Higgs bosons couple with the Z boson too weakly for observation to be possible in present collider experiments. For such parameter sets, we determine an upper bound on the charged Higgs mass that is attainable in LHC.

Calogero-Sutherland-Moser systems, Ruijsenaars-Schneider-van Diejen systems and orthogonal polynomials

Abstract: The equilibrium positions of the multi-particle classical Calogero-Sutherland-Moser (CSM) systems with rational/trigonometric potentials associated with the classical root systems are described by the classical orthogonal polynomials; the Hermite, Laguerre and Jacobi polynomials. The eigenfunctions of the corresponding single-particle quantum CSM systems are also expressed in terms of the same orthogonal polynomials. We show that this interesting property is inherited by the Ruijsenaars-Schneider-van Diejen (RSvD) systems, which are integrable deformation of the CSM systems; the equilibrium positions of the multi-particle classical RSvD systems and the eigenfunctions of the corresponding single-particle quantum RSvD systems are described by the same orthogonal polynomials, the continuous Hahn (special case), Wilson and Askey-Wilson polynomials. They belong to the Askey-scheme of the basic hypergeometric orthogonal polynomials and are deformation of the Hermite, Laguerre and Jacobi polynomials, respectively. The Hamiltonians of these single-particle quantum mechanical systems have two remarkable properties, factorization and shape invariance.

Gaussian expansion analysis of a matrix model with the spontaneous breakdown of rotational symmetry

Abstract: Recently, the Gaussian expansion method has been applied to investigate the dynamical generation of 4d space-time in the IIB matrix model, which is a conjectured nonperturbative definition of type IIB superstring theory in 10 dimensions. Evidence for such a phenomenon, which is associated with the spontaneous breaking of the SO(10) symmetry down to SO(4), has been obtained up to 7-th order calculations. Here we apply the same method to a simplified model, which is considered to exhibit an analogous spontaneous symmetry breaking via the same mechanism as conjectured for the IIB matrix model. The results up to 9-th order demonstrate a clear convergence, which allows us to unambiguously identify the actual symmetry breaking pattern by comparing the free energy of possible vacua and to calculate the extent of “space-time” in each direction.

Self-Force in the Radiation Reaction Formula: — Adiabatic Approximation of a Metric Perturbation and an Orbit —

Abstract: We investigate a calculation method for the gravitational evolution of an extreme mass ratio binary, i.e. a binary constituting of a galactic black hole and a stellar mass compact object. The inspiralling stage of this system is considered to be a possible source of detectable gravitational waves. Because of the extreme mass ratio, one may approximate such a system by a black hole geometry (a. Kerr black hole) plus a linear metric perturbation induced by a point particle. With this approximation, a self-force calculation was proposed for a practical calculation of the orbital evolution, including the effect of the gravitational radiation reaction, which is now known as the MiSaTaQuWa self-force. 1) In addition, a radiation reaction formula was proposed 2) as an extension of the well-known balance formula of Press and Teukolsky. 3) The radiation reaction formula provides a convenient method to calculate an infinite time averaged loss of the constants of motion (i.e. the orbital energy, the z component of the angular momentum, and the Carter constant) through the gravitational radiation reaction, with which one may approximately calculate the orbital evolution. Because these methods are approximately equivalent, we investigate the consequence of the orbital evolution using the radiation reaction formula. To this time, we have used the so-called adiabatic approximation of the orbital evolution and considered a method to evaluate the MiSaTaQuWa self-force by use of a linear metric perturbation. In this approach, we point out that there is a theoretical question concerning the choice of the gauge condition in the calculation of the MiSaTaQuWa self-force. Because of this gauge ambiguity, there is a case in which the MiSaTaQuWa self-force might not predict the orbital evolution in a physically expected manner, and this forces us to calculate a waveform only in the so-called dephasing time. We discuss the reason that such an unexpected thing happens and find that it is primarily because we consider the linear metric perturbation separately from the orbital evolution due to the self-force. We propose a new metric perturbation scheme under a possible constraint of the gauge conditions in which we obtain a physically expected prediction of the orbital evolution caused by the MiSaTaQuWa self-force. In this new scheme of a metric perturbation, an adiabatic approximation is applied to both the metric perturbation and the orbit. As a result, we are able to predict the gravitational evolution of the system in the so-called radiation reaction time scale, which is longer titan the dephasing time scale. However, for gravitational wave detection by LISA, this may still be insufficient. We further consider a gauge transformation in this new metric perturbation scheme, and find a special gauge condition with which we can calculate the gravitational waveform of a time scale long enough for gravitational wave detection by LISA.

Tauonic B decays in the Minimal Supersymmetric Standard Model

Abstract: We study new physics effects on B decay processes including a final T particle, namely B → Dτν and B → TV. An important feature of these processes is that a charged Higgs boson can contribute to the decay amplitude at the tree level in models such as Two Higgs Doublet Model and the Minimal Supersymmetric Standard Model (MSSM). We derive a resummed effective Lagrangian for charged-Higgs mediated interactions in the MSSM with the Minimal Flavor Violation. Including supersymmetric (SUSY) loop corrections for down-type-quark and charged-lepton Yukawa couplings, we calculate the branching ratios of the B → DTV and B → TV processes. We find that SUSY correction due to gluino-sbottom diagrams can change the Higgs exchange contribution by ±50%, whereas stau-neutralino diagrams can make corrections up to 20%. We also discuss relationship between SUSY corrections in the tauonic decays and flavor changing neutral current processes such as E s → μ + μ - and b → sγ.

New Numerical Methods to Evaluate Homogeneous Solutions of the Teukolsky Equation. II — Solutions of the Continued Fraction Equation —

Abstract: We investigate the solution of the continued fraction equation by which we determine “the renormalized angular momentum parameter”, ν, in the formalism developed by Leaver and Mano, Suzuki and Takasugi. In this formalism, we describe the homogeneous solutions of the radial Teukolsky equation, which is the basic equation of the black hole perturbation formalism. We find that, contrary to the assumption made in previous works, the solution, ν, becomes complex valued as ω (the angular frequency) becomes large for each l and m (the degree and order of the spin-weighted spheroidal harmonics). We compare the power radiated by gravitational waves from a particle in a circular orbit in the equatorial plane around a Kerr black hole in two ways, one using the Mano-Suzuki-Takasugi formalism with complex ν and the other using a direct numerical integration method. We find that the two methods produce consistent results. These facts prove the validity of using complex solutions to determine the homogeneous solutions of the Teukolsky equation.

The Fate of a Five-Dimensional Rotating Black Hole via Hawking Radiation

Abstract: We study the evolution of a five-dimensional rotating black hole emitting scalar field radiation via the Hawking process for arbitrary initial values of the two rotation parameters a and b. It is found that any such black hole whose initial rotation parameters are both nonzero evolves toward an asymptotic state a/M 1/2 = b/M 1/2 =c onst( =0 ), where this constant is independent of the initial values of a and b. The conventional view of black hole evaporation is that, regardless of its initial state, Hawking radiation will cause a black hole to approach an uncharged, zero angular momentum state long before all its mass has been lost. For this reason, in some works, it is assumed that as a black hole evaporates close to the Planck scale, where quantum gravity is required to determine its evolution, the final asymptotic state is described by Schwarzschild solution. However, Chambers, Hiscock and Taylor 1) investigated, in some detail, the evolution of a Kerr black hole emitting scalar field radiation via the Hawking process, and showed that the ratio of the black hole’s specific angular momentum to its mass, ˜ = a/M , evolves toward a stable nonzero value (˜ a → 0.555). This means that a rotating black hole will evolve toward a final state with non-zero angular momentum if there is a scalar field. In this Letter, we extend the analysis of Chambers, Hiscock and Taylor to a higher-dimensional case for the reasons described below. Considering the five-dimensional case specifically, we investigate the evolution of a five-dimensional rotating Myers-Perry (MP) black hole 2) with two rotation parameters through scalar

Strongly Coupled Gauge Mediation

Abstract: A model of gauge mediation with m 3/2 ≃ O(1)eV is considered to motivate 100 TeV colliders. Massive mediators with standard-model and supersymmetry-breaking gauge quantum numbers let low-scale dynamics induce sizable soft masses of the standard-model superpartners. We circumvent potential phenomenological difficulties that such low-scale models tend to cause.

Dirac Sea for Bosons. I Formulation of Negative Energy Sea for Bosons

Abstract: We propose the formulation of a second quantization of a bosonic theory by generalizing the method of filling the Dirac negative energy sea for the case of fermions. We interpret our results as implying that the correct vacuum for the bosonic theory is obtained by adding minus one boson to each single particle negative energy state while the positive energy states are empty. The boson states are divided into two sectors: the usual positive sector consisting of states with a positive (or zero) number of bosons, and the negative sector,consisting of states with a negative number of bosons. Once a state enters the negative sector, it cannot return to the usual positive sector through an ordinary interaction, due to the presence of a barrier. To study this problem, a toy model, in which the filling of the empty fermion Dirac sea and the removal of bosons from the negative energy states has not yet been performed, has been proposed. We put forward such a naive vacuum world in the present paper. A subsequent paper 1) will treat various properties: the analyticity of the wave functions, the interaction and a CPT-like theorem in the naive vacuum world.

Pre-Critical Phenomena of Two-Flavor Color Superconductivity in Heated Quark Matter — Diquark-Pair Fluctuations and Non-Fermi Liquid Behavior —

Abstract: We investigate the fluctuations of the diquark-pair field and their effects on observables above the critical temperature Tc in two-flavor color superconductivity (CSC) at moderate density using a Nambu-Jona-Lasinio-type effective model of QCD. Because of the strongcoupling nature of the dynamics, the fluctuations of the pair field develop a collective mode, which has a prominent strength even well above Tc. We show that the collective mode is actually the soft mode of CSC. We examine the effects of the pair fluctuations on the specific heat and the quark spectrum for T above but close to Tc. We find that the specific heat exhibits singular behavior because of the pair fluctuations, in accordance with the general theory of second-order phase transitions. The quarks display a typical non-Fermi liquid behavior, owing to the coupling with the soft mode, leading to a pseudo-gap in the density of states of the quarks in the vicinity of the critical point. Some experimental implications of the precursory phenomena are also discussed.

Absorbing Kernels to Study Resonances in the Generator Coordinate Method

Abstract: A method of absorbing kernels is proposed to calculate resonance energies and widths in the microscopic cluster model. The absorbing potential is placed in the spatial region in which the particle exchange can be ignored. This procedure allows us to calculate resonance parameters accurately in the numerical generator coordinate calculations in which no explicit construction of the resonating group kernels is required. The method is applied to the singlechannel and coupled-channel problems of the α+ 6 He system. Good agreement is found with solutions obtained in the standard scattering treatment.