We explore the application of the domain wall fermion formalism of lattice QCD to calculate the $\overrightarrow{K}\pi \pi$ decay amplitudes in terms of the $K^{+}\to {\pi }^{+}$ and $K^0\to 0$ hadronic matrix elements through relations derived in chiral perturbation theory. Numerical simulations are carried out in quenched QCD using the domain-wall fermion action for quarks and a renormalization group-improved gauge action for gluons on a ${16}^3\times 32\times 16$ and ${24}^3\times 32\times 16$ lattice at $\beta =2.6\mathrm{}$ corresponding to the lattice spacing $1/a\approx 2\mathrm{GeV}.$ Quark loop contractions which appear in Penguin diagrams are calculated by the random noise method, and the $\Delta I=1/2\mathrm{}$ matrix elements which require subtractions with the quark loop contractions are obtained with a statistical accuracy of about 10%. We investigate the chiral properties required of the $K^{+}\to {\pi }^{+}$ matrix elements. Matching the lattice matrix elements to those in the continuum at $\mu =1/a$ using the perturbative renormalization factor to one loop order, and running to the scale $\mu {=m}_c=1.3\mathrm{}\mathrm{GeV}$ with the renormalization group for $N_f=3\mathrm{}$ flavors, we calculate all the matrix elements needed for the decay amplitudes. With these matrix elements, the $\Delta I=3/2\mathrm{}$ decay amplitude $\mathrm{Re}{A}_2$ shows a good agreement with experiment after an extrapolation to the chiral limit. The $\Delta I=1/2\mathrm{}$ amplitude $\mathrm{Re}{A}_0,$ on the other hand, is about 50–60 % of the experimental one even after chiral extrapolation. In view of the insufficient enhancement of the $\Delta I=1/2\mathrm{}$ contribution, we employ the experimental values for the real parts of the decay amplitudes in our calculation of ${\varepsilon }^{\prime }/\varepsilon .$ The central values of our result indicate that the $\Delta I=3/2\mathrm{}$ contribution is larger than the $\Delta I=1/2\mathrm{}$ contribution so that ${\varepsilon }^{\prime }/\varepsilon$ is negative and has a magnitude of order ${10}^{-4}.$ We discuss in detail possible systematic uncertainties, which seem too large for a definite conclusion on the value of ${\varepsilon }^{\prime }/\varepsilon .$

A statistical model for the parton distributions in the nucleon has proven its efficiency in the analysis of deep inelastic scattering data, so we propose to extend this approach to the description of unpolarized fragmentation functions for the octet baryons. The characteristics of the model are determined by using some data on the inclusive production of the proton and Λ in unpolarized deep inelastic scattering and a next-to-leading analysis of the available experimental data on the production of unpolarized octet baryons in $e^{+}{e}^{-}$ annihilation. Our results show that both parton distributions and fragmentation functions are compatible with the statistical approach, in terms of a few free parameters, whose interpretation will be discussed.

We perform the analysis of existing light-targets deep-inelastic-scattering data in the leading-order, next-to-leading-order, and next-to-next-to-leading-order (NNLO) QCD approximations and extract parton distribution functions (PDFs) simultaneously with the value of the strong coupling constant ${\alpha }_s$ and the high-twist contribution to the structure functions. The main theoretical uncertainties and experimental uncertainties due to all sources of experimental errors in the data are estimated; the latter generally dominate for the obtained PDFs. The uncertainty in the Higgs boson production cross section due to errors in PDFs is $\sim 2\%$ for the CERN LHC and varies from 2% to 10% for the Fermilab collider under variation of the Higgs boson mass from $100\mathrm{GeV}$ to $300\mathrm{GeV}.$ For the W-boson production cross section the uncertainty is $\sim 2\%$ for the both colliders. The value of ${\alpha }_{\mathrm{s}}^{\mathrm{NNLO}}{(M}_{\mathrm{Z}})=0.1143\mathrm{}\pm 0.0014(\mathrm{expt})$ is obtained, while the high-twist terms do not vanish up to the NNLO as required by comparison to data.

Radiative properties of gravitational and electromagnetic fields generated by uniformly accelerated charged black holes in asymptotically de Sitter spacetime are studied by analyzing the C-metric exact solution of the Einstein-Maxwell equations with a positive cosmological constant Λ. Its global structure and physical properties are thoroughly discussed. We explicitly find and describe the specific pattern of radiation which exhibits the dependence of the fields on a null direction along which the (spacelike) conformal infinity is approached. This directional characteristic of radiation supplements the peeling behavior of the fields near infinity. The interpretation of the solution is achieved by means of various coordinate systems, and suitable tetrads. The relation to the Robinson-Trautman framework is also presented.

We discuss spontaneous baryogenesis in the warm inflation scenario. In contrast with standard inflation models, radiation always exists in the warm inflation scenario, and the inflaton must be directly coupled to it. Also, the transition to the post-inflationary radiation dominated phase is smooth and the entropy is not significantly increased at the end of the period of inflation. In addition, after the period of warm inflation ends, the inflaton does not oscillate coherently but slowly rolls. We show that as a consequence of these features of warm inflation, the scenario can well accommodate the spontaneous baryogenesis mechanism, provided that the decoupling temperature $T_D$ of the baryon or the $B-L$ violating interactions is higher than the temperature of radiation during the late stages of inflation.

Using the one-parameter internal symmetry group in the Bianchi type-I spacetime for cosmological models with a perfect fluid, we show that a system of coordinates exists in the associated internal space where two scale factors become equal. We find the general solution for an anisotropic model containing a perfect fluid with constant baryotropic index and investigate the asymptotic regimes. We obtain exact solutions for a set of anisotropic fluids which includes an anisotropic stiff fluid.

A trial application of the method of Feynman-Kleinert approximants is made to perturbation series arising in connection with the lattice Schwinger model. In extrapolating the lattice strong-coupling series to the weak-coupling continuum limit, the approximants do not converge well. In interpolating between the continuum perturbation series at large fermion mass and small fermion mass, however, the approximants do give good results. In the course of the calculations, we picked up and rectified an error in an earlier derivation of the continuum series coefficients.

We study the thermodynamics of the electroweak theory at a finite lepton number density. The phase diagram of the theory is calculated by relating the full 4-dimensional theory to a 3-dimensional effective theory which has been previously solved using nonperturbative methods. It is seen that the critical temperature increases and the value of the Higgs boson mass at which the first order phase transition line ends decreases with increasing leptonic chemical potential.

Several recent papers, using effective QCD chiral Lagrangians, reproduced results obtained with the general QCD parametrization (GP). These include the baryon $8+10$ mass formula, the octet magnetic moments and the coincidental nature of the “perfect” $({\mu }_p/{\mu }_n)=-\mathrm{}(3/2)\mathrm{}$ ratio. Although we anticipated that the GP covers the case of chiral treatments, the above results explicitly exemplify this fact. Also we show by the GP that, in any model or theory (chiral or nonchiral) reproducing the results of QCD, the Franklin (Coleman-Glashow) sum rule for the octet magnetic moments must be violated.

Binary systems of rapidly spinning compact objects, such as black holes or neutron stars, are prime targets for gravitational wave astronomers. The dynamics of these systems can be very complicated due to spin-orbit and spin-spin couplings. Contradictory results have been presented as to the nature of the dynamics. Here we confirm that the dynamics—as described by the second post-Newtonian approximation to general relativity—is formally chaotic, despite claims to the contrary. When dissipation due to higher order radiation reaction terms is included, the chaos is damped. The damping time scale is found to be comparable to, but shorter than, the time scale that characterizes the chaotic behavior. This result suggests that the gravitational waveforms computed to 2.5 post-Newtonian order from spinning compact binaries will not suffer from sensitive dependence on initial conditions. If the post-Newtonian approximation at this order is an adequate description, then the waves can be detected using standard hierarchical matched filtering techniques. On the other hand, the competition between chaotic decoherence and radiation induced dissipation is close enough that the merger history does retain an imprint of the chaotic behavior. Moreover, the time scales are sufficiently close, and the post-Newtonian approximation is sufficiently crude, that we cannot rule out the possibility that chaotic effects play a role in real binary systems.

We evaluate both the massless and the massive Dirac quasinormal mode frequencies in the Schwarzschild black hole spacetime using the WKB approximation. For the massless case, we find that, similar to those for the integral spin fields, the real parts of the frequencies increase with the angular momentum number κ, while the imaginary parts or the dampings increase with the mode number n for fixed κ. For the massive case, the oscillation frequencies increase with the mass m of the field, while the dampings decrease. Fields with higher masses will therefore decay more slowly.

Nonspherical stellar collapse to a black hole is one of the most promising gravitational wave sources for gravitational wave detectors. We numerically study gravitational waves from a slightly nonspherical stellar collapse to a black hole in linearized Einstein theory. We adopt a spherically collapsing star as the zeroth-order solution and gravitational waves are computed using perturbation theory on the spherical background. In this paper we focus on the perturbation of odd-parity modes. Using the polytropic equations of state with polytropic indices $n_p=1\mathrm{}$ and 3, we qualitatively study gravitational waves emitted during the collapse of neutron stars and supermassive stars to black holes from a marginally stable equilibrium configuration. Since the matter perturbation profiles can be chosen arbitrarily, we provide a few types for them. For $n_p=1,$ the gravitational waveforms are mainly characterized by a black hole quasinormal mode ringing, irrespective of perturbation profiles given initially. However, for $n_p=3,$ the waveforms depend strongly on the initial perturbation profiles. In other words, the gravitational waveforms strongly depend on the stellar configuration and, in turn, on the ad hoc choice of the functional form of the perturbation in the case of supermassive stars.

A recent suggestion that the emission of a quantum of energy corresponding to the asymptotic value of quasinormal modes of a Schwarzschild black hole should be associated with the loss of spin one punctures from the black hole horizon fixes the Immirzi parameter to a definite value. We show that saturating the horizon with spin one punctures reproduces the earlier formula for the black hole entropy, including the ln (area) correction with the definite coefficient $-3/2$ for a large area.

It is suggested that the mechanism responsible for the resolution of the gauge hierarchy problem within the warped geometry framework can be generalized to provide a new explanation of the extremely tiny vacuum energy density ${\rho }_V$ suggested by recent observations. We illustrate the mechanism with some 5D examples in which the true vacuum energy is assumed to vanish, and ${\rho }_V$ is associated with a false vacuum energy such that ${\rho }_V^{1/4}\sim {\mathrm{TeV}}^2{/M}_{\mathrm{Pl}}\sim {10}^{-3}\mathrm{eV},$ where $M_{\mathrm{Pl}}$ denotes the reduced Planck mass. We also consider a quintessence-like solution to the dark energy problem.

We investigate the asymptotic properties of the Bianchi type IX cosmological model in the brane-world scenario. The matter content is assumed to be a combination of a perfect fluid and a minimimally coupled scalar field that is restricted to the brane. A detailed qualitative analysis of the Bianchi type IX brane-world containing a scalar field having an exponential potential is undertaken. It is found that the brane-Robertson-Walker solution is a local source for the expanding Bianchi type IX models, and if $k^2<2\mathrm{}$ the ever-expanding Bianchi IX models asymptote to the power-law inflationary solution. The only other local sink is the contracting brane-Robertson Walker solution. An analysis of the Bianchi type IX models with a scalar field with a general potential is discussed, and it is shown that in the case of expanding models, for physical scalar field potentials close to the initial singularity, the scalar field is effectively massless, and the solution is approximated by the brane-Robertson Walker model.

We investigate whether the Affleck-Dine (AD) mechanism works when the contribution of the two-loop thermal correction to the potential is negative in gauge-mediated supersymmetry breaking models. The AD field is trapped far away from the origin by the negative thermal correction for a long time until the temperature of the Universe becomes low enough. The most striking feature is that the Hubble parameter becomes much smaller than the mass scale of the radial component of the AD field, during the trap. Then, the amplitude of the AD field decreases so slowly that the baryon number is not fixed even after the onset of radial oscillation. The resultant baryon asymmetry crucially depends on whether the Hubble parameter H is larger than the mass scale of the phase component of the AD field, $M_{\theta },$ at the beginning of oscillation. If $H<\mathrm{}{M}_{\theta }$ holds, the formation of Q balls plays an essential role in determining the baryon number, which is found to be washed out due to the nonlinear dynamics of Q-ball formation. On the other hand, if $H>\mathrm{}{M}_{\theta }$ holds, it is found that the dynamics of Q-ball formation does not affect the baryon asymmetry, and that it is possible to generate the right amount of baryon asymmetry.

We discuss what can be understood from ${\phi }_1$ and the $B_d^0\to {\pi }^{+}{\pi }^{-}$ decay mode. Using a convention without the weak phases ${\phi }_2$ and ${\phi }_3,$ we can solve the parameters from time-dependent $\mathrm{CP}$ asymmetry. If we can insert the condition that the contribution from the penguin diagram, except for the CKM factor included in the diagram, is small, then we are led to the allowed region of $R_t$ or ${\phi }_2$ by using this convention.

We analyze a model based on supersymmetric $\mathrm{SO}\left(10\right)\mathrm{}$ combined with $\mathrm{SU}\left(2\right)\mathrm{}$ family symmetry and symmetric mass matrices constructed by the authors recently. Previously, only the parameter space for the low mass, low probability and vacuum oscillation solutions was investigated. We indicate in this Brief Report the parameter space that leads to a large mixing angle solution to the solar neutrino problem with a slightly modified effective neutrino mass matrix. The symmetric mass textures arising from the left-right symmetry breaking and the $\mathrm{SU}\left(2\right)\mathrm{}$ symmetry breaking give rise to very good predictions for the quark and lepton masses and mixing angles. The prediction of our model for the $|U_{e{\nu }_3}|$ element in the Maki-Nakagawa-Sakata matrix is close to the sensitivity of current experiments; thus the validity of our model can be tested in the near future. We also investigate the correlation between the $|U_{e{\nu }_3}|$ element and ${\tan }^2{\theta }_{\odot }$ in a general two-zero neutrino mass texture.

The total cross section for Higgs boson production in bottom-quark annihilation is evaluated at next-to-next-to-leading order in QCD. This is the first time that all terms at order ${\alpha }_s^2$ are taken into account. We find a greatly reduced scale dependence with respect to lower order results, for both the factorization and the renormalization scales. The behavior of the result is consistent with earlier determinations of the appropriate factorization scale for this process of ${\mu }_F\approx M_H/4,$ and supports the validity of the bottom parton density approach for computing the total inclusive rate. We present precise predictions for the cross section at the Fermilab Tevatron and the CERN Large Hadron Collider.

We propose an analytic framework to study the nonperturbative solutions of Witten’s open string field theory. The method is based on the Moyal star formulation where the kinetic term can be split into two parts. The first one describes the spectrum of two identical half strings which are independent from each other. The second one, which we call midpoint correction, shifts the half string spectrum to that of the standard open string. We show that the nonlinear equation of motion of string field theory is exactly solvable at zeroth order in the midpoint correction. An infinite number of solutions are classified in terms of projection operators. Among them, there exists only one stable solution which is identical to the standard butterfly state. We include the effect of the midpoint correction around each exact zeroth order solution as a perturbation expansion which can be formally summed to the complete exact solution.