An analytic formula is given for the traceless transverse part of the anisotropic stress tensor due to free streaming neutrinos, and used to derive an integro-differential equation for the propagation of cosmological gravitational waves. The solution shows that anisotropic stress reduces the squared amplitude by 35.6% for wavelengths that enter the horizon during the radiation-dominated phase, independent of any cosmological parameters. This decreases the tensor temperature and polarization correlation functions for these wavelengths by the same amount. The effect is less for wavelengths that enter the horizon at later times. At the longest wavelengths the decrease in the tensor correlation functions due to neutrino free streaming ranges from 10.7% for ${\Omega }_M{h}^2=0.1\mathrm{}$ to 9.0% for ${\Omega }_M{h}^2=\mathrm{0.15.}\mathrm{}$ An appendix gives a general proof that tensor as well as scalar modes satisfy a conservation law for perturbations outside the horizon, even when the anisotropic stress tensor is not negligible.

A phase-locking configuration for LISA is proposed that provides a significantly simpler mode of operation. The scheme provides one Sagnac signal readout inherently insensitive to laser frequency noise and optical bench motion for a nonrotating LISA array. This Sagnac output is also insensitive to clock noise, requires no time shifting of data, nor absolute arm length knowledge. As all measurements are made at one spacecraft, neither clock synchronization nor exchange of phase information between spacecraft is required. The phase-locking configuration provides these advantages for only one Sagnac variable yet retains compatibility with the baseline approach for obtaining the other TDI combinations. The orbital motion of the LISA constellation is shown to produce a 14-km path length difference between the counterpropagating beams in the Sagnac interferometer. With this length difference a laser frequency noise spectral density of $1\mathrm{Hz}/\sqrt{\mathrm{Hz}}$ would consume the entire optical path noise budget of the Sagnac variables. A significant improvement of laser frequency stability (currently at $30\mathrm{Hz}/\sqrt{\mathrm{Hz}})$ would be needed for full-sensitivity LISA operation in the Sagnac mode. Alternatively, an additional level of time-delay processing could be applied to remove the laser frequency noise. The new time-delayed combinations of the phase measurements are presented.

We investigate matter-induced (or extrinsic) CPT violation effects in neutrino oscillations in matter. Especially, we present approximate analytical formulas for the CPT-violating probability differences for three flavor neutrino oscillations in matter with an arbitrary matter density profile. Note that we assume that the CPT invariance theorem holds, which means that the CPT violation effects arise entirely because of the presence of matter. As special cases of matter density profiles, we consider constant and step-function matter density profiles, which are relevant for neutrino oscillation physics in accelerator and reactor long baseline experiments as well as neutrino factories. Finally, the implications of extrinsic CPT violation on neutrino oscillations in matter for several past, present, and future long baseline experiments are estimated.

We study the supergravity solutions describing nonextremal enhançons. There are two branches of solutions: a “shell branch” connected to the extremal solution, and a “horizon branch” which connects to the Schwarzschild black hole at large mass. We show that the shell branch solutions violate the weak energy condition, and are hence unphysical. We investigate linearized perturbations of the horizon branch and the extremal solution numerically, completing an investigation initiated in a previous paper. We show that these solutions are stable against the perturbations we consider. This provides further evidence that these latter supergravity solutions are capturing some of the true physics of the enhançon.

We investigate one-flavor QCD with an additional chiral scalar field. For a large domain in the space of coupling constants, this model belongs to the same universality class as QCD, and the effects of the scalar become unobservable. This is connected to a “bound-state fixed point” of the renormalization flow for which all memory of the microscopic scalar interactions is lost. The QCD domain includes a microscopic scalar potential with minima at a nonzero field. On the other hand, for a scalar mass term $m^2$ below a critical value $m_{\mathrm{c}}^2,$ the universality class is characterized by perturbative spontaneous chiral symmetry breaking which renders the quarks massive. Our renormalization group analysis shows how this universality class is continuously connected with the QCD universality class.

In this paper, we construct for the first time, in the first post-Newtonian (1PN) approximation, a complete model of a quasirigid body by means of a new constraint on the mass current density and mass density. In our 1PN quasirigid body model most of the relations, such as the spin vector proportional to the angular velocity, the definition of the moment of inertia tensor, the key relation between the mass quadrupole moment and the moment of inertia tensor, the rigid rotating formulas for the mass quadrupole moment, and the moment of inertia tensor, are just an extension of the main relations in the Newtonian rigid body model. When all of the ${1/c}^2$ terms are neglected, the 1PN quasirigid body model and the corresponding formulas reduce to the Newtonian version. A key relation is obtained in this paper for the first time, which might be very useful in future applications to problems in geodynamics and astronomy.

We present covariant gravitational equations to describe a four-dimensional brane world in the case with a Gauss-Bonnet term in a bulk spacetime, assuming that gravity is confined on the $Z_2$ symmetric brane. It contains some components of the five-dimensional Weyl curvature ${(E}_{\mu \nu })$ which describes all effects from the bulk spacetime just as in the case of the Randall-Sundrum second model. Applying this formalism to cosmology, we derive the generalized Friedmann equation and calculate the Weyl curvature term, which is directly obtained from a black hole solution.

We analyze weak gravity in the braneworld model proposed by Dvali, Gabadadze, and Porrati, in which the unperturbed background spacetime is given by a five-dimensional Minkowski bulk with a brane which has an induced Einstein-Hilbert term. This model has a critical length scale $r_c.$ Naively, we expect that four-dimensional general relativity (4D GR) is approximately recovered at a scale below $r_c.$ However, the simple linear perturbation does not work in this regime. Only recently has the mechanism to recover 4D GR been clarified under the restriction to spherically symmetric configurations, and the leading correction to 4D GR been derived. Here, we develop an alternative formulation which can handle more general perturbations. We also generalize the model by adding a bulk cosmological constant and the brane tension.

We study gravitational lensing by a Reissner-Nordström black hole in the weak field limit. We obtain the basic equations for the deflection angle and time delay and find analytical expressions for the positions and amplifications of the primary and secondary images. Because of a net positive charge, the separation between images increases, but no change in the total magnification occurs.

We calculate the TeV-PeV neutrino fluxes of gamma-ray bursts associated with supernovae, based on the observed association between GRB 030329 and supernova SN 2003dh. The neutrino spectral flux distributions can test for possible delays between the supernova and gamma-ray burst events down to much shorter time scales than what can be resolved with photons. As an illustrative example, we calculate the probability of neutrino induced muon and electron cascade events in a km scale under-ice detector at the South Pole, from the GRB 030329. Our calculations demonstrate that km scale neutrino telescopes are expected to detect signals that will allow us to constrain supernova-GRB models.

In a previous paper, we presented a three-flavor oscillation analysis of the solar neutrino measurements and of the first data from the KamLAND experiment, in terms of the relevant mass-mixing parameters $(\delta m^2,{\theta }_{12},{\theta }_{13}).\mathrm{}$ The analysis, performed by including the terrestrial neutrino constraints coming from the CHOOZ (reactor), KEK-to-Kamioka (K2K, accelerator), and Super-Kamiokande (SK, atmospheric) experiments, provided a stringent upper limit on ${\theta }_{13},$ namely, ${\sin }^2{\theta }_{13}<0.05\mathrm{}$ at $3\sigma .$ We reexamine such an upper bound in light of a recent (although preliminary) reanalysis of atmospheric neutrino data performed by the SK Collaboration, which seems to shift the preferred value of the largest neutrino square mass difference $\Delta m^2$ downwards. By taking the results of the SK official reanalysis at face value, and by repeating the analysis of our previous paper with such new input, we find that the upper bound on ${\theta }_{13}$ is somewhat relaxed: ${\sin }^2{\theta }_{13}<0.067\mathrm{}$ at $3\sigma .$ Related phenomenological issues are briefly discussed.

We calculate baryon decuplet to octet electromagnetic transition form factors in quenched and partially quenched chiral perturbation theory. We work in the isospin limit of $\mathrm{SU}\left(3\right)\mathrm{}$ flavor, up to next-to-leading order in the chiral expansion, and to leading order in the heavy baryon expansion. Our results are necessary for proper extrapolation of lattice calculations of these transitions. We also derive expressions for the case of $\mathrm{SU}\left(2\right)\mathrm{}$ flavor away from the isospin limit.

The recently measured inclusive electron-proton cross section in the nucleon resonance region, performed with the CLAS detector at the Thomas Jefferson Laboratory, has provided new data for the nucleon structure function $F_2$ with previously unavailable precision. In this paper we propose a description of these experimental data based on a Regge-dual model for $F_2.$ The basic inputs in the model are nonlinear complex Regge trajectories producing both isobar resonances and a smooth background. The model is tested against the experimental data, and the $Q^2$ dependence of the moments is calculated. The fitted model for the structure function (inclusive cross section) is a limiting case of the more general scattering amplitude equally applicable to deeply virtual Compton scattering. The connection between the two is discussed.

We require that the primordial baryon asymmetry is not washed out in the seesaw model compatible with the recent results of WMAP and the neutrino oscillation experiments including the first results of KamLAND. We find that only the case of the normal neutrino mass hierarchy with an approximate $L_e$ symmetry satisfies this requirement. We further derive, depending on the signs of the neutrino mass eigenvalues, three types of the neutrino mass matrices, where the values of each element are rather precisely fixed.

In continuing our earlier research, we find the formulas needed to determine the arbitrary functions in the Lemaître-Tolman (LT) model when the evolution proceeds from a given initial velocity distribution to a final state that is determined either by a density distribution or by a velocity distribution. In each case the initial and final distributions uniquely determine the LT model that evolves between them, and the sign of the energy function is determined by a simple inequality. We also show how the final density profile can be more accurately fitted to observational data than was done in our previous paper. We work out new numerical examples of the evolution: the creation of a galaxy cluster out of different velocity distributions, reflecting the current data on temperature anisotropies of cosmic microwave background, the creation of the same out of different density distributions, and the creation of a void. The void in its present state is surrounded by a nonsingular wall of high density.

The relations existing between the auxiliary field (einbein field) formalism and the spinless Salpeter equation are studied in the case of two particles with the same mass, interacting via a confining potential. The problem of nonorthogonality for radial excited states in the auxiliary field formalism is discussed and found to be noncrucial. It is shown that the classical equations of motion of the rotating string model, derived from the QCD Lagrangian, reduce exactly to the classical equations of motion of the phenomenological semirelativistic flux tube model, provided all auxiliary fields are eliminated correctly from the rotating string Hamiltonian.

In this paper, we calculate the next-to-leading order (NLO) new physics contributions to the mass splitting $\Delta M_{B_d}$ and the branching ratio $\mathcal{B}\left(\overrightarrow{B}{X}_s\gamma \right)$ induced by the charged Higgs loop diagrams in the third type of two-Higgs-doublet models (model III) and draw the constraints on the free parameters of model III. For the model III under consideration, we find that (a) an upper limit $|{\lambda }_{\mathrm{tt}}|<~1.7$ is obtained from the precision data of $\Delta M_{B_d}=0.502\mathrm{}\pm 0.007{\mathrm{ps}}^{-1},$ while $|{\lambda }_{\mathrm{tt}}|\approx 0.5$ is favored phenomenologicaly, (b) for $\overrightarrow{B}{X}_s\gamma$ decay, the NLO QCD contributions tend to cancel the LO new physics contributions, (c) a light charged Higgs boson with a mass around or even less than 200 GeV is still allowed at the NLO level by the measured branching ratio $\mathcal{B}\left(\overrightarrow{B}{X}_s\gamma \right),$ numerically, $188<~M_H<~215\mathrm{GeV}$ for $(|{\lambda }_{\mathrm{tt}}|,|{\lambda }_{\mathrm{bb}}|)=(0.5,18),$ (d) the NLO QCD contributions tend to cancel the LO contributions effectively, the lower limit on $M_H$ being consequently decreased by about 200 GeV, and (e) the allowed region of $M_H$ will be shifted toward the heavy mass end for a nonzero relative phase $\theta$ between the Yukawa couplings ${\lambda }_{\mathrm{tt}}$ and ${\lambda }_{\mathrm{bb}}.$ The numerical results for the conventional model II are also presented for the sake of comparison.

We report results of a study of charmless B meson decays to three-body $K\pi \pi ,\mathrm{KK}\pi$ and $\mathrm{KKK}$ final states. Measurements of branching fractions for B decays to $K^{+\left(0\right)\mathrm{}}{\pi }^{+}{\pi }^{-},K^{+}{K}^{+}{K}^{-},K^0{K}^{+}{K}^{-},K^{+}{K}_S^0{K}_S^0$ and $K_S^0{K}_S^0{K}_S^0$ final states are presented. The decays $B^0\to K^0{K}^{+}{K}^{-},B^{+}\to K^{+}{K}_S^0{K}_S^0$ and $B^0\to K_S^0{K}_S^0{K}_S^0$ are observed for the first time. We also report evidence for $B^{+}\to K^{+}{K}^{-}{\pi }^{+}$ decay. For the three-body final states $K^0{K}^{+}{\pi }^{-},K_S^0{K}_S^0{\pi }^{+},K^{+}{K}^{+}{\pi }^{-}$ and $K^{-}{\pi }^{+}{\pi }^{+},$ 90% confidence level upper limits are reported. Finally, we discuss the possibility of using the three-body $B^0\to K_S^0{K}^{+}{K}^{-}$ decay for $\mathrm{CP}$ violation studies. The results are obtained with a 78 ${\mathrm{fb}}^{-1}$ data sample collected at the ${\rm Y}\mathrm{}\left(4S\right)\mathrm{}$ resonance by the Belle detector operating at the KEKB asymmetric energy $e^{+}{e}^{-}$ collider.

We point out the existence of some simple string solitons in ${\mathrm{AdS}}_5\times {\mathrm{S}}^5,$ which at the same time are spinning in ${\mathrm{AdS}}_5$ and pulsating in ${\mathrm{S}}^5,$ or vice versa. This introduces an additional arbitrary constant into the scaling relations between energy and spin or R charge. The arbitrary constant is not an angular momentum, but can be related to the amplitude of the pulsation. We discuss the solutions in detail and consider the scaling relations. Pulsating multispin or multi-R-charge solutions can also be constructed.