We calculate the $O\left(\alpha \right)$ electroweak corrections to charged- and neutral-current deep-inelastic neutrino scattering off an isoscalar target. The full one-loop-corrected cross sections, including hard photonic corrections, are evaluated and compared to an earlier result which was used in the NuTeV analysis. In particular, we compare results that differ in the input-parameter scheme, treatment of real photon radiation, and factorization scheme. The associated shifts in the theoretical prediction for the ratio of neutral- and charged-current cross sections can be larger than the experimental accuracy of the NuTeV result.

We introduce a parametrization of the effects of radiative corrections from new physics on the charged lepton and neutrino mass matrices, studying how several relevant quantities describing the pattern of neutrino masses and mixing are affected by these corrections. We find that the ratio $\omega \equiv \sin \theta /\tan {\theta }_{\mathrm{atm}}$ is remarkably stable, even when relatively large corrections are added to the original mass matrices. It is also found that if the lightest neutrino has a mass around 0.3 eV, the pattern of masses and mixings is considerably more stable under perturbations than for a lighter or heavier spectrum. We explore the consequences of perturbations on some flavor relations given in the literature. In addition, for a quasidegenerate neutrino spectrum it is shown that (i) starting from a bimaximal mixing scenario, the corrections to the mass matrices keep $\tan {\theta }_{\mathrm{atm}}$ very close to unity while they can lower $\tan {\theta }_{\odot }$ to its measured value, and (ii) beginning from a scenario with a vanishing Dirac phase, corrections can induce a Dirac phase large enough to yield CP violation observable in neutrino oscillations.

We present improved measurements of the differential production rates of stable charged particles in hadronic $Z^0$ decays, and of charged pions, kaons, and protons identified over a wide momentum range using the SLD Cherenkov ring imaging detector. In addition to flavor-inclusive $Z^0$ decays, measurements are made for $Z^0$ decays into light (u, d, s), c, and b primary flavors, selected using the upgraded vertex detector. Large differences between the flavors are observed that are qualitatively consistent with expectations based upon previously measured production and decay properties of heavy hadrons. These results are used to test the predictions of QCD in the modified leading logarithm approximation, with the ansatz of local parton-hadron duality, and the predictions of three models of the hadronization process. The light-flavor results provide improved tests of these predictions; the heavy-flavor results provide complementary model tests. In addition we have compared hadron and antihadron production in light quark (as opposed to antiquark) jets. Differences are observed at high momentum for all three charged hadron species, providing direct probes of leading particle effects, and stringent constraints on models.

We consider four-dimensional massive gravity with the Fierz-Pauli mass term. The analysis of the scalar sector has revealed recently that this theory becomes strongly coupled above the energy scale $\Lambda {=(M}_{\mathrm{Pl}}{m}^4{)}^{1/5}$ where m is the mass of the graviton. We confirm this scale by explicit calculations of the four-graviton scattering amplitude and of the loop correction to the interaction between conserved sources.

We consider the possibilities for obtaining information about the equation of state for quark matter by using future direct observational data on gravitational waves. We study the nonradial oscillations of both fluid and spacetime modes of pure quark stars. If we observe the f and the lowest $w_{\mathrm{II}}$ modes from quark stars, by using the simultaneously obtained radiation radius we can constrain the bag constant B with reasonable accuracy, independently of the s quark mass.

The ratio of the curvaton energy density to that of the dominant component of the background sources may be constant during a significant period in the evolution of the Universe. The possibility of having tracking curvatons, whose decay occurs prior to the nucleosynthesis epoch, is studied. It is argued that the tracking curvaton dynamics is disfavored since the value of the curvature perturbations prior to curvaton decay is smaller than the value required by observations. It is also argued, in a related context, that the minimal inflationary curvature scale compatible with the curvaton paradigm may be lowered in the case of low-scale quintessential inflation.

We discuss different aspects of modern cosmology through a scalar field potential construction method. We discuss the case of negative potential cosmologies and its relation to oscillatory cosmic evolution, models with an explicit interaction between dark energy and dark matter which address the coincidence problem, and also the case of nonzero curvature space.

We describe a model-independent method of estimating the qualitative dynamics of an accelerating universe from observations of distant type Ia supernovae. Our method is based on the luminosity-distance function, optimized to fit observed distances of supernovae, and the Hamiltonian representation of dynamics for the quintessential universe with a general form of the equation of state $p=w\left[a\right(z\left)\mathrm{}\right]\rho .$ Because of the Hamiltonian structure of Friedmann-Robertson-Walker (FRW) dynamics with the equation of state $p=w\left[a\right(z\left)\mathrm{}\right]\rho ,$ the dynamics is uniquely determined by the potential function $V\left(a\right)\mathrm{}$ of the system. The effectiveness of this method in the discrimination of model parameters of the Cardassian evolution scenario is also given. Our main result is the following: restricting consideration to the flat model with the current value of ${\Omega }_{m,0\mathrm{}}=0.3,$ the constraints at a $2\sigma$ confidence level to the presence of ${\rho }^n$ modification of the FRW models are $-0.50\lesssim n\lesssim \mathrm{0.36.}$

We perform the most attractive channel (MAC) analysis in the top mode standard model with TeV-scale extra dimensions, where the standard model gauge bosons and the third generation of quarks and leptons are put in $D(=6,8,10,\dots )$ dimensions. In such a model, bulk gauge couplings rapidly grow in the ultraviolet region. In order to make the scenario viable, only the attractive force of the top condensate should exceed the critical coupling, while other channels such as the bottom and tau condensates should not. We then find that the top condensate can be the MAC for $D=8,$ whereas the tau condensation is favored for $D=6.\mathrm{}$ The analysis for $D=10\mathrm{}$ strongly depends on the regularization scheme. We predict masses of the top ${(m}_t)$ and the Higgs boson ${(m}_H),$ $m_t=172\mathrm{}–175\mathrm{GeV}$ and $m_H=176\mathrm{}–188\mathrm{GeV}$ for $D=8,$ based on the renormalization group for the top Yukawa and Higgs quartic couplings with the compositeness conditions at the scale where the bulk top condenses. The Higgs boson in such a characteristic mass range will be immediately discovered in $\overrightarrow{H}{\mathrm{WW}}^{\left(*\right)}{/ZZ}^{\left(*\right)}$ once the CERN LHC starts.

In the preceding paper, a rigorous three-dimensional relativistic equation for two-gluon bound states was derived from QCD with massive gluons and represented in the angular momentum representation. In order to apply this equation to calculate the glueball spectrum, in this paper, the equation is recast in an equivalent three-dimensional relativistic equation satisfied by the two-gluon positive energy state amplitude. The interaction Hamiltonian in the equation is exactly derived and expressed as a perturbative series. The first term in the series describes the one-gluon exchange interaction which includes fully the retardation effect in it. This term plus the linear confining potential are chosen to be the interaction Hamiltonian and employed in the practical calculation. With the integrals containing three and four spherical Bessel functions in the QCD vertices being analytically calculated, the interaction Hamiltonian is given an explicit expression in the angular momentum representation. Numerically solving the relativistic equation with taking the contributions arising from the retardation effect and the longitudinal mode of gluon fields into account, a set of masses for the $0^{++}{,0\mathrm{}}^{-+}{,1\mathrm{}}^{++}{,1\mathrm{}}^{-+}{,2\mathrm{}}^{++},$ and $2^{-+}$ glueball states are obtained and are in fairly good agreement with the predictions given by the lattice simulation. In addition, some new glueball states are predicted.

A rigorous three-dimensional relativistic equation satisfied by two-gluon bound states is derived from QCD with massive gluons. With the gluon fields and the quark fields being expanded in terms of the gluon multipole fields and the spherical Dirac spinors, respectively, the equation is well established in the angular momentum representation and hence is very convenient for solving the problem of two-gluon glueball spectra. In particular, the interaction kernel in the equation is exactly derived and given a closed expression which includes all the interactions taking place in the two-gluon glueballs. The kernel contains only a few types of Green’s functions and commutators. Therefore, it is not only easily calculated by the perturbation method, but also provides a suitable basis for nonperturbative investigations.

Recently, we pointed out that chiral transformation properties of strong penguin operators change in the transition from unquenched to (partially) quenched QCD. As a consequence, new penguinlike operators appear in the (partially) quenched theory, along with new low-energy constants, which should be interpreted as a quenching artifact. Here, we extend the analysis of the contribution of the new low-energy constants to the $K^0\to {\pi }^{+}{\pi }^{-}$ amplitude, at leading order in chiral perturbation theory, and for arbitrary (momentum nonconserving) kinematics. Using these results, we provide a detailed discussion of the intrinsic systematic error due to this (partial) quenching artifact. We also give a simple recipe for the determination of the leading-order low-energy constant parametrizing the new operators in the case of strong LR penguins operators.

We present the calculation of the virtual and bremsstrahlung corrections of $O\left({\alpha }_s\right)$ to the matrix elements $〈{\mathrm{dl}}^{+}{l}^{-}|O_i|b〉.$ This is the missing piece in the full next-to-next-to-leading logarithmic (NNLL) results for various observables associated with the process $\overrightarrow{B}{X}_d{l}^{+}{l}^{-},$ such as the branching ratio, the CP-rate asymmetry, and the forward-backward asymmetry. This paper is an extension of analogous calculations done by some of us for the process $\overrightarrow{B}{X}_s{l}^{+}{l}^{-}.$ As the contributions of the diagrams induced by the four-quark operators $O_1^u$ and $O_2^u$ with a u quark running in the quark loop are strongly Cabibbo-Kobayashi-Maskawa suppressed, they were omitted in the analysis of $\overrightarrow{B}{X}_s{l}^{+}{l}^{-}.$ This is no longer possible for $\overrightarrow{B}{X}_d{l}^{+}{l}^{-},$ as the corresponding contributions are not suppressed. The main new work therefore consists of calculating the $O\left({\alpha }_s\right)$ corrections to $〈{\mathrm{dl}}^{+}{l}^{-}|O_{1,2}^u|b〉.$ In this paper we restrict ourselves to the range $0.05<~{s/m}_b^2<~0.25$ (s is the invariant mass of the lepton pair), which lies above the ρ and ω resonances and below the $J/\psi$ resonance. We present the analytic results for the mentioned observables related to the process $\overrightarrow{B}{X}_d{l}^{+}{l}^{-}$ as expansions in the small parameters $ŝ{=s/m}_b^2,$ ${z=m}_c^2{/m}_b^2,$ and ${s/(4m}_c^2).\mathrm{}$ In the phenomenological analysis at the end of the paper we discuss the impact of the NNLL corrections on the observables mentioned above.

We introduce a generalization of $\mathrm{}(1+1)\mathrm{}$-dimensional large $N_c$ QCD, which we refer to as “reduced” QCD (RQCD). In this model gluons and quark momenta live in $1+1$ dimensions only, but the quark spin and all other particles (leptons and the photon) live in the full $1+3$ dimensions. The bound states of quarks and antiquarks are identical to those originally described by ’t Hooft (except that there are new transversely polarized states previously excluded), so the model is exactly soluable. However, significant differences arise when the model is applied to electromagnetic interactions. After reviewing the strongly interacting sector of the theory, we discuss deep inelastic scattering (DIS) in this model, and show that the new states with transverse polarization give the Callan-Gross relation and remove the pathological features of the original (1+1)-dimensional description. We conclude that RQCD gives a satisfactory description of the phenomenology and provides a deep understanding of both duality and DIS.

Radiative corrections to neutrino mixing and CP violation are analyzed in the minimal seesaw model with two heavy right-handed neutrinos. We find that the textures of the effective Majorana neutrino mass matrix are essentially stable against renormalization effects. Taking into account the Frampton-Glashow-Yanagida Ansatz for the Dirac neutrino Yukawa coupling matrix, we calculate the running effects of light neutrino masses, lepton flavor mixing angles, and CP-violating phases for both the $m_1=0\mathrm{}$ (normal mass hierarchy) and $m_3=0\mathrm{}$ (inverted mass hierarchy) cases in the standard model and in its minimal supersymmetric extension. Very instructive predictions for the cosmological baryon number asymmetry via thermal leptogenesis are also given with the help of low-energy neutrino mixing quantities.

We examine the rotation of the plane of polarization for linearly polarized light rays by the weak gravitational field of an isolated physical system. Based on the rotation of inertial frames, we review the general integral expression for the net rotation. We apply this formula, an analogue to the usual electromagnetic Faraday effect, to some interesting astrophysical systems, namely uniformly shifting mass monopoles and a spinning external shell.

We solve the equation of motion of Witten’s cubic open string field theory in a series expansion using the regulated butterfly state. The expansion parameter is given by the regularization parameter of the butterfly state, which can be taken to be arbitrarily small. Unlike the case of level truncation, the equation of motion can be solved for an arbitrary component of the Fock space up to a positive power of the expansion parameter. The energy density of the solution is well defined and remains finite even in the singular butterfly limit, and it gives approximately 68% of the D25-brane tension for the solution at the leading order. Moreover, it simultaneously solves the equation of motion of vacuum string field theory, providing support for the conjecture at this order. We further improve our ansatz by taking into account next-to-leading terms, and find two numerical solutions which give approximately 88% and 109%, respectively, of the D25-brane tension for the energy density. These values are interestingly close to those by level truncation at level 2 without gauge fixing studied by Rastelli and Zwiebach and by Ellwood and Taylor.

We argue that already at the classical level the energy-momentum tensor for a scalar field on manifolds with boundaries in addition to the bulk part contains a contribution located on the boundary. Using the standard variational procedure for the action with the boundary term, the expression for the surface energy-momentum tensor is derived for arbitrary bulk and boundary geometries. Integral conservation laws are investigated. The corresponding conserved charges are constructed and their relation to the proper densities is discussed. Further, we study the vacuum expectation value of the energy-momentum tensor in the corresponding quantum field theory. It is shown that the surface term in the energy-momentum tensor is essential in obtaining the equality between the vacuum energy, evaluated as the sum of the zero-point energies for each normal mode of frequency, and the energy derived by the integration of the corresponding vacuum energy density. As an application, by using the zeta function technique, we evaluate the surface energy for a quantum scalar field confined inside a spherical shell.

In the first part of this article I present a system of retarded coordinates based at an arbitrary world line of an arbitrary curved spacetime. The retarded-time coordinate labels forward light cones that are centered on the world line, the radial coordinate is an affine parameter on the null generators of these light cones, and the angular coordinates are constant on each of these generators. The spacetime metric in the retarded coordinates is displayed as an expansion in powers of the radial coordinate and expressed in terms of the world line’s acceleration vector and the spacetime’s Riemann tensor evaluated at the world line. The formalism is illustrated in two examples, the first involving a comoving world line of a spatially flat cosmology, the other featuring an observer in circular motion in the Schwarzschild spacetime. The main application of the formalism is presented in the second part of the article, in which I consider the motion of a small black hole in an empty external universe. I use the retarded coordinates to construct the metric of the small black hole perturbed by the tidal field of the external universe, and the metric of the external universe perturbed by the presence of the black hole. Matching these metrics produces the MiSaTaQuWa equations of motion for the small black hole.

We analyze the quantum process in which a cosmic string breaks in a de Sitter (dS) background, and a pair of neutral or charged black holes is produced at the ends of the string. The energy to materialize and accelerate the pair comes from the positive cosmological constant and, in addition, from the string tension. The compact saddle point solutions without conical singularities (instantons) or with conical singularities (submaximal instantons) that describe this process are constructed through the analytical continuation of the dS C metric. Then, we explicitly compute the pair creation rate of the process. In particular, we find the nucleation rate of a cosmic string in a dS background, and the probability that it breaks and a pair of black holes is produced. Finally we verify that, as occurs with pair production processes in other background fields, the pair creation rate of black holes is proportional to $e^S,$ where the gravitational entropy of the black hole, S, is given by one-quarter of the area of the horizons present in the saddle point solution that mediates the process.