The pion form factor is computed using quenched twisted mass QCD and the GMRES-DR matrix inverter. The momentum averaging procedure of Frezzotti and Rossi is used to remove leading lattice spacing artifacts, and numerical results for the form factor show the expected improvement with respect to the standard Wilson action. Although some matrix inverters are known to fail when applied to twisted mass QCD, GMRES-DR is found to be a viable and powerful option. Results obtained for the pion form factor are consistent with the published results from other $O(a)$ improved actions and are also consistent with the available experimental data.

We calculate, at the one-loop level, penguin diagrams for improved staggered fermion operators constructed using various fat links. The main result is that diagonal mixing coefficients with penguin operators are identical between the unimproved operators and the improved operators using such fat links as Fat7, $\mathrm{F}\mathrm{a}\mathrm{t}7+\mathrm{L}\mathrm{e}\mathrm{p}\mathrm{a}\mathrm{g}\mathrm{e}$, $\overline{\mathrm{F}\mathrm{a}\mathrm{t}7}$, HYP (I) and HYP (II). In addition, it turns out that the off-diagonal mixing vanishes for those constructed using fat links of Fat7, $\overline{\mathrm{F}\mathrm{a}\mathrm{t}7}$ and HYP (II). This is a consequence of the fact that the improvement by various fat links changes only the mixing with higher dimension operators and off-diagonal operators. The results of this paper, combined with those for current-current diagrams, provide complete matching at the one-loop level with all corrections of $\mathcal{O}(g^2)$ included.

We show that it is possible to construct ${ϵ}^{\prime }/ϵ$ to next-to-leading order (NLO) using partially quenched chiral perturbation theory (PQChPT) from amplitudes that are computable on the lattice. We demonstrate that none of the needed amplitudes require 3-momentum on the lattice for either the full theory or the partially quenched theory; nondegenerate quark masses suffice. Furthermore, we find that the electro-weak penguin ($\Delta I=3/2$ and $1/2$) contributions to ${ϵ}^{\prime }/ϵ$ in PQChPT can be determined to NLO using only degenerate ($m_K=m_{\pi }$) $K\to \pi$ computations without momentum insertion. Issues pertaining to power divergent contributions, originating from mixing with lower dimensional operators, are addressed. Direct calculations of $K\to \pi \pi$ at unphysical kinematics are plagued with enhanced finite volume effects in the (partially) quenched theory, but in simulations when the sea quark mass is equal to the up and down quark mass the enhanced finite volume effects vanish to NLO in PQChPT. In embedding the QCD penguin left-right operator onto PQChPT an ambiguity arises, as first emphasized by Golterman and Pallante. With one version [the “PQS” (patially quenched singlet)] of the QCD penguin, the inputs needed from the lattice for constructing $K\to \pi \pi$ at NLO in PQChPT coincide with those needed for the full theory. Explicit expressions for the finite logarithms emerging from our NLO analysis to the above amplitudes also are given.

Motivated by recent experimental results we reconsider semileptonic $D\to P\ell {\nu }_{\ell }$ decays within a model which combines heavy quark symmetry and properties of the chiral Lagrangian. We include excited charm meson states, some of them recently observed, in our Lagrangian and determine their impact on the charm meson semileptonic form factors. We find that the inclusion of excited charm meson states in the model leads to a rather good agreement with the experimental results on the $q^2$ shape of the $F_{+}(q^2)$ form factor. We also calculate branching ratios for all $D\to P\ell {\nu }_{\ell }$ decays.

Using generalized Sehgal equations for magnetic moments of baryon octet and taking into account ${\Sigma }^0-\Lambda$ mixing and two particle corrections to independent quark contributions we obtain very good fit using experimental values for errors of such moments. We present sum rules for quark magnetic moments ratios and for integrated spin densities ratios. Because of the $SU(3)$ structure of our equations the results for magnetic moments of quarks and their densities depend on two additional parameters. Using information from deep inelastic scattering and baryon $\beta$-decays we discuss the dependence of antiquark polarizations on introduced parameters. For some plausible values of these parameters we show that these polarizations are small if we neglect angular momenta of quarks. Our very good fit to magnetic moments of baryon octet can still be improved by using specific model for angular momentum of quarks.

We study an $\mathcal{N}=1$ supersymmetric Yang-Mills theory defined on $M^4\times S^1$. The vacuum expectation values for adjoint scalar field in vector multiplet, though important, have been overlooked in evaluating one-loop effective potential of the theory. We correctly take the vacuum expectation values into account in addition to the Wilson line phases to give an expression for the effective potential, and gauge symmetry breaking is discussed. In evaluating the potential, we employ the Scherk-Schwarz mechanism and introduce bare mass for gaugino in order to break supersymmetry. We also obtain masses for the scalars, the adjoint scalar, and the component gauge field for the $S^1$ direction in the case of the SU(2) gauge group. We observe that large supersymmetry breaking gives larger mass for the scalar. This analysis is easily applied to the $M^4\times S^1/Z_2$ case.

We develop a four-dimensional effective theory for Randall-Sundrum models which allows us to calculate long-wavelength adiabatic perturbations in a regime where the ${\rho }^2$ terms characteristic of braneworld cosmology are significant. This extends previous work employing the moduli space approximation. We extend the treatment of the system to include higher derivative corrections present in the context of braneworld cosmology. The developed formalism allows us to study perturbations beyond the general long-wavelength, slow-velocity regime to which the usual moduli approximation is restricted. It enables us to extend the study to a wide range of braneworld cosmology models for which the extra terms play a significant role. As an example we discuss high-energy inflation on the brane and analyze the key observational features that distinguish braneworlds from ordinary inflation by considering scalar and tensor perturbations as well as non-Gaussianities. We also compare inflation and cyclic models and study how they can be distinguished in terms of these corrections.

We perform fully general relativistic simulations of rotating stellar core collapse in three spatial dimensions. The hydrodynamic equations are solved using a high-resolution shock-capturing scheme. A parametric equation of state is adopted to model collapsing stellar cores and neutron stars following Dimmelmeier et al. The early stage of the collapse is followed by an axisymmetric code. When the stellar core becomes compact enough, we start a three-dimensional simulation adding a bar-mode nonaxisymmetric density perturbation. The axisymmetric simulations are performed for a wide variety of initial conditions changing the rotational velocity profile, parameters of the equations of state, and the total mass. It is clarified that the maximum density, the maximum value of the compactness, and the maximum value of the ratio of the kinetic energy $T$ to the gravitational potential energy $W$ ($\beta \equiv T/W$) achieved during the stellar collapse and bounce depend sensitively on the velocity profile and the total mass of the initial core and equations of state. It is also found that for all the models with a high degree of differential rotation, a funnel structure is formed around the rotational axis after the formation of neutron stars. For selected models in which the maximum value of $\beta$ is larger than $\sim 0.27$, three-dimensional numerical simulations are performed. It is found that the bar-mode dynamical instability sets in for the case that the following conditions are satisfied: (i) the progenitor of the stellar core collapse should be rapidly rotating with the initial value of $0.01\lesssim \beta \lesssim 0.02$, (ii) the degree of differential rotation for the velocity profile of the initial condition should be sufficiently high, and (iii) a depletion factor of pressure in an early stage of collapse should be large enough to induce a significant contraction to form a compact stellar core for which an efficient spin-up can be achieved surmounting the strong centrifugal force. As a result of the onset of the bar-mode dynamical instabilities, the amplitude of gravitational waves can be by a factor of $\sim 10$ larger than that in the axisymmetric collapse. It is found that a dynamical instability with the $m=1$ mode is also induced for the dynamically unstable cases against the bar mode, but the perturbation does not grow significantly and, hence, it does not contribute to an outstanding amplification of gravitational waves. No evidence for fragmentation of the protoneutron stars is found in the first few 10 msec after the bounce.

We construct monopole-antimonopole chain and vortex solutions in Yang-Mills-Higgs theory coupled to Einstein gravity. The solutions are static, axially symmetric, and asymptotically flat. They are characterized by two integers $(m,n)$ where $m$ is related to the polar angle and $n$ to the azimuthal angle. Solutions with $n=1$ and $n=2$ correspond to chains of $m$ monopoles and antimonopoles. Here the Higgs field vanishes at $m$ isolated points along the symmetry axis. Larger values of $n$ give rise to vortex solutions, where the Higgs field vanishes on one or more rings, centered around the symmetry axis. When gravity is coupled to the flat space solutions, a branch of gravitating monopole-antimonopole chain or vortex solutions arises and merges at a maximal value of the coupling constant with a second branch of solutions. This upper branch has no flat space limit. Instead in the limit of vanishing coupling constant it either connects to a Bartnik-McKinnon or generalized Bartnik-McKinnon solution, or, for $m>4$, $n>4$, it connects to a new Einstein-Yang-Mills solution. In this latter case further branches of solutions appear. For small values of the coupling constant on the upper branches, the solutions correspond to composite systems, consisting of a scaled inner Einstein-Yang-Mills solution and an outer Yang-Mills-Higgs solution.

In this paper we investigate how the energy density due to a nonstandard choice of initial vacuum affects the expansion of the universe during inflation. To do this we introduce source terms in the Friedmann equations making sure that we respect the relation between gravity and thermodynamics. We find that the energy production automatically implies a slow rolling cosmological constant. Hence we also conclude that there is no well defined value for the cosmological constant in the presence of sources. We speculate that a nonstandard vacuum can provide slow roll inflation on its own.

Dark energy with the equation of state $w(z)$ rapidly evolving from the dustlike ($w\simeq 0$ at $z\sim 1$) to the phantomlike ($-1.2\lesssim w\lesssim -1$ at $z\simeq 0$) has been recently proposed as the best fit for the supernovae Ia data. Assuming that a dark energy component with an arbitrary scalar-field Lagrangian $p(\phi ,{\nabla }_{\mu }\phi )$ dominates in the flat Friedmann universe, we analyze the possibility of a dynamical transition from the states $(\phi ,\dot{\phi })$ with $w\ge -1$ to those with $w<-1$ or vice versa. We have found that generally such transitions are physically implausible because they are either realized by a discrete set of trajectories in the phase space or are unstable with respect to the cosmological perturbations. This conclusion is confirmed by a comparison of the analytic results with numerical solutions obtained for simple models. Without the assumption of the dark energy domination, this result still holds for a certain class of dark energy Lagrangians, in particular, for Lagrangians quadratic in ${\nabla }_{\mu }\phi$. The result is insensitive to topology of the Friedmann universe as well.

This paper discusses models of inflation based on global supersymmetry. It is shown that there are parameter ranges, consistent with observational constraints, for which warm inflation occurs and supergravity effects can be neglected. There is no need for any fine tuning of parameters. The thermal corrections to the inflaton potential are calculated and it is shown that they do not alter the warm inflationary evolution.

In this paper we establish dualities between inflationary, cyclic/ekpyrotic, and phantom cosmologies within the patch formalism approximating high-energy effects in scenarios with extra dimensions. The exact dualities relating the four-dimensional spectra are broken in favor of their braneworld counterparts; the dual solutions display new interesting features because of the modification of the effective Friedmann equation on the brane. We then address some qualitative issues about phantomlike cosmologies without phantom matter.

We consider Wilson’s $\mathrm{S}\mathrm{U}(N)$ lattice gauge theory (without fermions) at negative values of $\beta =2N/g^2$ and for $N=2$ or $3$. We show that in the limit $\beta \to -\infty$, the path integral is dominated by configurations where links variables are set to a nontrivial element of the center on selected nonintersecting lines. For $N=2$, these configurations can be characterized by a unique gauge invariant set of variables, while for $N=3$ a multiplicity growing with the volume as the number of configurations of an Ising model is observed. In general, there is a discontinuity in the average plaquette when $g^2$ changes its sign which prevents us from having a convergent series in $g^2$ for this quantity. For $N=2$, a change of variables relates the gauge invariant observables at positive and negative values of $\beta$. For $N=3$, we derive an identity relating the observables at $\beta$ with those at $\beta$ rotated by $\pm 2\pi /3$ in the complex plane and show numerical evidence for a Ising like first order phase transition near $\beta =-22$. We discuss the possibility of having lines of first order phase transitions ending at a second order phase transition in an extended bare parameter space.

If the exotic baryon ${\Theta }^{+}(1540)$ is a correlated $udud\overline{s}$ with $J^P=\frac{1^{+}}{2}$, then there should exist an exotic meson ${\vartheta }^{+}$ with strangeness $+2$, $J^P=1^{-}$, mass $\sim 1.6\mathrm{G}\mathrm{e}\mathrm{V}$, decaying to $K^{+}{K}^0$ with width $O(10–100)\mathrm{M}\mathrm{e}\mathrm{V}$. The ${\pi }_1(1400;1600)$ may be broad members of $\mathbf{10}\pm \overline{\mathbf{10}}$ in such a picture, and it is possible that vector mesons in the 1.4–1.7 GeV mass range are related to this multiplet. We suggest that dynamical correlations may limit the spectrum of $J^{P(C)}$ such that the $1^{-(\pm )}$ states are isolated.

We calculate the cross section of $J/\psi$ plus prompt-photon inclusive production in $\gamma \gamma$ collisions at next-to-leading order within the factorization formalism of nonrelativistic quantum chromodynamics (NRQCD) focusing on direct photoproduction. Apart from direct $J/\psi$ production, we also include the feed-down from directly produced ${\chi }_{cJ}$ and ${\psi }^{\prime }$ mesons. We discuss the analytical calculation, in particular the treatment of the various types of singularities and the NRQCD operator renormalization, in some detail. We present theoretical predictions for the future $e^{+}{e}^{-}$ linear collider TESLA, taking into account both brems- and beamstrahlung.

We present an improved calculation of $B\to$ light pseudoscalar form factors from light-cone sum rules, including one-loop radiative corrections to twist-2 and twist-3 contributions, and leading-order twist-4 corrections. The total theoretical uncertainty of our results at zero momentum transfer is 10 to 13% and can be improved, at least in part, by reducing the uncertainty of hadronic input parameters, in particular, those describing the twist-2 distribution amplitudes of the $\pi$, $K$, and $\eta$. We present our results in a way which details the dependence of the form factors on these parameters and facilitates the incorporation of future updates of their values from, e.g., lattice calculations.

Single scalar field inflation with a generic, nonquadratic in derivatives, field Lagrangian is considered. It is shown that non-Gaussianity of curvature perturbations is characterized by two dimensionless amplitudes. One of these amplitudes can be expressed in terms of the usual inflationary observables—the scalar power, the tensor power, and the tensor index. This consistency relation provides an observational test for the single scalar inflation.

Implications of some proposed theories of quantum gravity for neutrino flavor oscillations are explored within the context of modified dispersion relations of special relativity. In particular, approximate expressions for Planck scale-induced deviations from the standard oscillation length are obtained as functions of neutrino mass, energy, and propagation distance. Grounding on these expressions, it is pointed out that, in general, even those deviations that are suppressed by the second power of the Planck energy may be observable for ultra-high-energy neutrinos, provided they originate at cosmological distances. In fact, for neutrinos in the highest energy range of EeV to ZeV, deviations that are suppressed by as much as the seventh power of the Planck energy may become observable. Accordingly, realistic possibilities of experimentally verifying these deviations by means of the next generation neutrino detectors—such as IceCube and ANITA—are investigated.