The isosinglet combination of the chiral-odd twist-3 distribution function $e^u{\mathrm{}\left(x\right)+e}^d\mathrm{}\left(x\right)\mathrm{}$ of the nucleon has the outstanding properties that its first moment is proportional to the well-known $\pi N$ sigma term and that it contains a $\delta$-function singularity at $x=0.\mathrm{}$ These two features are inseparably connected in that the above sum rule would be violated if there is no such singularity in $e^u{\mathrm{}\left(x\right)+e}^d\mathrm{}\left(x\right).$ Very recently, we found that the physical origin of this $\delta$-function singularity can be traced back to the long-range quark-quark correlation of scalar type, which signals the spontaneous chiral symmetry breaking of the QCD vacuum. The main purpose of the present paper is to give complete theoretical predictions for the chiral-odd twist-3 distribution function $e^a\mathrm{}\left(x\right)\mathrm{}$ of each flavor a on the basis of the chiral quark soliton model, without recourse to the derivative-expansion-type approximation. These theoretical predictions are then compared with the empirical information extracted from the CLAS data of the semi-inclusive DIS processes by assuming the Collins mechanism only. A good agreement with the CLAS data is indicative of a sizable violation of the $\pi N$ sigma-term sum rule or, equivalently, the existence of a $\delta$-function singularity in $e^u{\mathrm{}\left(x\right)+e}^d\mathrm{}\left(x\right).$

We perform a detailed Regge analysis of NN, $\pi N,$ KN, ππ, and $\pi K$ scattering. From it, we find expressions that represent the ππ scattering amplitudes with an accuracy of a few percent for exchange of isospin zero and ∼15% for exchange of isospin 1, and this for energies $s^{1/2}>1.4\mathrm{}\mathrm{GeV}$ and for momentum transfers $|t{|}^{1/2}\lesssim 0.4\mathrm{GeV}.$ These Regge formulas are perfectly compatible with the low energy ${(s}^{1/2}\sim 1.4\mathrm{GeV})$ scattering amplitudes deduced from ππ phase shift analyses as well as with higher energy ${(s}^{1/2}\gtrsim 1.4\mathrm{GeV})$ experimental ππ cross sections. They are also compatible with NN, KN, and $\pi N$ experimental cross sections using factorization, a property that we check with precision. This contrasts with results from current phase shift analyses of the ππ scattering amplitude, which bear little resemblance to reality in the region $1.4<\mathrm{}{s}^{1/2}<2\mathrm{}\mathrm{GeV},$ as they are not well defined and increasingly violate a number of physical requirements when the energy grows. $\pi K$ scattering is also considered, and we present a Regge analysis for these processes valid for energies $s^{1/2}>1.7\mathrm{}\mathrm{GeV}.$ As a by-product of our analysis, we obtain also a fit of NN, $\pi N,$ and KN cross sections valid from c.m. kinetic energy $E_{\mathrm{kin}}\simeq 1\mathrm{GeV}$ to multi-TeV energies.

We construct a CP-violating observable which does not require flavor or CP tagging of the initial state. The proposed decay asymmetry could be measured at both threshold and non-threshold charm physics experiments and provides better sensitivity to small CP-violating parameters in charm decays.

At very early times, the Universe was not in a vacuum state. Under the assumption that the deviation from equilibrium was large, in particular, that it is higher than the scale of inflation, we analyze the conditions for local transitions between states that are related to different vacua. All pathways lead to an attractor solution of a description of the Universe by eternal inflation with domains that have different low energy parameters. The generic case favors transitions between states that have significantly different parameters rather than jumps between nearby states in parameter space. I argue that the strong CP problem presents a potential difficulty for this picture, more difficult than the hierarchy problem or the cosmological constant problem. Finally, I describe how the spectrum of quark masses may be a probe of the early dynamics of vacuum states. As an example, by specializing to the case of intersecting braneworld models, I show that the observed mass spectrum, which is approximately scale invariant, corresponds to a flat distribution in the intersection area of the branes, with a maximum area $A_{\max }\sim 100{\alpha }^{\prime }.$

The generalization of the Gross-Neveu model for noncommutative $3+1$ space-time has been analyzed. We find indications that chiral symmetry breaking occurs for an inhomogeneous background as in the Larkin-Ovchinnikov-Fulde-Ferrell phase in condensed matter.

We find a large class of supersymmetric solutions in the ${\mathrm{AdS}}_3\times {\mathrm{S}}^3$ background with Neveu-Schwarz fluxes. This two-parameter family of solutions preserves eight of the 16 supersymmetries of the background.

We derive some nonperturbative results in $1+1$ and $2+1$ dimensions within the context of the particle path-integral representation for a Dirac field propagator in the presence of an external field, in a formulation introduced by Migdal. We consider the specific properties of the path-integral expressions corresponding to the $\mathrm{}(1+1)\mathrm{}$- and $\mathrm{}(2+1)\mathrm{}$-dimensional cases, presenting a derivation of the chiral anomaly in the former and of the Chern-Simons current in the latter. We also discuss particle propagation in constant electromagnetic field backgrounds.

Gravitinos are expected to be produced in any local supersymmetric model. Using their abundance prediction as a function of the reheating energy scale, we argue that the next generation of cosmic microwave background experiments could exclude supergravity or strongly favor “thermal-like” inflation models if B mode polarized radiation were detected. Galactic cosmic-ray production by evaporating primordial black holes is also investigated as a way of constraining the Hubble mass at the end of inflation. Subsequent limits on the gravitino mass and on the related grand unification parameters are derived.

We study one- and two-soliton solutions of noncommutative Chern-Simons theory coupled to a nonrelativistic or a relativistic scalar field. In the nonrelativistic case, we find a tower of new stationary time-dependent solutions, all with the same charge density, but with increasing energies. The dynamics of these solitons cannot be studied using traditional moduli space techniques, but we do find a nontrivial symplectic form on the phase space indicating that the moduli space is not flat. In the relativistic case we find the metric on the two soliton moduli space.

Viscosity and magnetic fields drive differentially rotating stars toward uniform rotation, and this process has important consequences in many astrophysical contexts. For example, merging binary neutron stars can form a “hypermassive” remnant, i.e., a differentially rotating star with a mass greater than would be possible for a uniformly rotating star. The removal of the centrifugal support provided by differential rotation can lead to delayed collapse of the remnant to a black hole, accompanied by a delayed burst of gravitational radiation. Both magnetic fields and viscosity alter the structure of differentially rotating stars on secular time scales, and tracking this evolution presents a strenuous challenge to numerical hydrodynamic codes. Here, we present the first evolutions of rapidly rotating stars with shear viscosity in full general relativity. We self-consistently include viscosity in our relativistic hydrodynamic code by solving the fully relativistic Navier-Stokes equations. We perform these calculations both in axisymmetry and in full 3+1 dimensions. In axisymmetry, the resulting reduction in computational costs allows us to follow secular evolution with high resolution over dozens of rotation periods (thousands of $M).\mathrm{}$ We find that viscosity operating in a hypermassive star generically leads to the formation of a compact, uniformly rotating core surrounded by a low-density disk. These uniformly rotating cores are often unstable to gravitational collapse. We follow the collapse in such cases and determine the mass and the spin of the final black hole and ambient disk. However, viscous braking of differential rotation in hypermassive neutron stars does not always lead to catastrophic collapse, especially when viscous heating is substantial. The stabilizing influences of viscous heating, which generates enhanced thermal pressure, and centrifugal support prevent collapse in some cases, at least until the star cools. In all cases studied, the rest mass of the resulting disk is found to be 10–20 % of the original star, whether surrounding a uniformly rotating core or a rotating black hole. This study represents an important step toward understanding secular effects in relativistic stars and foreshadows more detailed, future simulations, including those involving magnetic fields.

We construct an exact quantum gravitational state describing the collapse of an inhomogeneous spherical dust cloud using a lattice regularization of the Wheeler-DeWitt equation. In the semiclassical approximation around a black hole, this state describes Hawking radiation. We show that the leading quantum gravitational correction to Hawking radiation renders the spectrum nonthermal.

From the theory of topological defect formation proposed for the early Universe, the so-called Kibble mechanism, it follows that the density correlation functions of defects and antidefects in a given system should be completely determined in terms of a single length scale $\xi ,$ the relevant domain size, which is proportional to the average interdefect separation $r_{\mathrm{av}}.$ Thus, when lengths are expressed in units of $r_{\mathrm{av}},$ these distributions should show universal behavior, depending only on the symmetry of the order parameter and space dimensions. We have verified this prediction by analyzing the distributions of defects and antidefects formed during the isotropic-nematic phase transition in a thin layer in a liquid crystal sample. Our experimental results confirm this prediction and are in reasonable agreement with the results of numerical simulations.

I present linear and second-order perturbation theory in dark energy models with an explicit interaction to matter in view of its application to N-body simulations and nonlinear phenomena. Several new or generalized results are obtained: the general equations for the linear perturbation growth, an analytical expression for the bias induced by a species-dependent interaction, the Yukawa correction to the gravitational potential due to dark energy interaction, and the second-order perturbation equations in coupled dark energy and their Newtonian limit. I also show that a density-dependent effective dark energy mass arises if the dark energy coupling is varying.

In order to detect the rare astrophysical events that generate gravitational wave (GW) radiation, a sufficient stability is required for GW antennas to allow long-term observation. In practice, seismic excitation is one of the most common disturbances effecting the stable operation of suspended-mirror laser interferometers. A straightforward means to allow a more stable operation is therefore to locate the antenna, the “observatory,” at a “quiet” site. A laser interferometer gravitational wave antenna with a baseline length of 20 m (LISM) was developed at a site 1000 m underground, near Kamioka, Japan. This project was a unique demonstration of a prototype laser interferometer for gravitational wave observation located underground. The extremely stable environment is the prime motivation for going underground. In this paper, the demonstrated ultrastable operation of the interferometer and a well-maintained antenna sensitivity are reported.

Using cooling for SU(2) lattice configurations, purely Abelian constant magnetic-field configurations were left over after the annihilation of constituents that formed metastable $Q=0\mathrm{}$ configurations. These so-called Dirac sheet configurations were found to be stable if emerging from the confined phase, close to the deconfinement phase transition, provided their Polyakov loop was sufficiently nontrivial. Here we show how this is related to the notion of marginal stability of the appropriate constant magnetic-field configurations. We find a perfect agreement between the analytic prediction for the dependence of stability on the value of the Polyakov loop (the holonomy) in a finite volume and the numerical results studied on a finite lattice in the context of the Dirac sheet configurations.

We show that combining forward and backward evolution allows us to extract the residues of the triple-pole Pomeron and of the other singularities for $10<~Q^2<~1000{\mathrm{GeV}}^2.$ In this approach, the essential singularity generated by the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution is considered as a numerical approximation to a triple-pole Pomeron. The $Q^2$-dependent form factors, unknown in Regge theory, are predicted by the DGLAP equation, and lead to a fit to the experimental data with a ${\chi }^2/dof$ of 1.02. In our case, Regge theory applies at all values of $Q^2.$ The method used here gives two main results: first, the parton content of the Pomeron is given at large $Q^2$ by DGLAP evolution, and second, we can evaluate the uncertainties on the gluon distribution which prove to be large at small x and small $Q^2.$

We study positive and negative parity nucleons on the lattice using the chirally improved lattice Dirac operator. Our analysis is based on a set of three operators ${\chi }_i$ with the nucleon quantum numbers but in different representations of the chiral group and with different diquark content. We use a variational method to separate the ground state and excited states and determine the mixing coefficients for the optimal nucleon operators in terms of the ${\chi }_i.$ We clearly identify the negative parity resonances $N\left(1535\right)\mathrm{}$ and $N\left(1650\right)\mathrm{}$ and their masses agree well with experimental data. The mass of the observed excited positive parity state is too high to be interpreted as the Roper state. Our results for the mixing coefficients indicate that chiral symmetry is important for $N\left(1535\right)\mathrm{}$ and $N\left(1650\right)\mathrm{}$ states. We confront our data for the mixing coefficients with quark models and provide insights into the physics of the nucleon system and the nature of strong decays.

We present a lattice QCD calculation of the heavy quark expansion parameters ${\mu }_{\pi }^2$ and ${\mu }_G^2$ for heavy-light mesons and heavy-light-light baryons. The calculation is carried out on a ${20}^3\times 48$ lattice at $\beta =6.0\mathrm{}$ in the quenched approximation, using the lattice NRQCD action for heavy quarks. We obtain the parameters ${\mu }_{\pi }^2$ and ${\mu }_G^2$ in two different methods: a direct calculation of the matrix elements and an indirect calculation through the mass spectrum, and confirm that both the methods give consistent results. We also discuss an application to the lifetime ratios.

The charge form factor of the pion is calculated in lattice QCD. The nonperturbatively improved Sheikholeslami-Wohlert action is used together with the $O\left(a\right)\mathrm{}$ improved vector current. Other choices for the current are examined. The form factor is extracted for pion masses from 970 down to 360 MeV and for momentum transfers $Q^2<~2{\mathrm{GeV}}^2.$ The mean square charge radius is extracted and compared to previous determinations, and its extrapolation to lower masses discussed.

The long-distance contribution via the two-photon intermediate state to the forward-backward asymmetries in decays $K^{+}\to {\pi }^{+}{\mathcal{l}}^{+}{\mathcal{l}}^{-}$ $(\mathcal{l}=e$ and $\mu )$ has been studied within the standard model. In order to evaluate the dispersive part of the $K^{+}\to {\pi }^{+}{\gamma }^{*}{\gamma }^{*}\to {\pi }^{+}{\mathcal{l}}^{+}{\mathcal{l}}^{-}$ amplitude, we employ a phenomenological form factor to soften the ultraviolet behavior of the transition. It is found that this long-distance transition, although subject to some theoretical uncertainties, can lead to significant contributions to the forward-backward asymmetries, which could be tested in future high-precise experiments.