Masses and topological charges of the $\eta$ and ${\eta }^{\prime }$ mesons are expressed in terms of the singlet-octet mixing angle $\theta$. Contributions of the pseudoscalar $0^{-}$ continuum are evaluated in a model independent way. Applications to the decay $\eta \to 3\pi$ and to the radiative decay of vector mesons involving $\eta$ and ${\eta }^{\prime }$ are considered. Agreement with experiment is, in general, good and the results quite stable for $-30.5°\lesssim \theta \lesssim -18.5°$.

We analytically perform the transverse momentum integrations in the real corrections to the longitudinal ${\gamma }_L^{*}$ impact factor. The resulting integrals are Feynman parameter integrals, and we provide a MATHEMATICA file which contains the integrands. The remaining integrals are carried out numerically. We perform a numerical test, and we compute those parts of the impact factor which depend upon the energy scale $s_0$: They are found to be negative and, with decreasing values of $s_0$, their absolute value increases.

We reanalyze the magnetic moments of the baryon octet, decuplet, and antidecuplet within the framework of the chiral quark-soliton model, with SU(3) symmetry-breaking taken into account. We consider the contributions of the mixing of higher representations to the magnetic moment operator arising from the SU(3) symmetry-breaking. Dynamical parameters of the model are fixed by experimental data for the magnetic moments of the baryon octet and from the masses of the octet, decuplet and of ${\Theta }^{+}$. The magnetic moment of ${\Theta }^{+}$ depends rather strongly on the pion-nucleon sigma term and reads $-1.19\mathrm{n}\mathrm{m}$ to $-0.33\mathrm{n}\mathrm{m}$ for ${\Sigma }_{\pi N}=45$ and 75 MeV, respectively. The recently reported mass of ${\Xi }_{\overline{10}}^{--}(1862)$ is compatible with ${\Sigma }_{\pi N}=73\mathrm{M}\mathrm{e}\mathrm{V}$. As a by-product the strange magnetic moment of the nucleon is obtained with a value of ${\mu }_N^{(s)}=+0.39\mathrm{n}\mathrm{m}$.

We present a study of the tensorial structure of the hadronic matrix elements of the angular momentum operators $\mathit{J}$. Well known results in the literature are shown to be incorrect, and we have taken pains to derive the correct expressions in three different ways, two involving explicit physical wave packets and the third, totally independent, based upon the rotational properties of the state vectors. Surprisingly it turns out that the results are very sensitive to the type of relativistic spin state used to describe the motion of the particle, i.e., whether a canonical (i.e., boost) state or a helicity state is utilized. We present results for the matrix elements of the angular momentum operators, valid in an arbitrary Lorentz frame, for both helicity states and canonical states. These results are relevant for the construction of angular momentum sum rules, relating the angular momentum of a nucleon to the spin and orbital angular momentum of its constituents. It turns out that it is necessary to distinguish carefully whether the motion of the partons is characterized via canonical or helicity spin states. Fortunately, for the simple parton model interpretation, when the proton moves along $OZ$, our results for the sum rule based upon the matrix elements of $J_z$ agree with the often used sum rule found in the literature. But for the components $J_x,J_y$ the results are different and lead to a new and very intuitive sum rule for transverse polarization.

We discuss the impact of the recent KamLAND constraint on the solar antineutrino flux on the analysis of solar neutrino data in the presence of Majorana neutrino transition magnetic moments and solar magnetic fields. We consider different stationary solar magnetic field models, both regular and random, highlighting the strong enhancement in the antineutrino production rates that characterize turbulent solar magnetic field models. Moreover, we show that for such magnetic fields inside the Sun, one can constrain the intrinsic neutrino magnetic moment down to the level of ${\mu }_{\nu }\lesssim \mathrm{f}\mathrm{e}\mathrm{w}\times {10}^{-12}{\mu }_B$ irrespective of details of the underlying turbulence model. This limit is more stringent than all current experimental sensitivities, and similar to the most stringent bounds obtained from stellar cooling. We also comment on the robustness of this limit and show that at most it might be weakened by 1 order of magnitude, under very unlikely circumstances.

We have searched for ${\theta }^{+}(1.54)\to K^{0}p$ decays using data from the 1999 run of the HyperCP experiment at Fermilab. We see no evidence for a narrow peak in the $K_S^{0}p$ mass distribution near $1.54\mathrm{G}\mathrm{e}\mathrm{V}/c$ among 106 000 $K_S^{0}p$ candidates, and obtain an upper limit for the fraction of ${\theta }^{+}(1.54)$ to $K_S^{0}p$ candidates of $<0.3\%$ at 90% confidence.

An effective $\mathrm{U}(1)$ gauge invariant theory is constructed for a noncommutative Schrödinger field coupled to a background $\mathrm{U}(1{)}_{\star }$ gauge field in $2+1$-dimensions using first order Seiberg-Witten map. We show that this effective theory can be cast in the form of usual Schrödinger action with interaction terms of noncommutative origin provided the gauge field is of background type with constant magnetic field. The Galilean symmetry is investigated and a violation is found in the boost sector. We also consider the problem of Hall conductivity in this framework.

Several years ago it was found that perturbation theory for two-dimensional $O(N)$ models depends on boundary conditions even after the infinite volume limit has been taken termwise, provided $N>2$. There ensued a discussion whether the boundary conditions introduced to show this phenomenon were somehow anomalous and there was a class of “reasonable” boundary conditions not suffering from this ambiguity. Here we present the results of some computations that may be interpreted as giving some support for the correctness of perturbation theory with conventional boundary conditions; however the fundamental underlying question of the correctness of perturbation theory in these models and, in particular, the perturbative $\beta$ function remain challenging problems of mathematical physics.

We consider scalar-tensor theories in $D$-dimensional spacetime, $D\ge 4$. They consist of a metric and a nonminimally coupled scalar field, with its nonminimal coupling characterized by a function. The probes couple minimally to the metric only. We obtain vacuum solutions—both cosmological and static spherically symmetric ones—and study their properties. We find that, as seen by the probes, there is no singularity in the cosmological solutions for a class of functions which obey certain constraints. It turns out that for the same class of functions, there are static spherically symmetric solutions which exhibit novel properties: e.g., near the “horizon,” the gravitational force as seen by the probe becomes repulsive.

We outline the covariant nature, with respect to the choice of a reference frame, of the chaos characterizing the generic cosmological solution near the initial singularity, i.e., the so-called inhomogeneous mixmaster model. Our analysis is based on a gauge independent Arnowitt-Deser-Misner reduction of the dynamics to the physical degrees of freedom. The resulting picture shows how the inhomogeneous mixmaster model is isomorphic point by point in space to a billiard on a Lobachevsky plane. Indeed, the existence of an asymptotic (energylike) constant of the motion allows one to construct the Jacobi metric associated with the geodesic flow and to calculate a nonzero Lyapunov exponent in each space point. The chaos covariance emerges from the independence of our scheme with respect to the form of the lapse function and the shift vector; the origin of this result relies on the dynamical decoupling of the space points which takes place near the singularity, due to the asymptotic approach of the potential term to infinite walls. At the ground of the obtained dynamical scheme is the choice of Misner-Chitré-like variables which allows one to fix the billiard potential walls.

We discuss the systematic uncertainties in the recovery of dark energy properties from the use of baryon acoustic oscillations as a standard ruler. We demonstrate that while unknown relativistic components in the universe prior to recombination would alter the sound speed, the inferences for dark energy from low-redshift surveys are unchanged so long as the microwave background anisotropies can measure the redshift of matter-radiation equality, which they can do to sufficient accuracy. The mismeasurement of the radiation and matter densities themselves (as opposed to their ratio) would manifest as an incorrect prediction for the Hubble constant at low-redshift. In addition, these anomalies do produce subtle but detectable features in the microwave anisotropies.

We discuss the potential of long-baseline neutrino oscillation experiments to determine deviations from maximal ${\nu }_{\mu }\mathrm{\text{−}}{\nu }_{\tau }$ mixing. We compare the obtainable sensitivities to predictions from neutrino mass models and to the size of quantum corrections. We find that the theoretical expectations for deviations are typically well within experimental reach.

The Weakly Interacting Massive Particle (WIMP) is one of the main candidates for the relic dark matter (DM). In the effective low-energy minimal supersymmetric standard model (effMSSM) the neutralino nucleon spin and scalar cross sections in the low-mass regime were calculated. The calculated cross sections are compared with almost all experimental currently available exclusion curves for spin-dependent WIMP-proton and WIMP-neutron cross sections. It is demonstrated that in general about 2 orders of magnitude improvement of the current DM experiment sensitivities is needed to reach the (effMSSM) supersymmetric (SUSY) predictions. At the current level of accuracy it looks reasonable to safely neglect subdominant spin WIMP nucleon contributions analyzing the data from spin-nonzero targets. To avoid misleading discrepancies between data and SUSY calculations it is, however, preferable to use a mixed spin-scalar coupling approach. This approach is applied to estimate future prospects of experiments with the odd-neutron high-spin isotope ${}^{\mathrm{73}}\mathrm{G}\mathrm{e}$. It is noticed that the DAMA evidence favors the light Higgs sector in the effMSSM, a high event rate in a ${}^{\mathrm{73}}\mathrm{G}\mathrm{e}$ detector and relatively high up-going muon fluxes from relic neutralino annihilations in the Earth and the Sun.

A CPT violating decoherence scenario can easily account for all the experimental evidence in the neutrino sector including Liquid Scincillator Neutrino Detector. In this work it is argued that this framework can also accommodate the dark energy content of the Universe, as well as the observed matter-antimatter asymmetry.

We study string interaction rates in the Brandenberger-Vafa scenario, the very early universe cosmology of a gas of strings. This cosmology starts with the assumption that all spatial dimensions are compact and initially have string scale radii; some dimensions grow due to some thermal or quantum fluctuation which acts as an initial expansion velocity. Based on simple arguments from the low-energy equations of motion and string thermodynamics, we demonstrate that the interaction rates of strings are negligible, so the common assumption of thermal equilibrium cannot apply. We also present a new analysis of the cosmological evolution of strings on compact manifolds of large radius. Then we discuss modifications that should be considered to the usual Brandenberger-Vafa scenario. To confirm our simple arguments, we give a numerical calculation of the annihilation rate of winding strings. In calculating the rate, we also show that the quantum mechanics of strings in small spaces is important.

We consider the low-energy description of 5D models of supergravity with boundaries comprizing a vector multiplet and the universal hypermultiplet in the bulk. We analyze the spontaneous breaking of supersymmetry induced by the vacuum expectation value of superpotentials on the boundary branes. When supersymmetry is broken, the moduli corresponding to the radion, the zero mode of the vector multiplet scalar field and the dilaton develop a potential in the effective action. We compute the resulting soft breaking terms and give some indications on the features of the corresponding particle spectrum. We consider some of the possible phenomenological implications when supersymmetry is broken on the hidden brane.

Using G-structure language, a systematic, iterative formalism for computing necessary and sufficient conditions for the existence of $N$ arbitrary linearly independent Killing spinors, in any supergravity, is presented. The key organizational tool is the common isotropy group of the Killing spinors. The formalism is illustrated for configurations in gauged SU(2) supergravity in seven dimensions admitting at least one null Killing spinor, and the possible isotropy groups are shown to be $[\mathrm{S}\mathrm{U}(2)⋉{\mathbb{R}}^4]\times \mathbb{R}$, SU(2), ${\mathbb{R}}^5$, or the identity. The constraints associated with the existence of certain additional Killing spinors are computed and used to derive numerous solutions. A discussion of the relevance of the formalism to the complete classification of all supersymmetric configurations in $d=11$ is given.

A closed form analytic solution is found for the electromagnetic field of the charged uniformly rotating conducting disk for all values of the tip speed $v$ up to $c$. For $v=c$ it becomes the magic field of the Kerr-Newman black hole with $G$ set to zero. The field energy, field angular momentum, and gyromagnetic ratio are calculated and compared with those of the electron. A new mathematical expression that sums products of three Legendre functions, each of a different argument, is demonstrated.

We consider localization of gravity on thick branes with a nontrivial structure. Double walls that generalize the thick Randall-Sundrum solution, and asymmetric walls that arise from a $Z_2$ symmetric scalar potential, are considered. We present a new asymmetric solution: a thick brane interpolating between two ${\mathrm{A}\mathrm{d}\mathrm{S}}_5$ spacetimes with different cosmological constants, which can be derived from a “fake supergravity” superpotential, and show that it is possible to confine gravity on such branes.

We study the matching of locally rotationally symmetric spatially homogeneous collapsing dust space-times with nonstationary vacuum exteriors in cylindrical symmetry. Given an interior with diagonal metric we prove existence and uniqueness results for the exterior. The matched solutions contain trapped surfaces and singularities and are determined up to a limit surface $\mathcal{H}$ in the exterior. The solutions cannot be asymptotically flat and we present evidence that they are singular on the limit surface.