We develop a general formalism to treat, in general relativity, the nonradial oscillations of a superfluid neutron star about static (non-rotating) configurations. The matter content of these stars can, as a first approximation, be described by a two-fluid model: one fluid is the neutron superfluid, which is believed to exist in the core and inner crust of mature neutron stars; the other fluid is a conglomerate of all charged constituents (crust nuclei, protons, electrons, etc.). We use a system of equations that governs the perturbations both of the metric and of the matter variables, whatever the equation of state for the two fluids. The entrainment effect is explicitly included. We also take the first step towards allowing for the superfluid to be confined to a part of the star by allowing for an outer envelope composed of ordinary fluid. We derive and implement the junction conditions for the metric and matter variables at the core-envelope interface, and briefly discuss the nature of the involved phase transition. We then determine the frequencies and gravitational-wave damping times for a simple model equation of state, incorporating entrainment through an approximation scheme which extends present Newtonian results to the general relativistic regime. We investigate how the quasinormal modes of a superfluid star are affected by changes in the entrainment parameter, and unveil a series of avoided crossings between the various modes. We provide a proof that, unless the equation of state is very special, all modes of a two-fluid star must radiate gravitationally. We also discuss the future detectability of pulsations in a superfluid star and argue that it may be possible (given advances in the relevant technology) to use gravitational-wave data to constrain the parameters of superfluid neutron stars.

We reexamine in some more detail a recent specific proposal for the breaking of the electroweak symmetry and of supersymmetry by a compact extra dimension. Possible mass terms for the Higgs boson and the matter hypermultiplets are considered and their effects on the spectrum analyzed. Previous conclusions are reinforced and put on firmer ground.

We explore CP violation in a left-right-model that reproduces the quark mass and CKM rotation angle hierarchies in a relatively natural way by fixing the bidoublet Higgs VEVs to be in the ratio $m_b{:m}_t.$ Our model is quite general and allows for CP to be broken by both the Higgs VEVs and the Yukawa couplings. Despite this generality, CP violation may be parametrized in terms of two basic phases. A very interesting feature of the model is that the mixing angles in the right-handed sector are found to be equal to their left-handed counterparts to a very good approximation. Furthermore, the right-handed analogue of the usual CKM phase ${\delta }_L$ is found to satisfy the relation ${\delta }_R\approx {\delta }_L.$ The parameter space of the model is explored by using an adaptive Monte Carlo algorithm and the allowed regions in parameter space are determined by enforcing experimental constraints from the K and B systems. This method of solution allows us to evaluate the left-and right-handed CKM matrices numerically for various combinations of the two fundamental CP-odd phases in the model. We find that all experimental constraints may be satisfied with right-handed W and flavor changing neutral Higgs boson masses as low as about 2 TeV and 7 TeV, respectively.

We discuss the behavior of two point functions for Polyakov loops in an $\mathrm{SU}\left(3\right)\mathrm{}$ gauge theory about the critical temperature $T_c.$ From a $Z\left(3\right)\mathrm{}$ model, in mean field theory we obtain a prediction for the ratio of masses at $T_c,$ extracted from correlation functions for the imaginary and real parts of the Polyakov loop. This ratio is $m_i{/m}_r=3\mathrm{}$ if the potential only includes terms up to quartic order in the Polyakov loop; its value changes as pentic and hexatic interactions become important. The Polyakov loop model then predicts how $m_i{/m}_r$ changes above $T_c.$

The coherent $\mu -e$ conversion rates in various nuclei are calculated for general lepton flavor violating interactions. We solve the Dirac equations numerically for the initial state muon and the final state electron in the Coulomb force, and perform the overlap integrations between the wave functions and the nucleon densities. The results indicate that the conversion branching ratio increases for a light nucleus up to the atomic number $Z\sim 30,$ is largest for $Z=30\mathrm{}–60,$ and becomes smaller for a heavy nucleus with $Z\gtrsim 60.$ We also discuss the uncertainty from the input proton and neutron densities. The atomic number dependence of the conversion ratio calculated here is useful to distinguish theoretical models with lepton flavor violation.

I compute the complete two-loop effective potential for the minimal supersymmetric standard model in the Landau gauge. This enables an accurate determination of the minimization conditions for the vacuum expectation values of the Higgs fields. Checks on the result follow from supersymmetric limits and from renormalization-scale invariance. The renormalization group equations for the field-independent vacuum energy and the vacuum expectation values are also presented. I provide numerical examples showing the improved accuracy and scale dependence obtained with the full two-loop effective potential.

New positivity bounds are derived for generalized (off-forward) parton distributions using the impact parameter representation. These inequalities are stable under the evolution to higher normalization points. The full set of inequalities is infinite. Several particular cases are considered explicitly.

The azimuthal spin asymmetries for pion production in semi-inclusive deep inelastic scattering of unpolarized charged lepton beams on longitudinally polarized nucleon targets are reanalyzed by taking into account an important sign correction to previous formulas. It is found that different approaches of distribution functions and fragmentation functions may lead to distinct predictions on the azimuthal asymmetries measured in the HERMES experiments; thus, the available data cannot be considered as a direct measurement of quark transversity distributions, although they still can serve to provide useful information on these distributions and on T-odd fragmentation functions. Predictions of the azimuthal spin asymmetries for kaon production are also presented, with different approaches of distribution and fragmentation functions. The unfavored fragmentation functions cannot be neglected for $K^{-}$ and $K_S^0$ production in semi-inclusive deep inelastic processes.

The $O\left({\alpha }^2\ln {(m}_{\mu }{/m}_e\right))$ corrections to the electron energy spectrum in muon decay are computed using the perturbative fragmentation function approach. The magnitude of these corrections is comparable to the anticipated precision of the TWIST experiment where the Michel parameters will be extracted from the measurement of the electron energy spectrum in muon decay.

We discuss the neutrino mass matrix which predicts zero or small values of $|V_{13}|$ in the MSSM and find the inequality, ${\sin }^{2}2{\theta }_{12}<~{\sin }^{2}2{\theta }_{\odot },$ where ${\sin }^{2}2{\theta }_{12}$ is the mixing angle at the $M_R$ scale and ${\sin }^{2}2{\theta }_{\odot }$ is the value determined by the solar neutrino oscillation. This constraint says that the model which predicts a larger value of ${\tan }^2{\theta }_{12}$ at $M_R$ than the experimental value is excluded. In particular, the bimaximal mixing scheme at the $M_R$ scale is excluded from the experimental value ${\tan }^2{\theta }_{\odot }<1.\mathrm{}$ In this model, $|V_{13}|$ and a Dirac phase at $m_Z$ which are induced radiatively may not be small.

The latest $g_{\mu }-2$ measurement by Brookhaven National Laboratory (BNL) confirms the earlier measurement with twice the precision. However, interpretation of the result requires specific assumptions regarding the errors in the hadronic light by light (LBL) correction and in the hadronic vacuum polarization correction. Under the assumption that the recent reanlayses of the LBL correction are valid, the new BNL result implies a deviation between experiment and the standard model of $1.6\sigma -2.6\sigma$ depending on the estimate of the hadronic vacuum polarization correction. We reexamine the $g_{\mu }-2$ constraint for minimal supergravity and its implications for the direct detection of sparticles at colliders and for the search for supersymmetric dark matter in view of the new evaluation.

We calculate the equation of state for degenerate quark matter to leading order in hard-dense-loop (HDL) perturbation theory. We solve the Tolman-Oppenheimer-Volkov equations to obtain the mass-radius relation for dense quark stars. Both the perturbative QCD and the HDL equations of state have a large variation with respect to the renormalization scale for $\mu \lesssim 1\mathrm{GeV}$ which leads to large theoretical uncertainties in the quark star mass-radius relation.

We investigate the role of adiabatic matter creation in driving the current cosmic acceleration. We consider a phenomenological model in which the particles source has the form $\Psi =3\mathrm{}\beta {\mathrm{nH}}_0{(H/H}_0{)}^{\alpha },$ where $\alpha$ and $\beta$ are dimensionless constants, n is the particle number density, and $H_0$ is the present value of the Hubble parameter. We introduce a cosmological constant in the model and use SNe Ia data to obtain confidence contours in the $({\Omega }_{m0\mathrm{}},$ $\beta )$ plane for fixed values of $\alpha .$ We conclude that current SNe Ia data do not impose strong constraints on possible values of the parameter $\beta$ if we do not consider any information on ${\Omega }_{m0\mathrm{}}.$ Assuming a Gaussian prior, such that ${\Omega }_{m0\mathrm{}}=0.27\mathrm{}\pm 0.06,$ the data now prefer values of $\beta$ close to zero, indicating that the particle creation mechanism is not favored to explain the cosmic acceleration. Finally, we simulate the data to be obtained with the proposed Supernova Acceleration Probe and estimate the constraints they will impose on $\beta .$

Recent observations suggest that the universe is in a state of accelerated cosmic expansion. Herewith we investigate this scenario within the Born-Infeld theory, which has been employed to describe open strings ending on D-branes. A multidimensional model with a topology $R\times S^3\times S^d,$ a cosmological constant, dust matter, and gauge fields is considered for that purpose. Two situations are subsequently discussed, according to whether string effects are (i) dominant or (ii) induce perturbations in the gauge field sector. Studying the set of equations governing the cosmological dynamics, we find that Born-Infeld cosmology can be compatible with the presently measured acceleration, together with a compactified internal space. This is shown to depend on the gauge field components in the internal dimensions as well as string modifications to the gauge matter sector. Furthermore, we argue regarding situation (i) that quintessence could constitute a transient stage.

We construct rotating hairy black holes in SU(2) Einstein-Yang-Mills theory. These stationary axially symmetric black holes are asymptotically flat. They possess non-trivial non-Abelian gauge fields outside their regular event horizon, and they carry non-Abelian electric charge. In the limit of vanishing angular momentum, they emerge from the neutral static spherically symmetric Einstein-Yang-Mills black holes, labeled by the node number of the gauge field function. With increasing angular momentum and mass, the non-Abelian electric charge of the solutions increases, but remains finite. The asymptotic expansion for these black hole solutions includes noninteger powers of the radial variable.

The remarkable agreement of electroweak data with standard model (SM) predictions motivates the study of extensions of the SM in which the Higgs boson is light and couples in a standard way to the weak gauge bosons. Postulated new light particles should have small couplings to the gauge bosons. Within this context it is natural to assume that the branching fractions of the light SM-like Higgs boson mimic those in the standard model. This assumption may be unwarranted, however, if there are nonstandard light particles coupled weakly to the gauge bosons but strongly to the Higgs field. In particular, the Higgs boson may effectively decay into hadronic jets, possibly without important bottom or charm flavor content. As an example, we present a simple extension of the SM, in which the predominant decay of the Higgs boson occurs into a pair of light bottom squarks that, in turn, manifest themselves as hadronic jets. Discovery of the Higgs boson remains possible at an electron-positron linear collider, but prospects at hadron colliders are diminished substantially.

We experiment with modifications of the BSSN form of the Einstein field equations (a reformulation of the ADM equations) and demonstrate how these modifications affect the stability of numerical black hole evolution calculations. We use excision to evolve both nonrotating and rotating Kerr-Schild black holes in octant and equatorial symmetry, and without any symmetry assumptions, and obtain accurate and stable simulations for specific angular momenta $J/M$ of up to about $0.9M.$

We consider a minisuperspace model for a closed universe with small and positive cosmological constant $\Lambda ,$ filled with a massive scalar field conformally coupled to gravity. In the quantum version of this model, the universe may undergo a tunneling transition through an effective barrier between regions of small and large scale factors. We solve numerically the minisuperspace Wheeler-DeWitt equation with tunneling boundary conditions for the wave function of the universe, and find that tunneling in quantum cosmology is quite different from that in quantum mechanics. Namely, the matter degree of freedom gets excited under the barrier, provided its interaction with the scale factor is not too weak, and makes a strong back reaction onto tunneling. In the semiclassical limit of small $\Lambda ,$ the matter energy behind the barrier is close to the height of the barrier: the system “climbs up” the barrier, and then evolves classically from its top. These features are even more pronounced for inhomogeneous modes of matter field. Extrapolating to field theory we thus argue that high momentum particles are copiously created in the tunneling process. Nevertheless, we find empirical evidence for the semiclassical-type scaling with $\Lambda$ of the wave function under and behind the barrier.

The ESA mission BepiColombo will explore the planet Mercury with equipment allowing an extremely accurate tracking. While determining its orbit around Mercury, it will be possible to indirectly observe the motion of its center of mass, with an accuracy several orders of magnitude better than what is possible by radar ranging to the planet’s surface. This is an opportunity to conduct a relativity experiment which will be a modern version of the traditional tests of general relativity, based upon Mercury’s perihelion advance and the relativistic light propagation near the Sun. We define the mathematical methods to be used to extract from the data of the BepiColombo mission, as presently designed, the best constraints on the main post-Newtonian parameters, especially $\beta ,\gamma$ and the Nordtvedt parameter $\eta ,$ but also the dynamic oblateness of the Sun $J_{2\odot }$ and the preferred frame parameters ${\alpha }_1,{\alpha }_2.$ We have performed a full cycle simulation of the BepiColombo radio science experiments, including this relativity experiment, with the purpose of assessing in a realistic (as opposed to formal) way the accuracy achievable on each parameter of interest. For $\gamma$ the best constraint can be obtained by means of a dedicated superior conjunction experiment, with a realistic accuracy $\simeq 2\times {10}^{-6}.$ For $\beta$ the main problem is the very strong correlation with $J_{2\odot };$ if the Nordtvedt relationship $\eta =4\mathrm{}\beta -\gamma -3$ is used, as it is legitimate in the metric theories of gravitation, a realistic accuracy of $\simeq 2\times {10}^{-6}$ for $\beta$ and $\simeq 2\times {10}^{-9}$ for $J_{2\odot }$ can be achieved, while $\eta$ itself is constrained within $\simeq {10}^{-5}.$ If the preferred frame parameters ${\alpha }_1,{\alpha }_2$ are included in the analysis, they can be constrained within $\simeq 8\times {10}^{-6}$ and $\simeq {10}^{-6},$ respectively, at the price of some degradation in $\beta ,$ $J_{2\odot }$ and $\eta .$ It is also possible to test the change with time of the gravitational constant G, but the results are severely limited because of the problems of absolute calibration of the ranging transponder, to the point that the improvement as compared with other techniques (such as lunar laser ranging) is not so important.

We investigate spherically symmetric self-similar solutions in Brans-Dicke theory. Assuming a perfect fluid with the equation of state $p=\left(\gamma -1\right)\mu (1\mathrm{}<~\gamma <2),$ we show that there are no nontrivial solutions which approach asymptotically to the flat Friedmann-Robertson-Walker spacetime if the energy density is positive. This result suggests that primordial black holes in Brans-Dicke theory cannot grow at the same rate as the size of the cosmological particle horizon.