We study vacuum structure of $\mathcal{N}=2$ supersymmetric (SUSY) QCD, based on the gauge group $SU(2)$ with $N_f=2$ flavors of massive hypermultiplet quarks, in the presence of nonzero baryon chemical potential ($\mu$). The theory has a classical vacuum preserving baryon number symmetry, when a mass term, which breaks $\mathcal{N}=2$ SUSY but preserves $\mathcal{N}=1$ SUSY, for the adjoint gauge chiral multiplet ($m_{\mathrm{ad}}$) is introduced. By using the exact result of $\mathcal{N}=2$ SUSY QCD, we analyze low energy effective potential at the leading order of perturbation with respect to small SUSY breaking parameters, $\mu$ and $m_{\mathrm{ad}}$. We find that the baryon number is broken as a consequence of the $SU(2)$ strong gauge dynamics, so that color superconductivity dynamically takes place at the non-SUSY vacuum.

A wide-field galaxy redshift survey allows one to probe galaxy clustering at largest spatial scales, which carries invaluable information on horizon-scale physics complementarily to the cosmic microwave background (CMB). Assuming the planned survey consisting of $z\sim 1$ and $z\sim 3$ surveys with areas of 2000 and $300{\mathrm{deg}}^2$, respectively, we study the prospects for probing dark energy clustering from the measured galaxy power spectrum, assuming the dynamical properties of dark energy are specified in terms of the equation of state and the effective sound speed $c_{\mathrm{e}}$ in the context of an adiabatic cold dark dominated matter model. The dark energy clustering adds a power to the galaxy power spectrum amplitude at spatial scales greater than the sound horizon, and the enhancement is sensitive to redshift evolution of the net dark energy density, i.e. the equation of state. We find that the galaxy survey, when combined with CMB expected from the Planck satellite mission, can distinguish dark energy clustering from a smooth dark energy model such as the quintessence model ($c_{\mathrm{e}}=1$), when $c_{\mathrm{e}}\lesssim 0.04$ (0.02) in the case of the constant equation of state $w_0=-0.9$ ($-0.95$). An ultimate full-sky survey of $z\sim 1$ galaxies allows the detection when $c_{\mathrm{e}}\lesssim 0.08$ (0.04) for $w_0=0.9$ ($-0.95$). These forecasts show a compatible power with an all-sky CMB and galaxy cross correlation that probes the integrated Sachs-Wolfe effect. We also investigate a degeneracy between the dark energy clustering and the nonrelativistic neutrinos implied from the neutrino oscillation experiments, because the two effects both induce a scale-dependent modification in the galaxy power spectrum shape at largest spatial scales accessible from the galaxy survey. It is shown that a wider redshift coverage can efficiently separate the two effects by utilizing the different redshift dependences, where dark energy clustering is apparent only at low redshifts $z\lesssim 1$.

We evaluate the mass function of virialized halos, by using Press & Schechter (PS) and/or Steth & Tormen (ST) expressions, for cosmologies where dark energy (DE) is due to a scalar self-interacting field, coupled with dark matter (DM). We keep to coupled DE (cDE) models known to fit linear observables. To implement the PS-ST approach, we start from reviewing and extending the results of a previous work on the growth of a spherical top-hat fluctuation in cDE models, confirming their most intriguing astrophysical feature, i.e. a significant baryon-DM segregation, occurring well before the onset of any hydrodynamical effect. Accordingly, the predicted mass function depends on how halo masses are measured. For any option, however, the coupling causes a distortion of the mass function, still at $z=0$. Furthermore, the $z$-dependence of cDE mass functions is mostly displaced, in respect to $\Lambda \mathrm{CDM}$, in the opposite way of uncoupled dynamical DE. This is an aspect of the basic underlying result, that even a little DM-DE coupling induces relevant modifications in the nonlinear evolution. Therefore, without causing great shifts in linear astrophysical observables, the DM-baryon segregation induced by the coupling can have an impact on a number of cosmological problems, e.g., galaxy satellite abundance, spiral disk formation, apparent baryon shortage, entropy input in clusters, etc..

We study the scattering lengths of charmonia ($J/\psi$ and ${\eta }_c$) with light hadrons ($\pi$, $\rho$, and $N$) by the quenched lattice QCD simulations on ${24}^3\times 48$, ${32}^3\times 48$, and ${48}^3\times 48$ lattices with the lattice spacing $a\simeq 0.068\mathrm{fm}$. The scattering length is extracted by using the Lüscher’s phase-shift formula together with the measurement of the energy shift $\Delta E$ of two hadrons on the lattice. We find that there exist attractive interactions in all channels, $J/\psi ({\eta }_c)\mathrm{\text{−}}\pi$, $J/\psi ({\eta }_c)\mathrm{\text{−}}\rho$, and $J/\psi ({\eta }_c)\mathrm{\text{−}}N$: The $s$-wave $J/\psi \mathrm{\text{−}}\pi$ (${\eta }_c\mathrm{\text{−}}\pi$) scattering length is determined as $0.0119\pm 0.0039\mathrm{fm}$ ($0.0113\pm 0.0035\mathrm{fm}$) and the corresponding elastic cross section at the threshold becomes ${0.018}_{-0.010}^{+0.013}\mathrm{mb}$ (${0.016}_{-0.008}^{+0.011}\mathrm{mb}$). Also, the $J/\psi \mathrm{\text{−}}N$ (${\eta }_c\mathrm{\text{−}}N$) spin-averaged scattering length is $0.71\pm 0.48\mathrm{fm}$ ($0.70\pm 0.66\mathrm{fm}$), which is at least an order of magnitude larger than the charmonium-pion scattering length. The volume dependence of the energy shifts is also investigated to check the expected $1/L^3$ behavior of $\Delta E$ at a large spatial size $L$.

As strong evidence for inflation, relic gravitational waves (RGW) have been extensively studied. Although they have not been detected yet, some constraints have been achieved by observations. Future experiments for RGW detection are mainly of two kinds: CMB experiments and laser interferometers. In this paper, we study these current constraints and the detective abilities of future experiments. We calculate the strength of RGW ${\Omega }_g(k)$ using two methods: the analytic method and the numerical method, by solving the inflationary flow equations. By the first method, we obtain a bound ${\Omega }_g<3.89\times {10}^{-16}$ at $\nu =0.1\mathrm{Hz}$, where we have used the current constraints on the scalar spectral index and the tensor-scalar ratio; furthermore, we have taken into account the redshift-suppression effect, the accelerating expansion effect, and the neutrino damping effect on RGW. But the analytic expression of ${\Omega }_g(k)$ depends on specific inflationary models and does not apply well for the waves with very high frequencies. The numerical method is more precise for the waves with high frequencies. It gives a bound ${\Omega }_g<8.62\times {10}^{-14}$, which is independent of the inflationary parameters, and applies to any single-field slow-roll inflationary model. After considering the current constraints on the inflationary parameters, this bound becomes ${\Omega }_g<2\times {10}^{-17}$. These two methods give consistent conclusions: the current constraints on RGW from LIGO, big bang nucleosynthesis, and pulsar timing are too loose to give any constraint for the single-field inflationary models, and the constraints from WMAP are relatively tighter. Future laser interferometers are more effective for detecting RGW with the smaller tensor-scalar ratio, but the CMB experiments are more effective for detecting the waves with the larger ratio. These detection methods are complementary to each other for the detection of RGW.

Recent type Ia supernova measurements and other astronomical observations suggest that our Universe is, at the present epoch, in an accelerating phase of evolution. While a dark energy of unknown form and origin is usually proposed as the most feasible mechanism for the acceleration, there appeared some generalizations of Einstein equations which could mimic dark energy. In this work we investigate observational constraints on a modified Friedmann equation obtained from the generalized Lagrangian $\mathcal{L}\propto R^n$ minimally coupled with matter via the Palatini first-order formalism. We mainly concentrate on such restrictions of model parameters which can be derived from distant supernovae and baryon oscillation tests. We obtain confidence levels for two parameters ($n$, ${\Omega }_{m,0}$) and find, from combined analysis, that the preferred value of ${\Omega }_{m,0}$ equals 0.3. For deeper statistical analysis and for comparison of our model with predictions of the $\Lambda \mathrm{CDM}$ concordance model, one applies Akaike and Bayesian information criteria of model selection. Finally, we conclude that the Friedmann-Robertson-Walker model merged with a first-order nonlinear gravity survives SNIa and baryon oscillation tests.

We construct an extension of the minimal supersymmetric standard model in which superpartners can naturally be heavier than the electroweak scale. This “little hierarchy” of scales is stable because the Higgs arises as a pseudo-Nambu-Goldstone boson in the breaking of an accidental $SU(4)$ symmetry of the Higgs sector. Supersymmetry and the global symmetry combine to forbid logarithmically divergent one-loop contributions to the Higgs mass. The accidental symmetry follows from a simple twin parity which exchanges the $SU(2)$ sectors in the $SU(3{)}_C\times SU(2{)}_L\times SU(2{)}_R\times U(1{)}_X$ gauge group.

We reinvestigate the problem of Gribov ambiguities within the Landau (or Lorentz) gauge for the ghost and gluon propagators in pure $SU(2)$ lattice gauge theory. We make use of the full symmetry group of the action taking into account large, i.e. nonperiodic, $\mathbb{Z}(2)$ gauge transformations leaving lattice plaquettes invariant. Enlarging in this way the gauge orbits for any given gauge field configuration the Landau gauge can be fixed at higher local extrema of the gauge functional in comparison with standard (overrelaxation) techniques. This has a clearly visible effect not only for the ghost propagator at small momenta but also for the gluon propagator, in contrast to the common belief.

We calculate the next-to-leading order (NLO) QCD corrections to $Wb\overline{b}$ production including full bottom-quark mass effects. We study the impact of NLO QCD corrections on the total cross section and invariant mass distribution of the bottom-quark jet pair at the Fermilab Tevatron $p\overline{p}$ collider. We perform a detailed comparison with a calculation that considers massless bottom quarks. We find that neglecting bottom-quark mass effects overestimates the NLO total cross section for $Wb\overline{b}$ production at the Tevatron by about 8% independent of the choice of renormalization and factorization scale.

We resum to next-to-leading order (NLO) the distribution in the light-cone momentum $p_{+}=E_X-|{\overrightarrow{p}}_X|$ and the spectrum in the electron energy $E_e$ in the semileptonic decays $B\to X_{u}l\nu$, where $E_X$ and ${\overrightarrow{p}}_X$ are the total energy and three-momentum of the final hadron state $X_u$ respectively. By expanding our formulae, we obtain the coefficients of all the infrared logarithms ${\alpha }_S^n{L}^k$ at $O({\alpha }_S^2)$ and at $O({\alpha }_S^3)$, with the exception of the ${\alpha }_S^{3}L$ coefficient. We explicitly show that the relation between these semileptonic spectra and the hadron mass distribution in the radiative decay $B\to X_s\gamma$ is not a purely short-distance one. By comparing our $O({\alpha }_S^2{n}_f)$ result for the $p_{+}$ distribution with a recent Feynman diagram computation, we obtain an explicit and nontrivial verification of our resummation scheme at the two-loop level ($n_f$ is the number of massless quark flavors). We also discuss the validity of the so-called Brodsky-Lepage-Mackenzie (BLM) scheme in the evaluation of the semileptonic spectra by comparing it with our results, finding that it is a reasonable approximation. Finally, we show that the long-distance phenomena, such as Fermi motion, are expected to have a smaller effect in the electron spectrum than in the hadron mass distribution.

We resum to next-to-leading order the distribution in the ratio of the invariant hadron mass $m_X$ to the total hadron energy $E_X$ and the distribution in $m_X$ in the semileptonic decays $B\to X_{u}l\nu$. By expanding our formulas, we obtain the coefficients of all the infrared logarithms at $O({\alpha }_S^2)$ and of the leading ones at $O({\alpha }_S^3)$. We explicitly show that the relation between these semileptonic spectra and the photon spectrum in the radiative decay $B\to X_s\gamma$ is not a purely short-distance one. There are long-distance effects in the semileptonic spectra which are not completely factorized by the structure function as measured in the radiative decay and have to be modeled in some way.

We evaluate threshold resummed spectra in $B\to X_{u}l\nu$ decays in next-to-leading order. We present results for the distribution in the hadronic variables $E_X$ and $m_X^2/E_X^2$, for the distribution in $E_X$ and for the distribution in $E_X$ and $E_l$, where $E_X$ and $m_X$ are the total energy and the invariant mass of the final hadronic state $X_u$ respectively and $E_l$ is the energy of the charged lepton. We explicitly show that all these spectra (where there is no integration over the hadronic energy) can be directly related to the photon spectrum in $B\to X_s\gamma$ via short-distance coefficient functions.

Phenomenological bounds on the neutrino mixing matrix $U$ are used to determine numerically the allowed range of real elements ($CP$ conserving case) for the symmetric neutrino mass matrix $M_{\nu }$ (Majorana case). For this purpose an adaptive Monte Carlo generator has been used. Histograms are constructed to show which forms of the neutrino mass matrix $M_{\nu }$ are possible and preferred. We confirm results found in the literature which are based on analytical calculations, though a few differences appear. These cases correspond to some textures with two zeros. The results show that, actually, both normal and inverted mass hierarchies are still possible at the $3\sigma$ confidence level.

We report on the results of a three-flavor oscillation analysis using Super-Kamiokande I atmospheric neutrino data, with the assumption of one mass scale dominance ($\Delta m_{12}^2=0$). No significant flux change due to matter effect, which occurs when neutrinos propagate inside the Earth for ${\theta }_{13}\ne 0$, has been seen either in a multi-GeV ${\nu }_e$-rich sample or in a ${\nu }_{\mu }$-rich sample. Both normal and inverted mass hierarchy hypotheses are tested and both are consistent with observation. Using Super-Kamiokande data only, 2-dimensional 90% confidence allowed regions are obtained: mixing angles are constrained to ${sin}^2{\theta }_{13}<0.14$ and $0.37<{sin}^2{\theta }_{23}<0.65$ for the normal mass hierarchy. Weaker constraints, ${sin}^2{\theta }_{13}<0.27$ and $0.37<{sin}^2{\theta }_{23}<0.69$, are obtained for the inverted mass hierarchy case.

We consider the problem of a scalar field, nonminimally coupled to gravity through a $-\xi {\varphi }^{2}R$ term, in the presence of a brane. Exact solutions, for a wide range of values of the coupling parameter $\xi$, for both $\varphi$-dependent and $\varphi$-independent brane tension, are derived and their behavior is studied. In the case of a Randall-Sundrum geometry, a class of the resulting scalar field solutions exhibits a folded-kink profile. We go beyond the Randall-Sundrum geometry studying general warp factor solutions in the presence of a kink scalar. Analytic and numerical results are provided for the case of a brane or for smooth geometries, where the scalar field acts as a thick brane. It is shown that finite geometries with warp factors that asymptotically decrease exponentially are realizable for a wide range of parameter values. We also study graviton localization in our setup and find that the localizing potential for gravitons with the characteristic volcanolike profile develops a local maximum located at the origin for high values of the coupling $\xi$.

We present improved worldline numerical algorithms for high-precision calculations of Casimir interaction energies induced by scalar-field fluctuations with Dirichlet boundary conditions for various Casimir geometries. Significant reduction of numerical cost is gained by exploiting the symmetries of the worldline ensemble in combination with those of the configurations. This facilitates high-precision calculations on standard PCs or small clusters. We illustrate our strategies using the experimentally most relevant sphere-plate and cylinder-plate configuration. We compute Casimir curvature effects for a wide parameter range, revealing the tight validity bounds of the commonly used proximity force approximation (PFA). We conclude that data analysis of future experiments aiming at a precision of 0.1% must no longer be based on the PFA. Revisiting the parallel-plate configuration, we find a mapping between the $D$-dimensional Casimir energy and properties of a random-chain polymer ensemble.

The pure-gravity sector of the minimal standard-model extension is studied in the limit of Riemann spacetime. A method is developed to extract the modified Einstein field equations in the limit of small metric fluctuations about the Minkowski vacuum, while allowing for the dynamics of the 20 independent coefficients for Lorentz violation. The linearized effective equations are solved to obtain the post-Newtonian metric. The corresponding post-Newtonian behavior of a perfect fluid is studied and applied to the gravitating many-body system. Illustrative examples of the methodology are provided using bumblebee models. The implications of the general theoretical results are studied for a variety of existing and proposed gravitational experiments, including lunar and satellite laser-ranging, laboratory experiments with gravimeters and torsion pendula, measurements of the spin precession of orbiting gyroscopes, timing studies of signals from binary pulsars, and the classic tests involving the perihelion precession and the time delay of light. For each type of experiment considered, estimates of the attainable sensitivities are provided. Numerous effects of local Lorentz violation can be studied in existing or near-future experiments at sensitivities ranging from parts in ${10}^4$ down to parts in ${10}^{15}$.

We study black hole formation in the head-on collision of ultrarelativistic charges. The metric of charged particles is obtained by boosting the Reissner-Nordström spacetime to the speed of light. Using the slice at the instant of collision, we study formation of the apparent horizon (AH) and derive a condition indicating that a critical value of the electric charge is necessary for formation to take place. Evaluating this condition for characteristic values at the LHC, we find that the presence of charge decreases the black hole production rate in accelerators. We comment on possible limitations of our approach.

Equations of motion for a real self-gravitating scalar field in the background of a black hole with negative cosmological constant were solved numerically. We obtain a sequence of static axisymmetric solutions representing thick domain wall cosmological black hole systems, depending on the mass of black hole, cosmological parameter and the parameter binding black hole mass with the width of the domain wall. For the case of extremal cosmological black hole the expulsion of scalar field from the black hole strongly depends on it.

We present some analytical solutions to the Einstein equations, describing radiating collapsing spheres in the diffusion approximation. Solutions allow for modeling physical reasonable situations. The temperature is calculated for each solution, using a hyperbolic transport equation, which permits to exhibit the influence of relaxational effects on the dynamics of the system.