In this paper we investigate a solution of the Dirac equation for a spin-$\frac{1}{2}$ particle in a scalar potential well with full spherical symmetry. The energy eigenvalues for the quark particle in $s_{1/2}$ states (with $\kappa =-1$) and $p_{1/2}$ states (with $\kappa =1$) are calculated. We also study the continuous Dirac wave function for a quark in such a potential, which is not necessarily infinite. Our results, at infinite limit, are in good agreement with the MIT bag model. We make some remarks about the sharpness value of the wave function on the wall. This model, for finite values of potential, also could serve as an effective model for the nucleus where $U(r)$ is the effective single particle potential.

Spin degrees of freedom of the Galilean covariant Dirac field in $(4+1)$ dimensions and its nonrelativistic counterpart in $(3+1)$ dimensions are examined. Two standard choices of spin operator, the Galilean covariant and Dirac spin operators, are considered. It is shown that the Dirac spin of the Galilean covariant Dirac field in $(4+1)$ dimensions is not conserved, and the role of non-Galilean boosts in its nonconservation is stressed out. After reduction to $(3+1)$ dimensions the Dirac field turns into a nonrelativistic Fermi field with a conserved Dirac spin. A generalized form of the Lévy-Leblond equations for the Fermi field is given. One-particle spin states are constructed. A particle-antiparticle system is discussed.

The Einstein constraint equations have been the subject of study for more than 50 years. The introduction of the conformal method in the 1970s as a parametrization of initial data for the Einstein equations led to increased interest in the development of a complete solution theory for the constraints, with the theory for constant mean curvature (CMC) spatial slices and closed manifolds completely developed by 1995. The first general non-CMC existence result was establish by Holst et al. in 2008, with extensions to rough data by Holst et al. in 2009, and to vacuum spacetimes by Maxwell in 2009. The non-CMC theory remains mostly open; moreover, recent work of Maxwell on specific symmetry models sheds light on fundamental nonuniqueness problems with the conformal method as a parametrization in non-CMC settings. In parallel with these mathematical developments, computational physicists have uncovered surprising behavior in numerical solutions to the extended conformal thin sandwich formulation of the Einstein constraints. In particular, numerical evidence suggests the existence of multiple solutions with a quadratic fold, and a recent analysis of a simplified model supports this conclusion. In this article, we examine this apparent bifurcation phenomena in a methodical way, using modern techniques in bifurcation theory and in numerical homotopy methods. We first review the evidence for the presence of bifurcation in the Hamiltonian constraint in the time-symmetric case. We give a brief introduction to the mathematical framework for analyzing bifurcation phenomena, and then develop the main ideas behind the construction of numerical homotopy, or path-following, methods in the analysis of bifurcation phenomena. We then apply the continuation software package AUTO to this problem, and verify the presence of the fold with homotopy-based numerical methods. We discuss these results and their physical significance, which lead to some interesting remaining questions to investigate further.

We compute the gravitational wave background (GWB) generated by a cosmological population of black hole-black hole (BH-BH) binaries using hybrid waveforms recently produced by numerical simulations of (BH-BH) coalescence, which include the inspiral, merger, and ring-down contributions. A large sample of binary systems is simulated using the population synthesis code SeBa, and we extract fundamental statistical information on (BH-BH) physical parameters (primary and secondary BH masses, orbital separations and eccentricities, formation, and merger time scales). We then derive the binary birth and merger rates using the theoretical cosmic star formation history obtained from a numerical study which reproduces the available observational data at redshifts $z<8$. We evaluate the contributions of the inspiral, merger, and ring-down signals to the GWB, and discuss how these depend on the parameters which critically affect the number of coalescing (BH-BH) systems. We find that Advanced LIGO/Virgo have a chance to detect the GWB signal from the inspiral phase with a $(S/N)=10$ only for the most optimistic model, which predicts the highest local merger rate of $0.85{\mathrm{Mpc}}^{-3}{\mathrm{Myr}}^{-1}$. Third generation detectors, such as the Einstein Telescope (ET), could reveal the GWB from the inspiral phase predicted by any of the considered models. In addition, ET could sample the merger phase of the evolution at least for models which predict local merger rates between $[0.053–0.85]{\mathrm{Mpc}}^{-3}{\mathrm{Myr}}^{-1}$, which are more than a factor 2 lower than the upper limit inferred from the analysis of the LIGO S5 run [J. Abadie et al., Phys. Rev. D 83, 122005 (2011)]. The frequency dependence and amplitude of the GWB generated during the coalescence is very sensitive to the adopted core mass threshold for BH formation. This opens up the possibility to better understand the final stages of the evolution of massive stellar binaries using observational constraints on the associated gravitational wave emission.

We investigate the dynamics of $r$ modes at amplitudes in the nonlinear regime for rapidly but uniformly rotating neutron stars with a polytropic equation of state. For this, we perform three-dimensional relativistic hydrodynamical simulations, making the simplifying assumption of a fixed spacetime. To excite $r$ modes, we linearly scale exact eigenfunctions to large amplitudes. We find that for initial dimensionless amplitudes around three, $r$ modes decay on time scales around ten oscillation periods, while at amplitudes of order unity, they are stable over the evolution time scale. Together with the decay, a strong differential rotation develops, conserving the total angular momentum, with angular velocities in the range $0.5\dots 1.2$ of the initial one. We evolved two models with different rotation rates and found slower decay for the more rapidly rotating one. We present $r$-mode eigenfunctions and frequencies, and compare them to known analytic results for slowly rotating Newtonian stars. As a diagnostic tool, we discuss conserved energy and angular momentum for the case of a fixed axisymmetric background metric and introduce a measure for the energy of nonaxisymmetric fluid oscillation modes.

We perform a detailed study of the modified gravity $f(R)$ models in the light of the basic geometrical symmetries, namely Lie and Noether point symmetries, which serve to illustrate the phenomenological viability of the modified gravity paradigm as a serious alternative to the traditional scalar field approaches. In particular, we utilize a model-independent selection rule based on first integrals, due to Noether symmetries of the equations of motion, in order to identify the viability of $f(R)$ models in the context of flat Friedmann-Lemaître-Robertson-Walker cosmologies. The Lie/Noether point symmetries are computed for six modified gravity models that include also a cold dark matter component. As it is expected, we confirm that all the proposed modified gravity models admit the trivial first integral, namely energy conservation. We find that only the $f(R)=(R^b-2\Lambda {)}^c$ model, which generalizes the concordance $\Lambda$ cosmology, accommodates extra Lie/Noether point symmetries. For this $f(R)$ model the existence of nontrivial Noether (first) integrals can be used to determine the integrability of the model. Indeed within this context we solve the problem analytically and thus we provide for the first time the evolution of the main cosmological functions such as the scale factor of the universe and the Hubble expansion rate.

The region surrounding the center of the Milky Way is both astrophysically rich and complex, and is predicted to contain very high densities of dark matter. Utilizing three years of data from the Fermi Gamma Ray Space Telescope (and the recently available Pass 7 ultraclean event class), we study the morphology and spectrum of the gamma ray emission from this region and find evidence of a spatially extended component which peaks at energies between 300 MeV and 10 GeV. We compare our results to those reported by other groups and find good agreement. The extended emission could potentially originate from either the annihilations of dark matter particles in the inner galaxy, or from the collisions of high-energy protons that are accelerated by the Milky Way’s supermassive black hole with gas. If interpreted as dark matter annihilation products, the emission spectrum favors dark matter particles with a mass in the range of 7–12 GeV (if annihilating dominantly to leptons) or 25–45 GeV (if annihilating dominantly to hadronic final states). The intensity of the emission corresponds to a dark matter annihilation cross section consistent with that required to generate the observed cosmological abundance in the early Universe ($\sigma v\sim 3\times {10}^{-26}{\mathrm{cm}}^3/\mathrm{s}$). We also present conservative limits on the dark matter annihilation cross section which are at least as stringent as those derived from other observations.

In this paper, a decay vacuum model ${\overline{\rho }}_{\Lambda }=3\sigma M_p^2{H}_{0}H$ is revisited by detailed analysis of background evolution and perturbation equations. We show the imprints on CMB temperature and matter power spectrum from the effective coupling terms between dark sectors by comparing to the standard cosmological constant model and observational data points (WMAP7 and SDSS DR7). We find that the decay vacuum model can describe the expansion rate at late times as well as the standard cosmological constant model but it fails to simultaneously reproduce the observed CMB and matter power spectrum. Its generalization ${\overline{\rho }}_{\Lambda }=3M_p^2({\xi }_1{H}_{0}H+{\xi }_2{H}^2)$ is also discussed. Detailed analysis of the background evolution shows that the dimensionless parameter ${\xi }_2$ would be zero to avoid the unnatural “fine-tuning” and to keep the positivity of energy density of dark matter and dark energy in the early epoch.

Radiation amplitude zeros have long been used to test the standard model. Here, we consider the supersymmetric radiation amplitude zero in chargino-neutralino associated production, which can be observed at the luminosity upgraded LHC. Such an amplitude zero only occurs if the neutralino has a large wino fraction and hence this observable can be used to determine the neutralino eigenstate content. We find that this observable can be measured by comparing the $p_T$ spectrum of the softest lepton in the trilepton ${\tilde{\chi }}_1^{\pm }{\tilde{\chi }}_2^0$ decay channel to that of a control process such as ${\tilde{\chi }}_1^{+}{\tilde{\chi }}_1^{-}$ or ${\tilde{\chi }}_2^0{\tilde{\chi }}_2^0$. We test this technique on a previously generated model sample of the 19 dimensional parameter space of the phenomenological minimal supersymmetric standard model, and find that it is effective in determining the wino content of the neutralino.

We study the phenomenology of the four-site Higgsless model, based on the $SU(2{)}_L\times SU(2{)}_1\times SU(2{)}_2\times U(1{)}_Y$ gauge symmetry, at present colliders. The model predicts the existence of two neutral and four charged extra gauge bosons, $Z_{1,2}$ and $W_{1,2}^{\pm }$. In this paper, we focus on the charged gauge sector. We first derive limits on $W_{1,2}$-boson masses and couplings to SM fermions from direct searches at the Tevatron. We then estimate at the 7 TeV LHC the exclusion limits with the actual $L=1{\mathrm{fb}}^{-1}$ and the discovery potential with the expected $L=10{\mathrm{fb}}^{-1}$. In contrast to the minimal (or three-site) Higgsless model which predicts almost fermiophobic extra gauge bosons, the next-to-minimal (or four-site) Higgsless model recovers sizable $W_{1,2}$-boson couplings to ordinary matter, expressing the nonfermiophobic multiresonance inner nature of extra-dimensional theories. Owing to this feature, we find that in one year from now the new heavy gauge bosons, $W_{1,2}^{\pm }$, could be discovered in the final state with an electron and large missing transverse energy at the 7 TeV LHC for $W_{1,2}$-boson masses in the TeV region, depending on model parameters.

We investigate the chiral magnetic effect by lattice QCD with a chiral chemical potential. In a chirally imbalanced matter, we obtain a finite induced current along an external magnetic field. We analyze the dependence on the lattice spacing, the temperature, the spatial volume, and the fermion mass. The present result indicates that the continuum limit is important for the quantitative argument of the strength of the induced current.

We study the fixed-point structure of four-fermion interactions in two-flavor QCD with $N_{\mathrm{c}}$ colors close to the finite-temperature phase boundary. In particular, we analyze how the fixed-point structure of four-fermion interactions is related to the confining dynamics in the gauge sector. We show that there exists indeed a mechanism which dynamically locks the chiral phase transition to the deconfinement phase transition. This mechanism allows us to determine a window for the values of physical observables in which the two phase transitions lie close to each other.

This paper describes an improved parametrization for proton-beryllium production of secondary $K^{+}$ mesons for experiments with primary proton beams from 8.89 to $24\mathrm{GeV}/c$. The parametrization is based on Feynman scaling in which the invariant cross section is described as a function of $x_F$ and $p_T$. This method is theoretically motivated and provides a better description of the energy dependence of kaon production at low beam energies than other parametrizations such as the commonly used modified Sanford-Wang model. This Feynman scaling parametrization has been used for the simulation of the neutrino flux from the Booster Neutrino Beam at Fermilab and has been shown to agree with the neutrino interaction data from the SciBooNE experiment. This parametrization will also be useful for future neutrino experiments with low primary beam energies, such as those planned for the Project X accelerator.

In models where lepton number is considered to be a spontaneously broken global symmetry a massless Goldstone boson, the Majoron ($J$), appears. We describe a procedure to explore the muon-electron-Majoron coupling using the results from $\mu -e$ conversion search experiments. To accomplish that, we determine how the energy spectrum of the muon decay into an electron and a Majoron is modified by binding effects in a muonic atom. We find that the future $\mu \to e$ conversion experiments may be able to produce bounds on the $\mu \to eJ$ rate which are comparable with the present ones from direct searches.

We study time-dependent perturbations to a family of five-dimensional black hole spacetimes constructed as a holographic model of the QCD phase diagram. We use the results to calculate two transport coefficients, the bulk viscosity and conductivity, as well as the associated baryon diffusion constant, throughout the phase diagram. Near the critical point in the $T-\mu$ plane, the transport coefficients remain finite, although their derivatives diverge, and the diffusion goes to zero. This provides further evidence that large-$N_c$ gauge theories suppress convective transport. We also find a divergence in the low-temperature bulk viscosity, outside the region expected to match QCD, and compare the results to the transport behavior of known $R$-charged black holes.

Homogeneous relaxation is a ubiquitous phenomenon in semiclassical kinetic theories where the quasiparticles are distributed uniformly in space, and the equilibration involves only their velocity distribution. For such solutions, the hydrodynamic variables remain constant. We construct asymptotically AdS solutions of Einstein’s gravity dual to such processes at strong coupling, perturbatively in the amplitude expansion, where the expansion parameter is the ratio of the amplitude of the nonhydrodynamic shear-stress tensor to the pressure. At each order, we sum over all time derivatives through exact recursion relations. We argue that the metric has a regular future horizon, order by order in the amplitude expansion, provided the shear-stress tensor follows an equation of motion. At the linear order, this equation of motion implies that the metric perturbations are composed of zero wavelength quasinormal modes. Our method allows us to calculate the nonlinear corrections to this equation perturbatively in the amplitude expansion. We thus derive a special case of our previous conjecture on the regularity condition on the boundary stress tensor that endows the bulk metric with a regular future horizon, and also refine it further. We also propose a new outlook for heavy-ion phenomenology at RHIC and ALICE.

We attempt to build systematically the low-energy effective Lagrangian for the Einstein-Cartan formulation of gravity theory that generally includes the torsion field. We list all invariant action terms in certain given order; some of the invariants are new. We show that in the leading order, the fermion action with torsion possesses additional $U(1{)}_L\times U(1{)}_R$ gauge symmetry, with $4+4$ components of the torsion (out of the general 24) playing the role of Abelian gauge bosons. The bosonic action quadratic in torsion gives masses to those gauge bosons. Integrating out torsion one obtains a pointlike 4-fermion action of a general form containing vector-vector, axial-vector, and axial-axial interactions. We present a quantum field-theoretic method to average the 4-fermion interaction over the fermion medium, and perform the explicit averaging for free fermions with given chemical potential and temperature. The result is different from that following from the “spin fluid” approach used previously. On the whole, we arrive to rather pessimistic conclusions on the possibility to observe effects of the torsion-induced 4-fermion interaction, although under certain circumstances it may have cosmological consequences.

A class of theories of gravity based on a Lagrangian $L=L(R^a{}_{bcd},g^{ab})$ which depends on the curvature and metric—but not on the derivatives of the curvature tensor—is of interest in several contexts including in the development of the paradigm that treats gravity as an emergent phenomenon. This class of models contains, as an important subset, all Lanczos-Lovelock models of gravity. I derive several identities and properties which are useful in the study of these models and clarify some of the issues that seem to have received insufficient attention in the past literature.

We investigate the thermodynamical properties of solutions to the 5D Einstein and Einstein-Maxwell-dilaton equations describing static black holes on asymptotically locally flat gravitational instantons. Some general expressions regarding the nut charge and potential are derived, as well as Smarr-like relations. The thermodynamics of two particular solutions representing a static black hole on Taub-Nut and Taub-Bolt instantons are examined in detail. Two different approaches for the computation of the mass and the tension, the Komar and counterterm methods, are applied and compared. A new charged black hole on the Taub-Bolt instanton is constructed and investigated.

In this paper, we analytically calculate the quasinormal modes of scalar, vector, tensor, and spinor perturbations of the warped ${\mathrm{dS}}_3$ black hole. There are two horizons for the warped ${\mathrm{dS}}_3$ black hole, namely, the black hole horizon $r_b$ and the cosmological horizon $r_c$. In the calculation, we impose the ingoing boundary condition at the black hole horizon and the outgoing boundary condition at the cosmological horizon. We also investigate the hidden conformal symmetry of the warped ${\mathrm{dS}}_3$ black hole in the region between the black hole horizon and the cosmological horizon $r_b<r<r_c$. We use the hidden conformal symmetry to construct the quasinormal modes in an algebraic way and find that the results agree with the analytically ones. It turns out that the frequencies of the quasinormal modes could be identified with the poles in the thermal boundary-boundary correlators.