The Large Hadron Collider will restart with higher energy and luminosity in 2015. This achievement opens the possibility of discovering new phenomena hardly described by the Standard Model, which is based on the following two neutral gauge bosons: the photon and the $Z$. This perspective imposes a deep and systematic study of models that predicts the existence of new neutral gauge bosons. One such model is based on the gauge group $SU(3{)}_C\times SU(3{)}_L\times U(1{)}_N$, called the 3-3-1 model for short. In this paper we perform a study with $Z^{\prime }$ predicted in two versions of the 3-3-1 model and compare the signature of this resonance in each model version. By considering the present and future LHC energy regimes, we obtain some distributions and the total cross section for the process $p+p\to {\ell }^{+}+{\ell }^{-}+X$. Additionally, we derive lower bounds on $Z^{\prime }$ mass from the latest LHC results. Finally we analyze the LHC potential for discovering this neutral gauge boson at 14 TeV center-of-mass energy.

By using the Laplace transformation, the analytical solutions of the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations at the leading-order and next-to-leading-order (NLO) approximations for the gluon, singlet, and nonsinglet quark polarization inside the nucleon are obtained. At NLO approximation, a second Laplace transformation is required. Complete NLO calculations need an iteration method, which we try to employ. As an efficiently mathematical tool, we employ the Jacobi polynomials to extract the polarized nucleon structure, using the analytical solutions for the polarized parton densities. Optimum nucleon structure functions are determined by a ${\chi }^2$ analysis of the available experimental data, and their uncertainties are estimated by the Hessian method. Our results for nucleon and deuteron structure functions are in good agreement with all available experimental data and fitting parametrization models.

New BES and Belle data show a peak in the $Y(4260)$ decay into $J/\psi$ plus one charged pion. We point out that the peak might correspond to a charged resonance at about 3880 MeV predicted some time ago within a tetraquark model. The same tetraquark model predicts another peak at about 100 MeV below the observed one. We discuss the possibility of having it in present data. On the other hand we expect that if the molecular picture were the correct one, a peak corresponding to a $D^{*}{\overline{D}}^{*}$ state should appear at about 4020 MeV.

Assuming Lorentz symmetry is broken by some fixed vector background, we study the spinor electrodynamics modified by two dimension-five Lorentz-violating interactions between fermions and photons. The effective polarization and magnetization are identified from the modified Maxwell equations, and the theoretical consequences are investigated. We also compute the corrections to the relativistic energy levels of hydrogen atom induced by these Lorentz-violating operators in the absence and presence of uniform external fields in first-order perturbation theory. We find that the hydrogen spectrum is insensitive to the breakdown of Lorentz boost symmetry.

If gravity is an emergent phenomenon, as suggested by several recent results, then the structure of the action principle for gravity should encode this fact. With this motivation we study several features of the Einstein-Hilbert action and establish direct connections with horizon thermodynamics. We begin by introducing the concept of holographically conjugate variables in terms of which the surface term in the action has a specific relationship with the bulk term. In addition to $g_{ab}$ and its conjugate momentum $\sqrt{-g}{M}^{cab}$, this procedure allows us to (re)discover and motivate strongly the use of $f^{ab}=\sqrt{-g}{g}^{ab}$ and its conjugate momentum $N_{ab}^c$. The gravitational action can then be interpreted as a momentum-space action for these variables. We also show that many expressions in classical gravity simplify considerably in this approach. For example, the field equations can be written in the form ${\partial }_c{f}^{ab}=\partial {\mathcal{H}}_g/\partial N_{ab}^c$, ${\partial }_c{N}_{ab}^c=-\partial {\mathcal{H}}_g/\partial f^{ab}$ (analogous to Hamilton’s equations) for a suitable Hamiltonian ${\mathcal{H}}_g$, if we use these variables. More importantly, the variation of the surface term, evaluated on any null surface which acts a local Rindler horizon can be given a direct thermodynamic interpretation. The term involving the variation of the dynamical variable leads to $T\delta S$ while the term involving the variation of the conjugate momentum leads to $S\delta T$. We have found this correspondence only for the choice of variables $(g_{ab},\sqrt{-g}{M}^{cab})$ or $(f^{ab},N_{ab}^c)$. We use this result to provide a direct thermodynamical interpretation of the boundary condition in the action principle, when it is formulated in a spacetime region bounded by the null surfaces. We analyze these features from several different perspectives and provide a detailed description, which offers insights about the nature of classical gravity and emergent paradigm.

We assume the cosmological dark sector to consist of pressureless matter and holographic dark energy with a cutoff length proportional to the Ricci scale. The requirement of separate energy-momentum conservation of the components is shown to establish a relation between the matter fraction and the (necessarily time-dependent) equation-of-state parameter of the dark energy. Focusing on intrinsically adiabatic pressure perturbations of the dark-energy component, the matter perturbations are found as linear combinations of the total energy-density perturbations of the cosmic medium and the relative (nonadiabatic) perturbations of the components. The resulting background dynamics is consistent with observations from supernovae of type Ia, baryonic acoustic oscillations and the differential age of old objects. The perturbation dynamics, on the other hand, is plagued by instabilities which excludes any phantom-type equation of state. The only stable configuration is singled out by a fixed relation between the present matter fraction ${\Omega }_{m0}$ and the present value ${\omega }_0$ of the equation-of-state parameter of the dark energy. However, this instability-avoiding configuration is only marginally consistent with the observationally preferred background values of the mentioned parameters.

We continue our earlier study of the phase structure of a $SU(2)$ gauge theory whose action contains additional chirally invariant four fermion interactions. Our lattice theory uses a reduced staggered fermion formalism to generate two Dirac flavors in the continuum limit. In the current study we have tried to reduce lattice spacing and taste breaking effects by using an improved fermion action incorporating stout smeared links. As in our earlier study we observe two regimes; for weak gauge coupling the chiral condensate behaves as an order parameter differentiating a phase at small four Fermi coupling where the condensate vanishes from a phase at strong four Fermi coupling in which chiral symmetry is spontaneously broken. This picture changes qualitatively when the gauge coupling is strong enough to cause confinement; in this case we observe a phase transition for some critical value of the four Fermi coupling associated with a strong enhancement of the chiral condensate. We present evidence that this transition is likely first order. Furthermore, we observe that the critical four Fermi coupling varies monotonically with bare gauge coupling—decreasing, as expected, as the gauge coupling is increased. We have checked that these results remain stable under differing levels of smearing. These results argue against the appearance of new fixed points associated with chirally invariant four fermion interactions in confining non-Abelian gauge theories.

Axial-vector mesons $a_1(1260)$, $f_1(1285)$, $h_1(1170)$, $K_1(1270)$, and $K_1(1400)$ can be produced in semileptonic $\tau \to AP{\nu }_{\tau }$ decays, where $P$ stands for the pseudoscalar mesons $\pi$ or $K$. We calculate the branching ratios based in a meson dominance model. The exclusive channels ${\tau }^{-}\to a_1(1260{)}^{-}{\pi }^0\nu$, ${\tau }^{-}\to a_1(1260{)}^0{\pi }^{-}\nu$, and ${\tau }^{-}\to h_1(1170){\pi }^{-}\nu$ turn out to be of order $\mathcal{O}({10}^{-3})$, the channel ${\tau }^{-}\to f_1(1285){\pi }^{-}\nu$ of order $\mathcal{O}({10}^{-4})$, and channels ${\tau }^{-}\to K_1(1270{)}^{-}{\pi }^0\nu$, ${\tau }^{-}\to K_1(1270{)}^0{\pi }^{-}\nu$, ${\tau }^{-}\to K_1(1400{)}^{-}{\pi }^0\nu$, and ${\tau }^{-}\to K_1(1400{)}^0{\pi }^{-}\nu$ of order $\mathcal{O}({10}^{-6})$. These results indicate that the branching ratios could be measured in experiments.

For particle collision near rapidly rotating Kerr black holes, the center-of-mass energy can be arbitrarily high if the angular momentum of either of the colliding particles is fine-tuned. Recently, it has been shown that particles which are produced by such a particle collision and escape to infinity cannot be very massive nor very energetic. For electrically charged black holes there is a similar phenomenon, where the center-of-mass energy for the collision of charged particles near the horizon can be arbitrarily high. One might expect that there would exist a similar bound on the energy and mass of particles that are produced by such a particle collision and escape to infinity. In this paper, however, we see that this expectation is not the case. We explicitly show that superheavy and highly energetic charged particles produced by the collision near maximally charged black holes can escape to infinity at least within classical theory if the backreaction and self-force of the particle can be neglected.

We develop a framework to test the equivalence principle under conditions where the quantum aspects of nature cannot be neglected, specifically in the context of interference phenomena with unstable particles. We derive the nonrelativistic quantum equation that describes the evolution of the wave function of unstable particles under the assumption of the validity of the equivalence principle and when small deviations are assumed to occur. As an example, we study the propagation of unstable particles in a COW experiment, and we briefly discuss the experimental implications of our formalism.

An interesting class of background field configurations in quantum electrodynamics (QED) is the $O(2)\times O(3)$ symmetric fields, originally introduced by S. L. Adler in 1972. Those backgrounds have some instantonlike properties and yield a one-loop effective action that is highly nontrivial but amenable to numerical calculation. Here, we use the recently developed “partial-wave-cutoff method” for a full mass range numerical analysis of the effective action for the “standard” $O(2)\times O(3)$ symmetric field, modified by a radial suppression factor. At large mass, we are able to match the asymptotics of the physically renormalized effective action against the leading two mass levels of the inverse mass expansion. For small masses, with a suitable choice of the renormalization scheme, we obtain stable numerical results even in the massless limit. We analyze the $N$-point functions in this background and show that, even in the absence of the radial suppression factor, the two-point contribution to the effective action is the only obstacle to taking its massless limit. The standard $O(2)\times O(3)$ background leads to a chiral anomaly term in the effective action, and both our perturbative and nonperturbative results strongly suggest that the small-mass asymptotic behavior of the effective action is, after the subtraction of the two-point contribution, dominated by this anomaly term as the only source of a logarithmic mass dependence. This confirms a conjecture by M. Fry.

According to the no-hair theorem, astrophysical black holes are uniquely described by the Kerr metric. In order to test this theorem with observations in either the electromagnetic or gravitational-wave spectra, several Kerr-like spacetimes have been constructed which describe potential deviations from the Kerr spacetime in parametric form. For electromagnetic tests of the no-hair theorem, such metrics allow for the proper modeling of the accretion flows around candidate black holes and the radiation emitted from them. In many of these models, the location of the inner edge of the accretion disk is of special importance. This inner edge is often taken to coincide with the innermost stable circular orbit, which can serve as a direct probe of the spin and the deviation from the Kerr metric. In certain cases, however, an innermost stable circular orbit does not exist, and the inner edge of an accretion disk is instead determined by an instability against small perturbations in the direction vertical to the disk. In this paper, I analyze the properties of accretion disks in the Kerr-like metric proposed by Johannsen and Psaltis [Phys. Rev. D 83, 124015 (2011)], whose inner edges are located at the radii where this vertical instability occurs. I derive expressions of the energy and axial angular momentum of disk particles that move on circular equatorial orbits and calculate the locations of the inner disk edges. As a possible observable of such accretion disks, I simulate profiles of relativistically broadened iron lines and show that they depend significantly on the values of the spin and the deviation parameter.

We investigate the influence of plasma presence on relativistic images formed by Schwarzschild black hole lensing. When a gravitating body is surrounded by a plasma, the lensing angle depends on a frequency of the electromagnetic wave due to refraction properties, and the dispersion properties of the light propagation in gravitational field in plasma. The last effect leads to a difference, even in uniform plasma, of the gravitational deflection angle in plasma from the vacuum case. This angle depends on the photon frequency, which resembles the properties of the refractive prism spectrometer. Here we consider the case of a strong deflection angle for the light, traveling near the Schwarzschild black hole, surrounded by a uniform plasma. Asymptotic formulas are obtained for the case of a very large deflection angle, exceeding $2\pi$. We apply these formulas for calculation of position and magnification of relativistic images in a homogeneous plasma, which are formed by the photons performing one or several revolutions around the central object. We conclude that the presence of the uniform plasma increases the angular size of relativistic rings or the angular separation of point images from the gravitating center. The presence of the uniform plasma increases also a magnification of relativistic images. The angular separation and the magnification become significantly larger than in the vacuum case, when the photon frequency goes to a plasma frequency.

We obtain and analyze an exact solution to Einstein-Maxwell-scalar theory in ($2+1$) dimensions, in which the scalar field couples to gravity in a nonminimal way, and it also couples to itself with the self-interacting potential solely determined by the metric ansatz. A negative cosmological constant naturally emerges as a constant term in the scalar potential. The metric is static and circularly symmetric and contains a curvature singularity at the origin. The conditions for the metric to contain 0, 1, and 2 horizons are identified, and the effects of the scalar and electric charges on the size of the black hole radius are discussed. Under proper choices of parameters, the metric degenerates into some previously known solutions in ($2+1$)-dimensional gravity.

The scale invariance of the quantum fluctuations in de Sitter space leads to the appearance of de Sitter symmetry breaking infrared logarithms in the graviton propagator. We investigate physical effects of soft gravitons on the local dynamics of matter fields well inside the cosmological horizon. We show that the IR logarithms do not spoil Lorentz invariance in scalar and Dirac field theory. The leading IR logarithms can be absorbed by a time dependent wave function renormalization factor in both cases. In the interacting field theory with $\lambda {\varphi }^4$ and Yukawa interaction, we find that the couplings become time dependent with definite scaling exponents. We argue that the relative scaling exponents of the couplings are gauge invariant and physical as we can use the evolution of a coupling as a physical time.

The cosmological power spectrum of the coherent matter flow is measured exploiting an improved prescription for the apparent anisotropic clustering pattern in redshift space. New statistical analysis is presented to provide an optimal observational platform to link the improved redshift distortion theoretical model to future real data sets. The statistical power as well as robustness of our method are tested against 60 realizations of $8{\mathrm{h}}^{-3}{\mathrm{Gpc}}^3$ dark matter simulation maps mocking the precision level of upcoming wide-deep surveys. We showed that we can accurately extract the velocity power spectrum up to quasilinear scales of $k\sim 0.1\mathrm{h}{\mathrm{Mpc}}^{-1}$ at $z=0.35$ and up to $k\sim 0.15\mathrm{h}{\mathrm{Mpc}}^{-1}$ at higher redshifts within a couple of percentage precision levels. Our understanding of redshift space distortion is proved to be appropriate for precision cosmology, and our statistical method will guide us to a righteous path to meet the real world.

In the framework of QCD sum rules, we present an improved study of our previous work [Phys. Rev. D 80, 056004 (2009)], particularly on the $\overline{D}{D}^{*}$ molecular state, to investigate the possibility that the newly observed $Z_c(3900)$ is a $S$-wave $\overline{D}{D}^{*}$ molecular state. To ensure the quality of QCD sum rule analysis, contributions of up to dimension nine are calculated to test the convergence of operator product expansion (OPE). We find that the two-quark condensate $⟨\overline{q}q⟩$ is very large and makes the standard OPE convergence (i.e. the perturbative at least larger than each condensate contribution) happen at very large values of Borel parameters. By releasing the rigid OPE convergence criterion, one could find that the OPE convergence is still under control. We arrive at the numerical result $3.86\pm 0.27\mathrm{GeV}$ for $\overline{D}{D}^{*}$, which agrees with the mass of $Z_c(3900)$ and could support the explanation of $Z_c(3900)$ in terms of a $S$-wave $\overline{D}{D}^{*}$ molecular state.

We investigate QCD magnetic susceptibility ${\chi }_q$ for light-flavor SU(2) at finite temperature ($T$) beyond the chiral limit, using the liquid instanton model for $N_c=3$, defined in Euclidean space and modified by the $T$-dependent caloron solution. The background electromagnetic fields are included in the QCD vacuum, employing the Schwinger method. We first compute the scalar (chiral) and tensor condensates as functions of $T$ and the current-quark mass $m$, signaling the correct universal chiral restoration patterns. It turns out that ${\chi }_q$, given by the ratio of the two condensates, is a smoothly decreasing function of $T$, showing about 20% reduction of its strength at the chiral transition $T\equiv T_0$, in comparison to that at $T=0$, and decreases almost linearly beyond $T_0$ for $m\ne 0$. We observe that the present numerical results are in qualitatively good agreement with other theoretical results, including the lattice simulations. Finally, we examine the effects of the external magnetic field on the tensor-polarization VEV, which plays the role of the chiral order parameter.