The measurements of the neutrino and quark mixing angles satisfy the empirical relations called quark-lepton complementarity. These empirical relations suggest the existence of a correlation between the mixing matrices of leptons and quarks. In this work, we examine the possibility that this correlation between the mixing angles of quarks and leptons originates in the similar hierarchy of quarks and charged lepton masses and the seesaw mechanism type I, that gives mass to the Majorana neutrinos. We assume that the similar mass hierarchies of charged lepton and quark masses allows us to represent all the mass matrices of Dirac fermions in terms of a universal form with four texture zeroes.

Recently, Bjerrum-Bohr, Damgaard, Feng, and Sondergaard derived a set of new interesting quadratic identities of the Yang-Mills (YM) tree scattering amplitudes, besides Bern-Carrasco-Johansson (BCJ) identities. Here we comment that these quadratic identities of YM amplitudes actually follow directly from the KLT (Kawai-Lewellen-Tye) relation for graviton-dilaton-axion scattering amplitudes (in four-dimensional spacetime). This clarifies their physical origin and also provides a simpler version of the new identities. We also comment that the recently discovered BCJ identities of YM helicity amplitudes, at least for the maximal helicity-violating case, can be verified by using (repeatedly) the Schouten identity. We also point out additional quadratic identities that can be written down from the KLT relations.

There is considered an extension of gauge theories according to the assumption of a generalized uncertainty principle which implies a minimal length scale. A modification of the usual uncertainty principle implies an extended shape of matter field equations like the Dirac equation. If there is postulated invariance of such a generalized field equation under local gauge transformations, the usual covariant derivative containing the gauge potential has to be replaced by a generalized covariant derivative. This leads to a generalized interaction between the matter field and the gauge field as well as to an additional self-interaction of the gauge field. Since the existence of a minimal length scale seems to be a necessary assumption of any consistent quantum theory of gravity, the gauge principle is a constitutive ingredient of the standard model, and even gravity can be described as gauge theory of local translations or Lorentz transformations, the presented extension of gauge theories appears as a very important consideration.

We have written and tested a new general relativistic magnetohydrodynamics code, capable of evolving magnetohydrodynamics (MHD) fluids in dynamical spacetimes with adaptive-mesh refinement (AMR). Our code solves the Einstein-Maxwell-MHD system of coupled equations in full $3+1$ dimensions, evolving the metric via the Baumgarte-Shapiro Shibata-Nakamura formalism and the MHD and magnetic induction equations via a conservative, high-resolution shock-capturing scheme. The induction equations are recast as an evolution equation for the magnetic vector potential, which exists on a grid that is staggered with respect to the hydrodynamic and metric variables. The divergenceless constraint $\mathbf{\nabla }·\mathit{B}=0$ is enforced by the curl of the vector potential. Our MHD scheme is fully compatible with AMR, so that fluids at AMR refinement boundaries maintain $\mathbf{\nabla }·\mathit{B}=0$. In simulations with uniform grid spacing, our MHD scheme is numerically equivalent to a commonly used, staggered-mesh constrained-transport scheme. We present code validation test results, both in Minkowski and curved spacetimes. They include magnetized shocks, nonlinear Alfvén waves, cylindrical explosions, cylindrical rotating disks, magnetized Bondi tests, and the collapse of a magnetized rotating star. Some of the more stringent tests involve black holes. We find good agreement between analytic and numerical solutions in these tests, and achieve convergence at the expected order.

A few years ago, Campos investigated the critical phenomena of thick branes in warped spacetimes [Phys. Rev. Lett. 88, 141602 (2002)]. Inspired by his work, we consider a toy model of thick branes generated by a real scalar field with the potential $V(\varphi )=a{\varphi }^2-b{\varphi }^4+c{\varphi }^6$, and investigate the variation of the mass parameter $a$ on the branes as well as the localization and resonances of fermions. An interesting result is found: there is a critical value for the mass parameter $a$, and when the critical value of $a$ is reached the solution of the background scalar field is not unique and has the shape of a double kink. This happens in both cases with and without gravity. It is also shown that the numbers of the bound Kaluza-Klein modes of fermions on the gravity-free brane and the resonant states of fermions on the brane with gravity increase with the value of $a$.

We study the possibility of detecting a signature of particle dark matter in the spectrum of gamma-ray photons from active galactic nuclei (AGNs) resulting from the scattering of high-energy particles in the AGN jet off of dark matter particles. We consider particle dark matter models in the context of both supersymmetry and universal extra dimensions , and we present the complete lowest-order calculation for processes where a photon is emitted in dark matter-electron and/or dark matter-proton scattering, where electrons and protons belong to the AGN jet. We find that the process is dominated by a resonance whose energy is dictated by the particle spectrum in the dark matter sector (neutralino and selectron for the case of supersymmetry, Kaluza-Klein photon and electron for universal extra dimensions ). The resulting gamma-ray spectrum exhibits a very characteristic spectral feature, consisting of a sharp break to a hard power-law behavior. Although the normalization of the gamma-ray flux depends strongly on assumptions on both the AGN jet geometry, composition and particle spectrum as well as on the particle dark matter model and density distribution, we show that for realistic parameters choices, and for two prominent nearby AGNs (Centaurus A and M87), the detection of this effect is in principle possible. Finally, we compare our predictions and results with recent gamma-ray observations from the Fermi, H.E.S.S., and VERITAS telescopes.

It has been suggested previously that the observed cosmological constant $\Lambda$ corresponds to the remnant vacuum energy density of dynamical processes taking place at a cosmic age set by the mass scale $M\sim E_{\mathrm{ew}}$ of ultramassive particles with electroweak interactions. Here, a simple modification of the nondissipative dynamic equations of $q$-theory is presented, which produces a remnant vacuum energy density (effective cosmological constant) of the correct order of magnitude. Combined with the observed value of $\Lambda$, a first estimate of the required value of the energy scale $E_{\mathrm{ew}}$ ranges from 3 to 9 TeV, depending on the number of species of ultramassive particles and assuming a dissipative coupling constant of order unity. If correct, this estimate implies the existence of new TeV-scale physics beyond the standard model.

We propose a modified version of the TeV-scale $B-L$ extension of the standard model, where neutrino masses are generated through the inverse seesaw mechanism. We show that heavy neutrinos in this model can be accessible via clean signals at the LHC. The search for the extra gauge boson $Z_{B-L}^{\prime }$ through the decay into dileptons or two dileptons plus missing energy is studied. We also show that the $B-L$ extra Higgs boson can be directly probed at the LHC via a clean dilepton and missing energy signal.

We present an analysis of the baryon-octet and -decuplet masses using covariant SU(3)-flavor chiral perturbation theory up to next-to-leading order. Besides the description of the physical masses we address the problem of the lattice QCD extrapolation. Using the PACS-CS Collaboration data we show that a good description of the lattice points can be achieved at next-to-leading order with the covariant loop amplitudes and phenomenologically determined values for the meson-baryon couplings. Moreover, the extrapolation to the physical point up to this order is found to be better than the linear one given at leading-order by the Gell-Mann-Okubo approach. The importance that a reliable combination of lattice QCD and chiral perturbation theory may have for hadron phenomenology is emphasized with the prediction of the pion-baryon and strange-baryon sigma terms.

We investigate the relation between the eigenvalues and eigenfunctions of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) and Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner (JIMWLK/KLWMIJ) Hamiltonians. We show that the eigenvalues of the BFKL Hamiltonians are also exact eigenvalues of the KLWMIJ (and JIMWLK) Hamiltonian, albeit corresponding to possibly non-normalizable eigenfunctions. The question whether a given eigenfunction of BFKL corresponds to a normalizable eigenfunction of KLWMIJ is rather complicated, except in some obvious cases, and requires independent investigation. As an example to illustrate this relation we concentrate on the color octet exchange in the framework of KLWMIJ Hamiltonian. We show that it corresponds to the reggeized gluon exchange of BFKL, and find first correction to the BFKL wave function, which has the meaning of the impact factor for shadowing correction to the Reggeized gluon. We also show that the bootstrap condition in the KLWMIJ framework is satisfied automatically and does not carry any additional information to that contained in the second quantized structure of the KLWMIJ Hamiltonian. This is an example of how the bootstrap condition inherent in the $t$-channel unitarity arises in the $s$-channel picture.

We give a complete and detailed description of the computation of black hole entropy in loop quantum gravity by employing the most recently introduced number-theoretic and combinatorial methods. The use of these techniques allows us to perform a detailed analysis of the precise structure of the entropy spectrum for small black holes, showing some relevant features that were not discernible in previous computations. The ability to manipulate and understand the spectrum up to the level of detail that we describe in the paper is a crucial step toward obtaining the behavior of entropy in the asymptotic (large horizon area) regime.

At the time of recombination, baryons and photons decoupled and the sound speed in the baryonic fluid dropped from relativistic, $\sim c/\sqrt{3}$, to the thermal velocities of the hydrogen atoms, $\sim 2\times {10}^{-5}c$. This is less than the relative velocities of baryons and dark matter computed via linear perturbation theory, so we infer that there are supersonic coherent flows of the baryons relative to the underlying potential wells created by the dark matter. As a result, the advection of small-scale perturbations (near the baryonic Jeans scale) by large-scale velocity flows is important for the formation of the first structures. This effect involves a quadratic term in the cosmological perturbation theory equations and hence has not been included in studies based on linear perturbation theory. We show that the relative motion suppresses the abundance of the first bound objects, even if one only investigates dark matter haloes, and leads to qualitative changes in their spatial distribution, such as introducing scale-dependent bias and stochasticity. We further discuss the possible observable implications of this effect for high-redshift galaxy clustering and reionization.

We discuss the existence of a conformal phase in $\mathrm{SU}(N)$ gauge theories in four dimensions. In this lattice study, we explore the model in the bare parameter space, varying the lattice coupling and bare mass. Simulations are carried out with three colors and 12 flavors of dynamical staggered fermions in the fundamental representation. The analysis of the chiral order parameter and the mass spectrum of the theory indicates the restoration of chiral symmetry at zero temperature and the presence of a Coulomb-like phase, depicting a scenario compatible with the existence of an infrared stable fixed point at nonzero coupling. Our analysis supports the conclusion that the onset of the conformal window for QCD-like theories is smaller than $N_f=12$, before the loss of asymptotic freedom at 16 and 1/2 flavors. We discuss open questions and future directions.

We argue that in cold, dense quark matter, in the limit of a large number of colors the ground state is unstable with respect to creation of a complicated quarkyonic chiral spiral state, in which both chiral and translational symmetries are spontaneously broken. The entire Fermi surface is covered with patches of quarkyonic chiral spirals, whose number increases as the quark density does. The low energy excitations are gapless, given by the Wess-Zumino-Novikov-Witten model plus transverse kinetic terms localized about different patches.

I propose to change the sign of the dilaton in the infrared (IR) soft-wall anti-de Sitter/QCD model, in order to implement confinement. The deformed model exhibits interesting properties, especially in describing chiral symmetry breaking. The expectation value of the scalar field $X$, which determines the quark mass and condensate, approaches a constant in the IR limit, rather than blows up in the original model. In contrast to the estimate in [M. Shifman and A. Vainshtein, Phys. Rev. D 77, 034002 (2008).], this kind of solution will not lead to chiral symmetry restoration for highly-excited states due to the property of the harmonic-oscillator equation. Instead, it will guarantee the Regge behavior of the axial meson spectrum and also the pseudoscalar mesons. The value of the condensate can be fixed by requiring that the pion be massless in the chiral limit, but only under some approximation in the present model. We also find that, by relaxing the IR boundary conditions, the unphysical massless state in the vector channel can be eliminated.

Superstatistics permits the calculation of the Feynman propagator of a relativistic particle in a novel way from a superstatistical average over nonrelativistic single-particle paths. We illustrate this for the Klein-Gordon particle in the Feshbach-Villars representation, and for the Dirac particle in the Schrödinger-Dirac representation. As a by-product we recover the worldline representation of Klein-Gordon and Dirac propagators, and discuss the role of the smearing distributions in fixing the reparametrization freedom. The emergent relativity picture that follows from our approach together with a novel representation of the Lorentz group for the Feshbach-Villars particle are also discussed.

For landscapes of field-theory vacua, we identify an effect that can greatly enhance the decay rates to wildly distant minima—so much so that such transitions may dominate over transitions to near neighbors. We exhibit these “giant leaps” in both a toy two-field model and, in the thin-wall limit, amongst the four-dimensional vacua of six-dimensional Einstein-Maxwell theory, and it is argued that they are generic to landscapes arising from flux compactifications. We discuss the implications for the cosmological constant and the stability of stringy de Sitter.

Primordial gravitational waves provide a very important stochastic background that could be detected soon with interferometric gravitational wave antennas or indirectly via the induced patterns in the polarization anisotropies of the cosmic microwave background. The detection of these waves will open a new window into the early Universe, and therefore it is important to characterize in detail all possible sources of primordial gravitational waves. In this paper we develop theoretical and numerical methods to study the production of gravitational waves from out-of-equilibrium gauge fields at preheating. We then consider models of preheating after hybrid inflation, where the symmetry breaking field is charged under a local $U(1)$ symmetry. We analyze in detail the dynamics of the system in both momentum and configuration space. We show that gauge fields leave specific imprints in the resulting gravitational wave spectra, mainly through the appearance of new peaks at characteristic frequencies that are related to the mass scales in the problem. We also show how these new features in the spectra correlate with stringlike spatial configurations in both the Higgs and gauge fields that arise due to the appearance of topological winding numbers of the Higgs around Nielsen-Olesen strings. We study in detail the time evolution of the spectrum of gauge fields and gravitational waves as these strings evolve and decay before entering a turbulent regime where the gravitational wave energy density saturates.

The mass function of cluster-size halos and their redshift distribution are computed for 12 distinct accelerating cosmological scenarios and confronted to the predictions of the conventional flat $\Lambda \mathrm{CDM}$ model. The comparison with $\Lambda \mathrm{CDM}$ is performed by a two-step process. First, we determine the free parameters of all models through a joint analysis involving the latest cosmological data, using supernovae type Ia, the cosmic microwave background shift parameter, and baryon acoustic oscillations. Apart from a braneworld inspired cosmology, it is found that the derived Hubble relation of the remaining models reproduces the $\Lambda \mathrm{CDM}$ results approximately with the same degree of statistical confidence. Second, in order to attempt to distinguish the different dark energy models from the expectations of $\Lambda \mathrm{CDM}$, we analyze the predicted cluster-size halo redshift distribution on the basis of two future cluster surveys: (i) an X-ray survey based on the eROSITA satellite, and (ii) a Sunayev-Zeldovich survey based on the South Pole Telescope. As a result, we find that the predictions of 8 out of 12 dark energy models can be clearly distinguished from the $\Lambda \mathrm{CDM}$ cosmology, while the predictions of 4 models are statistically equivalent to those of the $\Lambda \mathrm{CDM}$ model, as far as the expected cluster mass function and redshift distribution are concerned. The present analysis suggests that such a technique appears to be very competitive to independent tests probing the late time evolution of the Universe and the associated dark energy effects.