We study the charged Higgs couplings to fermions in the democratic three-Higgs-doublet model, in which one doublet couples to down-type quarks, one to up-type quarks, and one to charged leptons. Flavor-changing neutral Higgs couplings are absent because the Glashow-Weinberg-Paschos condition for natural flavor conservation is in effect. We show that this model reproduces the coupling structure of the charged Higgs boson in the recently-proposed Yukawa-aligned two-Higgs-doublet model, with two subtle constraints that arise from the unitarity of the charged-Higgs mixing matrix. Adding a fourth Higgs doublet with no couplings to fermions eliminates these constraints.

QCD lattice simulations with $2+1$ flavors (when two quark flavors are mass degenerate) typically start at rather large up-down and strange quark masses and extrapolate first the strange quark mass and then the up-down quark mass to its respective physical value. Here we discuss an alternative method of tuning the quark masses, in which the singlet quark mass is kept fixed. Using group theory the possible quark mass polynomials for a Taylor expansion about the flavor symmetric line are found, first for the general $1+1+1$ flavor case and then for the $2+1$ flavor case. This ensures that the kaon always has mass less than the physical kaon mass. This method of tuning quark masses then enables highly constrained polynomial fits to be used in the extrapolation of hadron masses to their physical values. Numerical results for the $2+1$ flavor case confirm the usefulness of this expansion and an extrapolation to the physical pion mass gives hadron mass values to within a few percent of their experimental values. Singlet quantities remain constant which allows the lattice spacing to be determined from hadron masses (without necessarily being at the physical point). Furthermore an extension of this program to include partially quenched results is given.

The color fields created by the static tetraquark system are computed in quenched SU(3) lattice QCD, in a ${24}^3\times 48$ lattice at $\beta =6.2$ corresponding to a lattice spacing $a=0.07261(85)\mathrm{fm}$. We find that the tetraquark color fields are well described by a double-Y, or butterfly, shaped flux tube. The two flux-tube junction points are compatible with Fermat points minimizing the total flux-tube length. We also compare the diquark-diantiquark central flux-tube profile in the tetraquark with the quark-antiquark fundamental flux-tube profile in the meson, and they match, thus showing that the tetraquark flux tubes are composed of fundamental flux tubes.

The common lore in the literature of neutrino mass generation is that the canonical seesaw mechanism beautifully offers an explanation for the tiny neutrino mass but at the cost of introducing right-handed neutrinos at a scale that is out of range for the current experiments. The inverse seesaw mechanism is an interesting alternative to the canonical one once it leads to tiny neutrino masses with the advantage of being testable at the TeV scale. However, this last mechanism suffers from an issue of naturalness concerning the scale responsible for such small masses, namely, the parameter $\mu$ that is related to lepton number violation and is supposed to be at the keV scale, much lower than the electroweak one. However, no theoretical framework was built that offers an explanation for obtaining this specific scale. In this work, we propose a variation of the inverse seesaw mechanism by assuming a minimal scalar and fermionic set of singlet fields, along with a $Z_5\otimes Z_2$ symmetry, that allows a dynamical explanation for the smallness of $\mu$, recovering the neat canonical seesaw formula and with right-handed (RH) neutrinos free to be at the electroweak scale, thus testable at LHC and current neutrino experiments.

We study the interplay of thermal and diffractive effects in Casimir energies. We consider plates with edges, oriented either parallel or perpendicular to each other, as well as a single plate with a slit. We compute the Casimir energy at finite temperature using a formalism in which the diffractive effects are encoded in a lower dimensional nonlocal field theory that lives in the gap between the plates. The formalism allows for a clean separation between direct or geometric effects and diffractive effects, and makes an analytic derivation of the temperature dependence of the free energy possible. At low temperatures, with Dirichlet boundary conditions on the plates, we find that diffractive effects make a correction to the free energy which scales as $T^6$ for perpendicular plates, as $T^4$ for slits, and as $T^4\log T$ for parallel plates.

We investigate the thermodynamics of rotating Lovelock-Lifshitz black branes. We calculate the conserved and thermodynamic quantities of the solutions and obtain a relation between energy, entropy, and angular momentum densities with temperature and angular velocity. We also obtain a Smarr-type formula for the energy density as a function of entropy and angular momentum densities, and we show that the thermodynamic quantities calculated in this paper satisfy the first law of thermodynamics. Finally, we investigate the stability of black brane solutions in both canonical and grand-canonical ensemble. We find that the solutions are thermally stable for $z\le n-1$, while they can be unstable for $z>n-1$.

Vector fields in the expanding Universe are considered within the multidimensional theory of general relativity. Vector fields in general relativity form a three-parametric variety. Our consideration includes the fields with a nonzero covariant divergence. Depending on the relations between the particular parameters and the symmetry of a problem, the vector fields can be longitudinal and/or transverse, ultrarelativistic (i.e. massless) or nonrelativistic (massive), and so on. The longitudinal and transverse vector fields are considered separately in detail in the background of the de Sitter cosmological metric. In most cases the field equations reduce to Bessel equations, and their temporal evolution is analyzed analytically. The energy-momentum tensor of the most simple zero-mass longitudinal vector fields enters the Einstein equations as an additive to the cosmological constant. In this case the de Sitter metric is the exact solution of the Einstein equations. Hence, the most simple zero-mass longitudinal vector field pretends to be an adequate tool for macroscopic description of dark energy as a source of the expansion of the Universe at a constant rate. The zero-mass vector field does not vanish in the process of expansion. On the contrary, massive fields vanish with time. Though their amplitude is falling down, the massive fields make the expansion accelerated.

We consider Lemaitre-Tolman-Bondi spacetimes from the point of view of a tilted observer, i.e. one with respect to which the fluid is radially moving. The imperfect fluid and the congruence described by its four-velocity, as seen by the tilted observer, is studied in detail. It is shown that from the point of view of such tilted observer, the fluid evolves nonreversibly (i.e. with nonvanishing rate of entropy production). The nongeodesic character of the tilted congruence is related to the nonvanishing of the divergence of the 4-vector entropy flow. We determine the factor related to the existence of energy-density inhomogeneities and describe its evolution; these results are compared with those obtained for the nontilted observer. Finally, we exhibit a peculiar situation where the nontilted congruence might be unstable.

We shall present here a general apt technique to induce connections along bundle reductions, which is different from the standard restriction. This clarifies and generalizes the standard procedure to define Barbero-Immirzi (BI) connection, though on spacetime. The standard spacial BI connection used in LQG is then obtained by its spacetime version by standard restriction. The general prescription to define such a reduced connection is interesting from a mathematical viewpoint, and it allows a general and direct control on transformation laws of the induced object. Moreover, unlike what happens by using standard restriction, we shall show that once a bundle reduction is given, then any connection induces a reduced connection with no constraint on the original holonomy as it happens when connections are simply restricted.

One of the principle efforts in cosmic microwave background (CMB) research is measurement of the parameter $f_{\mathrm{nl}}$ that quantifies the departure from Gaussianity in a large class of nonminimal inflationary (and other) models. Estimators for $f_{\mathrm{nl}}$ are composed of a sum of products of the temperatures in three different pixels in the CMB map. Since the number $\sim N_{\mathrm{pix}}^2$ of terms in this sum exceeds the number $N_{\mathrm{pix}}$ of measurements, these $\sim N_{\mathrm{pix}}^2$ terms cannot be statistically independent. Therefore, the central-limit theorem does not necessarily apply, and the probability distribution function (PDF) for the $f_{\mathrm{nl}}$ estimator does not necessarily approach a Gaussian distribution for $N_{\mathrm{pix}}\gg 1$. Although the variance of the estimators is known, the significance of a measurement of $f_{\mathrm{nl}}$ depends on knowledge of the full shape of its PDF. Here we use Monte Carlo realizations of CMB maps to determine the PDF for two minimum-variance estimators: the standard estimator, constructed under the null hypothesis ($f_{\mathrm{nl}}=0$), and an improved estimator with a smaller variance for $f_{\mathrm{nl}}\ne 0$. While the PDF for the null-hypothesis estimator is very nearly Gaussian when the true value of $f_{\mathrm{nl}}$ is zero, the PDF becomes significantly non-Gaussian when $f_{\mathrm{nl}}\ne 0$. In this case we find that the PDF for the null-hypothesis estimator $\widehat{f_{\mathrm{nl}}}$ is skewed, with a long non-Gaussian tail at $\widehat{f_{\mathrm{nl}}}>|f_{\mathrm{nl}}|$ and less probability at $\widehat{f_{\mathrm{nl}}}<|f_{\mathrm{nl}}|$ than in the Gaussian case. We provide an analytic fit to these PDFs. On the other hand, we find that the PDF for the improved estimator is nearly Gaussian for observationally allowed values of $f_{\mathrm{nl}}$. We discuss briefly the implications for trispectrum (and other higher-order correlation) estimators.

We examine the potential of using colliders to distinguish models with parity ($Z_2$) stabilized dark matter (DM) from models in which the DM is stabilized by other symmetries, taking the latter to be a $Z_3$ symmetry for illustration. The key observation is that a heavier mother particle charged under a $Z_3$ stabilization symmetry can decay into one or two DM particles along with standard model particles. This can be contrasted with the decay of a mother particle charged under a parity symmetry; typically, only one DM particle appears in the decay chain. The arXiv:1003.0899 studied the distributions of visible invariant mass from the decay of a single such mother particle in order to highlight the resulting distinctive signatures of $Z_3$ symmetry versus parity symmetry stabilized dark matter candidates. We now describe a complementary study which focuses on decay chains of the two mother particles which are necessarily present in these events. We also include in our analysis the missing energy/momentum in the event. For the $Z_3$ symmetry stabilized mothers, the resulting inclusive final state can have two, three or four DM particles. In contrast, models with $Z_2$ symmetry can have only two. We show that the shapes and edges of the distribution of $M_{T2}$-type variables, along with ratio of the visible momentum/energy on the two sides of the event, are powerful in distinguishing these different scenarios. Finally we conclude by outlining future work which focuses on reducing combinatoric ambiguities from reconstructing multijet events. Increasing the reconstruction efficiency can allow better reconstruction of events with two or three dark matter candidates in the final state.

Lattice measurements of spatial distributions of the light quark bilinear densities in static mesons allow one to test directly and in detail the wave functions of quark models. These distributions are gauge invariant quantities directly related to the spatial distribution of wave functions. We make a detailed comparison of the recent lattice QCD results with our own relativistic quark models, formulated previously for quite different purposes. We find a striking agreement not only between our two quark models, but also with the lattice QCD data for the ground state in an important range of distances $r\lesssim 4{\mathrm{GeV}}^{-1}$. Moreover the agreement extends to the $L=1$ states [$j^P=(1/2{)}^{+}$]. An explanation of several particular features completely at odds with the nonrelativistic approximation is provided. A rather direct, somewhat unexpected, and of course approximate relation between wave functions of certain quark models and QCD has been established.

In a continuing effort to understand divergences which occur when quantum fields are confined by bounding surfaces, we investigate local energy densities (and the local energy-momentum tensor) in the vicinity of a wall. In this paper, attention is largely confined to a scalar field. If the wall is an infinite Dirichlet plane, well-known volume and surface divergences are found, which are regulated by a temporal point-splitting parameter. If the wall is represented by a linear potential in one coordinate $z$, the divergences are softened. The case of a general wall, described by a potential of the form $z^{\alpha }$ for $z>0$ is considered. If $\alpha >2$, there are no surface divergences, which in any case vanish if the conformal stress tensor is employed. Divergences within the wall are also considered.

Using hyperbolic temporal and spatial cutoffs to define four-dimensional asymptotically flat spacetimes, we show that supertranslation ambiguities in the asymptotic fields can all be removed even in the presence of gravitational magnetic charges. We then show that configurations with different electric and magnetic four-momenta can be consistently considered in the Mann-Marolf variational principle. This generalizes the previous result where variations over asymptotically flat configurations with fixed magnetic four-momenta were considered. We also express the Kerr Taub-NUT metric to the leading and next-to-leading order in the Beig-Schmidt form, and compare the asymptotic form with the tensor harmonics on three-dimensional de Sitter space.

We propose a new variant model of the modulated reheating. If particles have large scale fluctuations on their velocities, or equivalently their Lorentz factors, the decay rate also fluctuates and the curvature perturbation is induced via their decay processes in analogy with modulated reheating. For example, if they are produced nonthermally by the decay of another field with its mass fluctuating on large scales, such a situation is realized. We explicitly calculate the resulting curvature perturbation and nonlinearity parameters and show that the effect of velocity-modulation is not negligible if the particles are semirelativistic at the decay.

In the framework of a 3-3-1 model with a minimal scalar sector we make a detailed study concerning the implementation of the Peccei-Quinn symmetry in order to solve the strong $CP$ problem. For the original version of the model, with only two scalar triplets, we show that the entire Lagrangian is invariant under a Peccei-Quinn-like symmetry but no axion is produced since a $U(1)$ subgroup remains unbroken. Although in this case the strong $CP$ problem can still be solved, the solution is largely disfavored since three quark states are left massless to all orders in perturbation theory. The addition of a third scalar triplet removes the massless quark states but the resulting axion is visible. In order to become realistic the model must be extended to account for massive quarks and an invisible axion. We show that the addition of a scalar singlet together with a $Z_N$ discrete gauge symmetry can successfully accomplish these tasks and protect the axion field against quantum gravitational effects. To make sure that the protecting discrete gauge symmetry is anomaly-free we use a discrete version of the Green-Schwarz mechanism.

We use gauge-gravity duality to model the crossover from a conformal critical point to a confining Fermi liquid, driven by a change in fermion density. The short-distance conformal physics is represented by an anti–de Sitter geometry, which terminates into a confining state along the emergent spatial direction. The Luttinger relation, relating the area enclosed by the Fermi surfaces to the fermion density, is shown to follow from Gauss’s law for the bulk electric field. We argue that all low energy modes are consistent with Landau’s Fermi liquid theory. An explicit solution is obtained for the Fermi liquid for the case of hard-wall boundary conditions in the infrared.

We investigate strong coupling effects in a covariant massive gravity model, which is a candidate for a ghost-free nonlinear completion of Fierz-Pauli. We analyze the conditions to recover general relativity via the Vainshtein mechanism in the weak field limit, and find three main cases depending on the choice of parameters. In the first case, the potential is such that all nonlinearities disappear and the vDVZ discontinuity cannot be avoided. In the second case, the Vainshtein mechanism allows to recover general relativity within a macroscopic radius from a source. In the last case, the strong coupling of the scalar graviton completely shields the massless graviton, and weakens gravity when approaching the source. In the second part of the paper, we explore new exact vacuum solutions, that asymptote to de Sitter or anti de Sitter space depending on the choice of parameters. The curvature of the space is proportional to the mass of the graviton, thus providing a cosmological background which may explain the present-day acceleration in terms of the graviton mass. Moreover, by expressing the potential for nonlinear massive gravity in a convenient form, we also suggest possible connections with a higher-dimensional framework.

It is shown that in the static, spherically symmetric spacetime, the problem of metric $f(R)$ gravity coupled with nonlinear Yang-Mills (YM) field constructed from the Wu-Yang ansatz as source can be solved in all dimensions. By nonlinearity it is meant that the YM Lagrangian depends arbitrarily on its invariant. A particular form is considered to be in the power-law form with limit of the standard YM theory. The formalism admits black hole solutions with single or double horizons in which $f(R)$ can be obtained, in general numerically. In 6-dimensional case we obtain an exact solution given by $f(R)=\sqrt{R}$ gravity that couples with the YM field in a consistent manner.