In this article we investigate a conformal extension of the standard model in which the scalar sector consists of a standard model Higgs doublet, a real gauge singlet and a real $SU(2{)}_L$ triplet. Focusing on the scenario where the Higgs boson found at the LHC is identified as the pseudo-Nambu-Goldstone boson of broken scale invariance, various theoretical and phenomenological features of the model are discussed. In particular, we analyze the decay pattern of the new scalar resonance. We also show that when the mass of this new scalar resonance is far below the $WW$ threshold, the natural regions of the parameter space are reduced by a constraint associated with the symmetry enhancement due to the decoupling of the singlet scalar from the rest of the system.

We study microscopic processes responsible for chirality flips in the thermal bath of quantum chromodynamics at finite temperature and zero baryon chemical potential. We focus on the temperature range where the crossover from chirally broken phase to quark-gluon plasma takes place, namely, $T\simeq (150,200)\mathrm{MeV}$. The processes we consider are quark-quark scatterings mediated by collective excitations with the quantum number of pions and $\sigma$ meson; hence we refer to these processes simply as one-pion (one-$\sigma$) exchanges. We use a Nambu-Jona-Lasinio model to compute equilibrium properties of the thermal bath, as well as the relevant scattering kernel to be used in the collision integral to estimate the chiral relaxation time $\tau$. We find $\tau \simeq 0.1÷1\mathrm{fm}/\mathrm{c}$ around the chiral crossover.

The D0 collaboration has recently reported a narrow peak structure in the $B_s^0{\pi }^{\pm }$ invariant-mass spectrum, which is called $X(5568)$. Its proposed quantum numbers $J^P=0^{+}/1^{+}$ are not determined unambiguously, and we show that one can fit the data assuming $J^P=1^{-}$ with the same mass and width for the resonance signal. The corresponding isovector $P$-wave coupled-channel scattering involving the states $B_s\pi$, $B_s^{*}\pi$, $B\overline{K}$ and $B^{*}\overline{K}$ is studied employing leading-order heavy meson chiral perturbation theory, which is then unitarized making use of standard techniques from unitary chiral perturbation theory. The subtraction constants that appear in the unitarization process are determined by a $u$-channel crossing symmetry constraint or by naturalness arguments, being the numerical values obtained in both cases quite closed, and no further freedom is left in the model. A crucial point is that if the $X(5568)$ is $1^{-}$ and decaying into $B_s^0{\pi }^{\pm }$ then it should appear as a pole in the $T$-matrix elements. It finally turns out that no $X(5568)$ pole is found that can be qualified as dynamically generated from the isovector $P$-wave coupled-channel dynamics. This result disfavors the interpretation of the $X(5568)$ within a “molecular” picture.

Four exotic charmoniumlike states, i.e., $X(4140)$, $X(4274)$, $X(4500)$, and $X(4700)$, have been observed very recently by the LHCb Collaboration in the decay process $B^{+}\to J/\psi \varphi K^{+}$ using the $3{\mathrm{fb}}^{-1}$ data of $p\overline{p}$ collisions at $\sqrt{s}=7$ and 8 TeV. In this paper, we investigate systematically the properties of hidden charm tetraquark states. The hidden charm tetraquarks form an octet configuration and a singlet configuration according to flavor SU(3) symmetry. Based on a diquark-antidiquark model, the hidden charm tetraquarks spectra are given. The previous $XYZ$ exotic states, altogether with the new ones, $X(4140)$, $X(4274)$, $X(4500)$, and $X(4700)$, can be well classified into certain representations. The spin parities and masses of the $XYZ$ are predicted, most of which are in agreement with the data. We particularly find that $Z_c(4430)$ may be treated as the first radial excitation of $Z_c(3900)$, while the $Y(1^{--})$ states can be obtained by the first orbital excitation of the $X/Z$ states. Besides, we calculate the decay widths of the hidden charm tetraquarks into two charmed mesons. This work gives a general tetraquark description for the $XYZ$ states, which is helpful to uncover their inner structures.

We construct a list of minimal scale-invariant models at the TeV scale that generate one-loop neutrino mass and give viable dark matter candidates. The models generically contain a singlet scalar and a $Z_2$-odd sector comprised of singlet, doublet, and/or triplet SU(2) multiplets. The dark matter may reside in a single multiplet or arise as an admixture of several multiplets. We find 15 independent models, for which the dark matter is a viable candidate and neutrino mass results from a diagram with just one of the irreducible scale-invariant one-loop topologies. Further “nonpure” cases give hybrid one-/two-loop masses. All models predict new TeV scale physics, including a singlet scalar that generically mixes with the Higgs boson.

Future dark matter detectors plan to have sensitivities such that solar neutrinos will start to become a problematic background. In this work, we show that a polarized helium-3 detector would, in principle, be able to eliminate 98% of these events when the orientation of the polarization axis is antiparallel to the direction of the Sun. We comment on the possible improvement in sensitivity of dark matter direct detection experiments due to this effect and the feasibility of building such a detector.

A new measurement of the parity-violating asymmetry in the electron-deuteron quasielastic scattering for backward angles at $⟨Q^2⟩=0.224{(\mathrm{GeV}/c)}^2$, obtained in the A4 experiment at the Mainz Microtron accelerator (MAMI) facility, is presented. The measured asymmetry is $A_{PV}^d=(-20.11\pm 0.87_{\mathrm{stat}}\pm 1.03_{\mathrm{sys}})\times {10}^{-6}$. A combination of these data with the proton measurements of the parity-violating asymmetry in the A4 experiment yields a value for the effective isovector axial-vector form factor of $G_A^{e,(T=1)}=-0.19\pm 0.43$ and $R_A^{(T=1),\mathrm{anap}}=-0.41\pm 0.35$ for the anapole radiative correction. When combined with a reanalysis of measurements obtained in the G0 experiment at the Thomas Jefferson National Accelerator Facility, the uncertainties are further reduced to $G_M^s=0.17\pm 0.11$ for the magnetic strange form factors, and $R_A^{(T=1),\mathrm{anap}}=-0.54\pm 0.26$.

We address the issue of the renormalizability of the gauge-invariant nonlocal dimension-two operator $A_{\min }^2$, whose minimization is defined along the gauge orbit. Despite its nonlocal character, we show that the operator $A_{\min }^2$ can be cast in local form through the introduction of an auxiliary Stueckelberg field. The localization procedure gives rise to an unconventional kind of Stueckelberg-type action that turns out to be renormalizable to all orders of perturbation theory. In particular, as a consequence of its gauge invariance, the anomalous dimension of the operator $A_{\min }^2$ turns out to be independent from the gauge parameter $\alpha$ entering the gauge-fixing condition, thus being given by the anomalous dimension of the operator $A^2$ in the Landau gauge.

For the case of spin zero, we construct conjugate pairs of operators on Fock space. On states multiplied by polarization vectors, coordinate operators $Q$ conjugate to the momentum operators $P$ exist. In the massive case the notion of interest is derived from a geometrical quantity, the massless case is realized by taking the limit $m^2\to 0$ on the one hand, on the other, starting with $m^2=0$ directly, from conformal transformations. The norm problem of the states on which the $Q$’s act is crucial: the states determine eventually how many independent conjugate pairs exist. It is intriguing that (light-) wedge variables and, hence, the wedge-local case seem to be preferred.

Preconjugate variables $X$ have commutation relations with the energy-momentum $P$ of the respective system which are of a more general form than just the Hamiltonian one. Since they have been proven useful in their own right for finding new spacetimes, we present a study of them here. Interesting examples $X$ can be found via geometry—motions on the mass shell for massive and massless systems—and via group theory—invariance under special conformal transformations of the mass shell and light cone, respectively. Both find representations on Fock space. We work mainly in ordinary four-dimensional Minkowski space and spin zero. The limit process from nonzero to vanishing mass turns out to be nontrivial and leads naturally to wedge variables. We point out some applications and extensions to more general spacetimes. In a companion paper, we discuss the transition to conjugate pairs.

We study the lowest-mass eigenstates of ${\varphi }_{1+1}^4$ theory with both odd and even numbers of constituents. The calculation is carried out as a diagonalization of the light-front Hamiltonian in a Fock-space representation. In each Fock sector a fully symmetric polynomial basis is used to represent the Fock wave function. Convergence is investigated with respect to the number of basis polynomials in each sector and with respect to the number of sectors. The dependence of the spectrum on the coupling strength is used to estimate the critical coupling for the positive-mass-squared case. An apparent discrepancy with equal-time calculations of the critical coupling is resolved by an appropriate mass renormalization.

We examine an Unruh-DeWitt particle detector that is coupled linearly to the scalar density of a massless Dirac field in Minkowski spacetimes of dimension $d\ge 2$ and on the static Minkowski cylinder in spacetime dimension two, allowing the detector’s motion to remain arbitrary and working to leading order in perturbation theory. In $d$-dimensional Minkowski, with the field in the usual Fock vacuum, we show that the detector’s response is identical to that of a detector coupled linearly to a massless scalar field in $2d$-dimensional Minkowski. In the special case of uniform linear acceleration, the detector’s response hence exhibits the Unruh effect with a Planckian factor in both even and odd dimensions, in contrast to the Rindler power spectrum of the Dirac field, which has a Planckian factor for odd $d$ but a Fermi-Dirac factor for even $d$. On the two-dimensional cylinder, we set the oscillator modes in the usual Fock vacuum but allow an arbitrary state for the zero mode of the periodic spinor. We show that the detector’s response distinguishes the periodic and antiperiodic spin structures, and the zero mode of the periodic spinor contributes to the response by a state-dependent but well-defined amount. Explicit analytic and numerical results on the cylinder are obtained for inertial and uniformly accelerated trajectories, recovering the $d=2$ Minkowski results in the limit of large circumference. The detector’s response has no infrared ambiguity for $d=2$, neither in Minkowski nor on the cylinder.

We study the propagation of low-frequency shallow water waves on a one-dimensional flow of varying depth. When taking into account dispersive effects, the linear propagation of long-wavelength modes on uneven bottoms excites new solutions of the dispersion relation which possess a much shorter wavelength. The peculiarity is that one of these new solutions has a negative energy. When the flow becomes supercritical, this mode has been shown to be responsible for the (classical) analog of the Hawking effect. For subcritical flows, the production of this mode has been observed numerically and experimentally, but the precise physics governing the scattering remained unclear. In this work, we provide an analytic treatment of this effect in subcritical flows. We analyze the scattering of low-frequency waves using a new perturbative series, derived from a generalization of the Bremmer series. We show that the production of short-wavelength modes is governed by a complex value of the position: a complex turning point. Using this method, we investigate various flow profiles and derive the main characteristics of the induced spectrum.

In previous work, the Lorentzian proper vertex amplitude for a spin-foam model of quantum gravity was derived. In the present work, the asymptotics of this amplitude are studied in the semiclassical limit. The starting point of the analysis is an expression for the amplitude as an action integral with action differing from that in the Engle-Pereira-Rovelli-Livine (EPRL) case by an extra “projector” term. This extra term scales linearly with spins only in the asymptotic limit, and is discontinuous on a (lower dimensional) submanifold of the integration domain in the sense that its value at each such point depends on the direction of approach. New tools are introduced to generalize stationary phase methods to this case. For the case of boundary data which can be glued to a nondegenerate Lorentzian 4-simplex, the asymptotic limit of the amplitude is shown to equal the single Feynman term, showing that the extra term in the asymptotics of the EPRL amplitude has been eliminated.

Spin foam models, an approach to defining the dynamics of loop quantum gravity, make use of the Plebanski formulation of gravity, in which gravity is recovered from a topological field theory via certain constraints called simplicity constraints. However, the simplicity constraints in their usual form select more than just one gravitational sector as well as a degenerate sector. This was shown, in previous work, to be the reason for the “extra” terms appearing in the semiclassical limit of the Euclidean Engle-Pereira-Rovelli-Livine amplitude. In this previous work, a way to eliminate the extra sectors, and hence terms, was developed, leading to what was called the Euclidean proper vertex amplitude. In the present work, these results are extended to the Lorentzian signature, establishing what is called the Lorentzian proper vertex amplitude. This extension is nontrivial and involves a number of new elements since, for Lorentzian bivectors, the split into self-dual and antiself-dual parts, on which the Euclidean derivation was based, is no longer available. In fact, the classical parts of the present derivation provide not only an extension to the Lorentzian case, but also, with minor modifications, a new, more four-dimensionally covariant derivation for the Euclidean case. The new elements in the quantum part of the derivation are due to the different structure of unitary representations of the Lorentz group.

Shape dynamics is a 3D conformally invariant theory of gravity that possesses a large set of solutions in common with general relativity. When looked at closely, these solutions are found to behave in surprising ways; in order to probe the fitness of shape dynamics as a viable alternative to General Relativity one must find and understand increasingly more-complex, less-symmetrical exact solutions on which to base perturbative studies and numerical analyses to compare them with data. Spherically symmetric exact solutions have been studied, but only in a static vacuum setup. In this work we construct a class of time-dependent exact solutions of Shape Dynamics from first principles, representing a central inhomogeneity in an evolving cosmological environment. By assuming only a perfect fluid source in a spherically symmetric geometry, we show that this fully dynamic nonvacuum solution satisfies in all generality the Hamiltonian structure of shape dynamics. The simplest choice of solutions is shown to be a member of the McVittie family.

We study the relation between the Jordan-Einstein frame transition and the possible description of the crossing of singularities in flat Friedmann universes, using the fact that the regular evolution in one frame can correspond to crossing singularities in the other frame. We show that some interesting effects arise in simple models such as one with a massless scalar field or another wherein the potential is constant in the Einstein frame. The dynamics in these models and in their conformally coupled counterparts are described in detail, and a method for the continuation of such cosmological evolutions beyond the singularity is developed. We compare our approach with some other, recently developed, approaches to the problem of the crossing of singularities.

We revisit the compatibility between chaotic inflation, which provides a natural solution to the initial condition problem, and the metastable electroweak vacuum, which is suggested by the results of the LHC and the current mass measurements of the top quark and Higgs boson. It is known that chaotic inflation poses a threat to the stability of the electroweak vacuum because it easily generates large Higgs fluctuations during inflation or preheating and triggers the catastrophic vacuum decay. In this paper, we propose a simple cosmological solution in which the vacuum is stabilized during chaotic inflation, preheating, and afterwards. This simple solution naturally predicts formation of primordial black holes. We find interesting parameter regions where the present dark matter density is provided by them. Also, the thermal leptogensis can be accommodated in our scenario.

Prerecombination acoustic oscillations induce nonadiabatic perturbations between baryons and dark matter, corresponding to a constant relative-density ${\delta }_{bc}$ and decaying relative-velocity perturbation ${\mathit{v}}_{bc}$. Due to their significant large-scale correlations and prominent baryon acoustic oscillation (BAO) features, these modes are potentially important for the use of the BAO as standard ruler. We present a complete treatment of the effects of the baryon–cold dark matter perturbations on galaxy clustering in the context of a rigorous perturbative bias expansion. The leading effects are proportional to ${\delta }_{bc}$ and ${\theta }_{bc}={\partial }_i{v}_{bc}^i$. We estimate the magnitude of these terms through the excursion set approach. The contribution from $v_{bc}^2$, which has attracted significant attention recently, contributes at subleading (one-loop) order. The relative-density contribution ${\delta }_{bc}$ is expected to be by far the largest contribution. We also point out contributions to the galaxy velocity bias, the largest of which is simply $v_{bc}$, leading to a term $\propto {\mu }^2{\theta }_{bc}$ in the redshift-space galaxy power spectrum $P_g^s(k,\mu )$. Complete expressions of the galaxy power spectrum at one-loop order are given, which contain several new terms.

We study a geometric transition in a nonperturbative topological string. We consider two cases. One is the geometric transition from the closed topological string on the local ${\mathcal{B}}_3$ to the closed topological string on the resolved conifold. The other is the geometric transition from the closed topological string on the local ${\mathcal{B}}_3$ to the open topological string on the resolved conifold with a toric A-brane. We find that, in both cases, the geometric transition can be applied for the nonperturbative topological string. We also find the corrections of the value of the Kähler parameters at which the geometric transition occurs.