The recent measured ${\gamma }^{*}\gamma \to {\pi }^0$ transition form factor in the spacelike region by the Belle Collaboration together with the previously published results by CLEO, CELLO, and BABAR collaborations, are analyzed using the mathematical theory of Padé approximants. The theory provides a good and systematic description of the low-energy region exemplified here with the extraction of the slope $a_{\pi }$ and curvature $b_{\pi }$ of the form factor in a model-independent way. Their impact on the pion exchange contribution to the hadronic light-by-light scattering part of the anomalous magnetic moment $a_{\mu }$ is also discussed.

Employing induced representations of the Lorentz group (Wigner’s little group construction), formalism for constructing heavy particle effective Lagrangians is developed, and Lagrangian constraints enforcing Lorentz invariance of the $S$ matrix are derived. The relationship between Lorentz invariance and reparametrization invariance is established and it is shown why a standard ansatz for implementing reparametrization invariance in heavy fermion effective Lagrangians breaks down at order $1/M^4$. Formalism for fields of arbitrary spin and for self-conjugate fields is presented, and the extension to effective theories of massless fields is discussed.

In this paper we show that the flat-space Galilean theories with up to three scalars in the equation of motion (the quartic Galileons) are recovered in the decoupling limit of certain scalar theories nonminimally coupled to gravity, the so-called “Slotheonic” theories. These theories are also invariant under the generalized Galilean shifts in curved spacetime. While Galilean self-(derivative) couplings are not explicit in the action, they appear after integrating out gravity. We then argue that Galilean supersymmetric theories may only be found in the context of supergravity. Finally, we discuss the possibility that Slotheonic theories are the effective four-dimensional theories of consistent Dvali-Gabadadze-Porrati-like models with self-accelerating cosmological solutions. Moreover, we show that the quartic and cubic Galileons in consistent Dvali-Gabadadze-Porrati models cannot be decoupled.

Using an exact expression for the domain wall tension in a supersymmetric model, we show that a spectrum crossover takes place in passing from weak to strong coupling. In the weak coupling regime, elementary excitations are the lightest states, while in the strong coupling regime, solitonic objects of a special type—bubbles—assume the role of the lightest states. The crossover occurs at ${\lambda }^2/(4\pi )\sim 0.4$.

We derive non-Abelian localization formulas for supersymmetric Yang-Mills-Chern-Simons theory with matters on a Seifert manifold $M$, which is the three-dimensional space of a circle bundle over a two-dimensional Riemann surface $\Sigma$, by using the cohomological approach introduced by Källén. We find that the partition function and the vacuum expectation value of the supersymmetric Wilson loop reduces to a finite dimensional integral and summation over classical flux configurations labeled by discrete integers. We also find that the partition function reduces further to just a discrete sum over integers in some cases, and evaluate the supersymmetric index (Witten index) exactly on $S^1\times \Sigma$. The index completely agrees with the previous prediction from field theory and branes. We discuss a vacuum structure of the Aharony-Bergman-Jafferis-Maldacena theory deduced from the localization.

Traditional approaches to the study of the dynamics of spacetime curvature in a very real sense hide the intricacies of the nonlinear regime. Whether it be huge formulas, or mountains of numerical data, standard methods of presentation make little use of our remarkable skill, as humans, at pattern recognition. Here we introduce a new approach to the visualization of spacetime curvature. We examine the flows associated with the gradient fields of scalar invariants derived from the spacetime. These flows reveal a remarkably rich structure, and offer fresh insights, even for well-known analytical solutions to Einstein’s equations. The intent, however, is to go beyond idealized analytical solutions and eventually consider physically realistic situations. This requires a careful analysis of exactly which invariants that can actually be used in this approach. The present analysis serves as an overview and as an introduction to this program.

Aretakis has proved the existence of an instability of a massless scalar field at the horizon of an extreme Kerr or Reissner-Nordström black hole: for generic initial data, a transverse derivative of the scalar field at the horizon does not decay, and higher transverse derivatives blow up. We show that a similar instability occurs for linearized gravitational, and electromagnetic, perturbations of an extreme Kerr black hole. We show also that the massless scalar field instability occurs for extreme black hole solutions of a large class of theories in various spacetime dimensions.

We study the contribution to the decay of de Sitter vacua from bounces with $\mathrm{O}(3)\times \mathrm{O}(2)$ symmetry. These correspond to the thermal production of a vacuum bubble at the center of a horizon volume with radius $r_H$ and a temperature defined by the horizon. They are analogues of the flat spacetime bounces, independent of Euclidean time, that correspond to thermal production of a critical bubble. If either the strength of gravity or the false vacuum energy are increased, with all other parameters held fixed, the bounces approach, and eventually merge with, the Hawking-Moss solution. Increasing the height of the barrier separating the true and false vacuum, and thus the tension in the bubble wall, causes the center of the bubble wall to approach, but never reach, the horizon. This is in contrast with the prediction of the thin-wall approximation, which inevitably breaks down when the wall is near the horizon. Our numerical results show that the Euclidean action of our solutions is always greater than that of the corresponding O(4)-symmetric Coleman-De Luccia bounce.

We present the simplest possible model for a semilocal string defect in which a U(1) gauged subgroup of an otherwise global SU(2) is broken to produce local cosmic strings endowed with current-carrying properties. Restricting attention to type II vortices for which the non-current-carrying state is unstable, we show that a condensate must form microscopically and macroscopically evolve towards a chiral configuration. It has been suggested that such configurations could potentially exist in a stable state, thereby inducing large cosmological consequences based on equilibrium angular momentum supported loop configurations (vortons). Here we show that the current itself induces a macroscopic (longitudinal) instability: we conclude that type II semilocal cosmic strings cannot form in a cosmological context.

We estimate fermion loop corrections to the two-point correlation function of primordial tensor perturbations in a slow-roll inflationary background. We particularly compute an explicit term of one-loop correction from a massless fermion and then extend to the complete interaction Hamiltonian. After that, we study one-loop corrections contributed by a massive fermion to primordial tensor fluctuations. The loop correction arisen from a massless fermion field contains logarithms and thus may constrain the validity of perturbation theory in inflationary cosmology, but the situation could be relaxed once the fermion’s mass is taken into account. Another one-loop diagram for a massive fermion that involves one vertex is constrained by a UV cutoff as expected by quantum field theory. Our result shows that loop corrections of a fermion field have the same sign as those of a scalar field and, thus, implies that the inclusion of fermion loop corrections may not help to alleviate the issue of IR divergence in inflationary cosmology.

It is well-known that allowing for spatial curvature affects constraints on cosmological parameters such as the dark energy equation of state parameters. Here we study the effect of curvature on constraints on parameters used to test general relativity (GR) at cosmological scales, commonly known as modified growth (MG) parameters. While current data taken in the context of the $\Lambda \mathrm{CDM}$ model points to a universe that is spatially flat, this constraint does not necessarily hold in modified gravity theories or even in relativistic inhomogeneous cosmological models. Using the latest cosmological data sets we find that MG parameters are correlated with the curvature parameter ${\Omega }_k$ and the constraints on the MG parameters are weakened compared to when ${\Omega }_k$ is not included in the parameter analysis. We next use various future simulated data sets, including cosmic microwave background, weak lensing, and Integrated Sachs-Wolfe-galaxy cross-correlations, where the fiducial model is spatially curved but we assume a flat model when fitting the MG parameters. We find the assumption of a spatially flat model on a spatially curved universe does indeed cause an artificial shift in the constraints on the MG parameters, in some cases even producing an apparent deviation from GR in the MG parameter space. For our simulated data, tension with GR begins to manifest itself for fiducial models with $|{\Omega }_k|\ge 0.02$ and apparent deviations appear for $|{\Omega }_k|\ge 0.05$. We find that for negatively curved models the apparent deviation is more significant. The manifestation of this apparent deviation from GR due to the assumption of spatial flatness above leads one to conclude that, when using future high-precision data to perform these tests, spatial curvature must be included in the parameter analysis along with the other core cosmological parameters and the MG parameters.

Based on recent LHC Higgs analyses and in anticipation of future results we revisit theories where Higgs bosons can couple to weak gauge bosons with enhanced strength relative to the Standard Model value. Specifically, we look at the Georgi-Machacek model and its generalizations where higher “spin” representations of $SU(2{)}_L$ break electroweak symmetry while maintaining custodial $SU(2)$. In these theories, there is not only a Higgs-like boson but partner Higgs scalars transforming under representations of custodial $SU(2)$, leading to a rich phenomenology. These theories serve as a consistent theoretical and experimental framework to explain enhanced couplings to gauge bosons, including fermiophobic Higgses. We focus on the phenomenology of a neutral scalar partner to the Higgs, which is determined once the Higgs couplings are specified. Depending on the parameter space, this partner could have (i) enhanced fermion and gauge boson couplings and should be searched for at high mass ($>600\mathrm{GeV}$), (ii) suppressed couplings and could be searched for at lower masses, where the Standard Model Higgs has already been ruled out, and (iii) fermiophilic couplings, where it can be searched for in heavy Higgs and top resonance searches. In the first two regions, the partner also has substantial decay rates into a pair of Higgs bosons. We touch briefly on the more model-dependent effects of the nontrivial $SU(2{)}_C$ multiplets, which have exotic signals, such as a doubly charged Higgs. We also discuss how the loop induced effects of these scalars tend to reduce the Higgs decay rate to photons, adding an additional uncertainty when extracting the couplings for the Higgs boson.

The measurement of the forward-backward asymmetry at LHC could be an important instrument to pinpoint the features of extra neutral gauge particles obtained by an extension of the gauge symmetry group of the standard model. For definitiveness, in this work, we consider an extension of the gauge group of the minimal supersymmetric standard model by an extra anomalous U(1) gauge symmetry. We focus on $pp\to e^{+}{e}^{-}$ at LHC and use four different definitions of the asymmetry obtained implementing four different cuts on the directions and momenta of the final states of our process of interest. The calculations are performed without imposing constraints on the charges of the extra $Z$’s of our model, since the anomaly is cancelled by a Green-Schwarz type mechanism. Our final result is a fit of our data with a polynomial in the charges of the extra U(1) that is used to extract the values of the charges, given the experimental result.

New physics in the chromomagnetic flavor changing transition $s\to d{g}^{*}$ can avoid the strong Glashow-Iliopoulos-Maiani suppression of the standard model and lead to large contributions to $CP$-violating observables, in particular to the ${ϵ}^{\prime }$ parameter, that we address here. We discuss the case of the left-right symmetric models, where this contribution implies bounds on the phases of the right-handed quark mixing matrix, or in generic models with large phases a strong bound on the left-right symmetry scale. To the leading order, a numeric formula for ${ϵ}^{\prime }$ as a function of the short-distance coefficients for a wide class of models of new physics is given.

We present a study of the many-body interaction between a $D^{*}$ and multi-$\rho$. We use an extrapolation to SU(4) of the hidden gauge formalism, which produced dynamically the resonances $f_2(1270)$ in the $\rho \rho$ interaction and $D_2^{*}(2460)$ in the $\rho D^{*}$ interaction. We then let a third particle, $\rho$, $D^{*}$, or a resonance, collide with them, evaluating the scattering amplitudes in terms of the fixed center approximation of the Faddeev equations. We find several clear resonant structures above 2800 MeV in the multibody scattering amplitudes. They would correspond to new charmed resonances, $D_3^{*}$, $D_4^{*}$, $D_5^{*}$, and $D_6^{*}$, which are not yet listed in the Particle Data Group, which would be analogous to the ${\rho }_3(1690)$, $f_4(2050)$, ${\rho }_5(2350)$, $f_6(2510)$ and $K_3^{*}(1780)$, $K_4^{*}(2045)$, $K_5^{*}(2380)$ described before as multi-$\rho$ and $K^{*}$-multi-$\rho$ states, respectively.

In SU(3) lattice QCD formalism, we propose a method to extract gauge fields from link variables analytically. With this method, we perform the first study on effective mass generation of off-diagonal gluons and infrared Abelian dominance in the maximally Abelian gauge in the SU(3) case. Using SU(3) lattice QCD, we investigate the propagator and the effective mass of the gluon fields in the maximally Abelian gauge with $\mathrm{U}(1{)}_3\times \mathrm{U}(1{)}_8$ Landau gauge fixing. The Monte Carlo simulation is performed on ${16}^4$ at $\beta =5.7$, 5.8, and 6.0 at the quenched level. The off-diagonal gluons behave as massive vector bosons with the approximate effective mass $M_{\mathrm{off}}\simeq 1.0–1.1\mathrm{GeV}$ in the region of $r=0.3–0.8\mathrm{fm}$, and the propagation is limited within a short range, while the propagation of diagonal gluons remains even in a large range. In this way, infrared Abelian dominance is shown in terms of short-range propagation of off-diagonal gluons. Furthermore, we investigate the functional form of the off-diagonal gluon propagator. The functional form is well described by the four-dimensional Euclidean Yukawa-type function $e^{-m_{\mathrm{off}}r}/r$ with $m_{\mathrm{off}}\simeq 1.2–1.3\mathrm{GeV}$ for $r=0.1–0.8\mathrm{fm}$. This also indicates that the spectral function of off-diagonal gluons has the negative-value region.

We analyze the neutron fluxes correlated with thunderstorm activity recently measured at mountain altitudes by the Tien-Shan, Tibet, and Aragats groups. We perform simulations of the photonuclear reactions of gamma rays born in the electron-gamma ray avalanches and calculate the expected count rates of the neutron detectors used by the three groups. We also present results of an independent experiment performed at the Nor Amberd high altitude research station in Armenia. Our analysis supports the Tibet and Aragats groups’ conclusions on the photonuclear nature of thunderstorm-correlated neutrons (directly in the neutron monitor and in the atmosphere). The photonuclear reactions of the gamma rays born in the electron-photon avalanches in the thunderstorm atmospheres interacting with the air atoms and with lead producer of a neutron monitor can provide neutron yield compatible with additional count of neutron monitors registered during thunderstorm ground enhancements.

The amplitude of the diphoton decay of the Higgs boson is considered in an extension of the Standard Model involving heavy vectorlike fermions, which was recently suggested in the literature in order to explain a possible enhancement of the $h\to \gamma \gamma$ decay rate. It is pointed out that generally in such models the decay amplitude acquires a sizable $CP$-odd contribution from the complex phases in the mass matrix of the new heavy fermions. The resulting $CP$ violation in the diphoton decay can be studied experimentally when both photons are converted into $e^{+}{e}^{-}$ pairs by measuring the distribution over the angle between the planes of the pairs. Such measurement, if feasible, would be of great interest on its own, regardless of specific models.

In recent papers, we and colleagues have introduced a way to visualize the full vacuum Riemann curvature tensor using frame-drag vortex lines and their vorticities, and tidal tendex lines and their tendicities. We have also introduced the concepts of horizon vortexes and tendexes and three-dimensional vortexes and tendexes (regions on or outside the horizon where vorticities or tendicities are large). In this paper, using these concepts, we discover a number of previously unknown features of quasinormal modes of Schwarzschild and Kerr black holes. These modes can be classified by a radial quantum number $n$, spheroidal harmonic orders $(l,m)$, and parity, which can be electric $[(-1{)}^l]$ or magnetic $[(-1{)}^{l+1}]$. Among our discoveries are these: (i) There is a near duality between modes of the same $(n,l,m)$: a duality in which the tendex and vortex structures of electric-parity modes are interchanged with the vortex and tendex structures (respectively) of magnetic-parity modes. (ii) This near duality is perfect for the modes’ complex eigenfrequencies (which are well known to be identical) and perfect on the horizon; it is slightly broken in the equatorial plane of a nonspinning hole, and the breaking becomes greater out of the equatorial plane, and greater as the hole is spun up; but even out of the plane for fast-spinning holes, the duality is surprisingly good. (iii) Electric-parity modes can be regarded as generated by three-dimensional tendexes that stick radially out of the horizon. As these “longitudinal,” near-zone tendexes rotate or oscillate, they generate longitudinal-transverse near-zone vortexes and tendexes and outgoing and ingoing gravitational waves. The ingoing waves act back on the longitudinal tendexes, driving them to slide off the horizon, which results in decay of the mode’s strength. (iv) By duality, magnetic-parity modes are driven in this same manner by longitudinal, near-zone vortexes that stick out of the horizon. (v) When visualized, the three-dimensional vortexes and tendexes of a $(l,m)=(2,2)$ mode, and also a (2,1) mode, spiral outward and backward like water from a whirling sprinkler, becoming outgoing gravitational waves. By contrast, a (2,2) mode superposed on a $(2,-2)$ mode, has oscillating horizon vortexes or tendexes that eject three-dimensional vortexes and tendexes, which propagate outward becoming gravitational waves; and so does a (2,0) mode. (vi) For magnetic-parity modes of a Schwarzschild black hole, the perturbative frame-drag field, and hence also the perturbative vortexes and vortex lines, are strictly gauge invariant (unaffected by infinitesimal magnetic-parity changes of time slicing and spatial coordinates). (vii) We have computed the vortex and tendex structures of electric-parity modes of Schwarzschild in two very different gauges and find essentially no discernible differences in their pictorial visualizations. (viii) We have compared the vortex lines, from a numerical-relativity simulation of a black hole binary in its final ringdown stage, with the vortex lines of a (2,2) electric-parity mode of a Kerr black hole with the same spin ($a/M=0.945$) and find remarkably good agreement.