Search Results (7)

Anomaly-free $U\left(1\right)$ extensions of the standard model (SM) predict a new neutral gauge boson $Z^{\prime }$. When $Z^{\prime }$ obtains its mass from the spontaneous breaking of the new $U\left(1\right)$ symmetry by a new complex scalar field, the model also predicts a second real scalar s, and the search for the new scalar and the search for the new gauge boson become intertwined. We present the computation of production cross sections and decay widths of such a scalar s in models with a light $Z^{\prime }$ boson when the decay $h\to Z^{\prime }{Z}^{\prime }$ may have a sizeable branching ratio. We show how the Higgs signal strength measurement in this channel can provide stricter exclusion bounds on the parameters of the model than those obtained from the total signal strength for Higgs boson production. Full article

In this paper, we study the localization of the five-dimensional $U\left(1\right)$ gauge field coupled with a background scalar potential on symmetric and asymmetric degenerate Bloch branes. By decomposing the $U\left(1\right)$ gauge field $A_M$ into its vector part (${\widehat{A}}_M$) and scalar components, we found that the Lagrangian of the five-dimensional $U\left(1\right)$ gauge field can be rewritten as two independent parts: one for the vector field and the other for two scalar fields. Regarding the vector part, the effective potential exhibits a volcano-like shape with finite depth. We obtain a massless vector field on both types of Bloch branes and a set of massive KK resonances. For the scalar part, their massless modes are coupled with each other, while two sets of massive scalar KK modes are independent. Similar to the vector effective potential, the scalar potentials create infinite wells for both types of degenerate Bloch brane solutions. Therefore, there is only one independent massless scalar mode and two sets of massive scalar Kaluza–Klein resonances. Furthermore, we also observed that, for the two types of Bloch brane solutions, the asymmetric parameter $c_0$ has different effects on the localization of scalar modes. Full article

In this paper, we study the theory of second gradient electromagnetostatics as the static version of second gradient electrodynamics. The theory of second gradient electrodynamics is a linear generalization of higher order of classical Maxwell electrodynamics whose Lagrangian is both Lorentz and $U\left(1\right)$ -gauge invariant. Second gradient electromagnetostatics is a gradient field theory with up to second-order derivatives of the electromagnetic field strengths in the Lagrangian. Moreover, it possesses a weak nonlocality in space and gives a regularization based on higher-order partial differential equations. From the group theoretical point of view, in second gradient electromagnetostatics the (isotropic) constitutive relations involve an invariant scalar differential operator of fourth order in addition to scalar constitutive parameters. We investigate the classical static problems of an electric point charge, and electric and magnetic dipoles in the framework of second gradient electromagnetostatics, and we show that all the electromagnetic fields (potential, field strength, interaction energy, interaction force) are singularity-free, unlike the corresponding solutions in the classical Maxwell electromagnetism and in the Bopp–Podolsky theory. The theory of second gradient electromagnetostatics delivers a singularity-free electromagnetic field theory with weak spatial nonlocality. Full article

We discuss the possibility that inflation is driven by supersymmetry breaking with the scalar component of the goldstino superfield (sgoldstino) playing the role of the inflaton and charged under a gauged $U\left(1\right)$ R-symmetry. Imposing a linear superpotential allows us to satisfy easily the slow-roll conditions, avoiding the so-called $\eta$ -problem, and leads to an interesting class of small field inflation models, characterised by an inflationary plateau around the maximum of the scalar potential near the origin, where R-symmetry is restored with the inflaton rolling down to a minimum describing the present phase of the Universe. Inflation can be driven by either an F- or a D-term, while the minimum has a positive tuneable vacuum energy. The models agree with cosmological observations and in the simplest case predict a rather small tensor-to-scalar ratio of primordial perturbations. We propose a generalisation of Fayet-Iliopoulos model as a microscopic model leading to this class of inflation models at low energy. Full article

We consider an anomaly free extension of the standard model gauge group $G_{\mathrm{SM}}$ by an abelian group to $G_{\mathrm{SM}}\otimes U{\left(1\right)}_Z$ . The condition of anomaly cancellation is known to fix the Z-charges of the particles, but two. We fix one remaining charge by allowing for all possible Yukawa interactions of the known left-handed neutrinos and new right-handed ones that obtain their masses through interaction with a new scalar field with spontaneously broken vacuum. We discuss some of the possible consequences of the model. Full article

In recent literature, one-loop tests of the higher-spin AdS ${}_{d+1}$ /CFT ${}_d$ correspondences were carried out. Here, we extend these results to a more general set of theories in $d>2$ . First, we consider the Type B higher spin theories, which have been conjectured to be dual to CFTs consisting of the singlet sector of N free fermion fields. In addition to the case of N Dirac fermions, we carefully study the projections to Weyl, Majorana, symplectic and Majorana–Weyl fermions in the dimensions where they exist. Second, we explore theories involving elements of both Type A and Type B theories, which we call Type AB. Their spectrum includes fields of every half-integer spin, and they are expected to be related to the $U\left(N\right)/O\left(N\right)$ singlet sector of the CFT of N free complex/real scalar and fermionic fields. Finally, we explore the Type C theories, which have been conjectured to be dual to the CFTs of p-form gauge fields, where $p=\frac{d}{2}-1$ . In most cases, we find that the free energies at $O\left(N^0\right)$ either vanish or give contributions proportional to the free-energy of a single free field in the conjectured dual CFT. Interpreting these non-vanishing values as shifts of the bulk coupling constant $G_N\sim 1/(N-k)$ , we find the values $k=-1,-1/2,0,1/2,1,2$ . Exceptions to this rule are the Type B and AB theories in odd d; for them, we find a mismatch between the bulk and boundary free energies that has a simple structure, but does not follow from a simple shift of the bulk coupling constant. Full article

We elucidate how Quantum Thermodynamics at temperature T emerges from pure and classical $SU(2)$ Yang–Mills theory on a four-dimensional Euclidean spacetime slice $S_1\times {\mathbf{R}}^3$ . The concept of a (deconfining) thermal ground state, composed of certain solutions to the fundamental, classical Yang–Mills equation, allows for a unified addressation of both (classical) wave- and (quantum) particle-like excitations thereof. More definitely, the thermal ground state represents the interplay between nonpropagating, periodic configurations which are electric-magnetically (anti)selfdual in a non-trivial way and possess topological charge modulus unity. Their trivial-holonomy versions—Harrington–Shepard (HS) (anti)calorons—yield an accurate a priori estimate of the thermal ground state in terms of spatially coarse-grained centers, each containing one quantum of action ℏ localized at its inmost spacetime point, which induce an inert adjoint scalar field $\varphi$ ( $|\varphi |$ spatio-temporally constant). The field $\varphi$ , in turn, implies an effective pure-gauge configuration, $a_{\mu }^{\mathrm{gs}}$ , accurately describing HS (anti)caloron overlap. Spatial homogeneity of the thermal ground-state estimate $\varphi ,a_{\mu }^{\mathrm{gs}}$ demands that (anti)caloron centers are densely packed, thus representing a collective departure from (anti)selfduality. Effectively, such a “nervous” microscopic situation gives rise to two static phenomena: finite ground-state energy density ${\rho }_{\mathrm{gs}}$ and pressure $P_{\mathrm{gs}}$ with ${\rho }_{\mathrm{gs}}=-P_{\mathrm{gs}}$ as well as the (adjoint) Higgs mechanism. The peripheries of HS (anti)calorons are static and resemble (anti)selfdual dipole fields whose apparent dipole moments are determined by $|\varphi |$ and T, protecting them against deformation potentially caused by overlap. Such a protection extends to the spatial density of HS (anti)caloron centers. Thus the vacuum electric permittivity ${ϵ}_0$ and magnetic permeability ${\mu }_0$ , supporting the propagation of wave-like disturbances in the $U(1)$ Cartan subalgebra of $SU(2)$ , can be reliably calculated for disturbances which do not probe HS (anti)caloron centers. Both ${ϵ}_0$ and ${\mu }_0$ turn out to be temperature independent in thermal equilibrium but also for an isolated, monochromatic $U(1)$ wave. HS (anti)caloron centers, on the other hand, react onto wave-like disturbances, which would resolve their spatio-temporal structure, by indeterministic emissions of quanta of energy and momentum. Thermodynamically seen, such events are Boltzmann weighted and occur independently at distinct locations in space and instants in (Minkowskian) time, entailing the Bose–Einstein distribution. Small correlative ramifications associate with effective radiative corrections, e.g., in terms of polarization tensors. We comment on an $SU(2)$ × $SU(2)$ based gauge-theory model, describing wave- and particle-like aspects of electromagnetic disturbances within the so far experimentally/observationally investigated spectrum. Full article