Solution of the Higgs scalar-tensor theory without Higgs particles for static stars

Within the scalar-tensor theory of gravity with Higgs mechanism without Higgs particles, we prove that the excited Higgs potential (the scalar field) vanishes inside and outside of stellar matter for static, spherically symmetric configurations. The field equation for the metric (the tensorial gravitational field) turns out to be essentially the Einsteinian one.     

Monte Carlo study of a lattice gauge theory with a radially varied Higgs field

The phase structure of a gauge-scalar (Higgs) field system is studied by Monte Carlo simulations without freezing the radial mode of the scalar field. We consider Z₂ lattice gauge theory coupled to a Higgs field which is approximated by a discrete real one. Most of our analysis is done on a 4⁴ lattice. We find that the phase diagram of our model consists of three distinct phases, Higgs and confined regions being divided by a phase boundary. This phase structure forms a contrast with that presented in the model with a fixed-length Higgs field.     

Higgs bosons in supersymmetric models (I)

We describe the properties of Higgs bosons in a class of supersymmetric theories. We consider models in which the low-energy sector contains two weak complex doublets and perhaps one complex gauge-singlet Higgs field. Supersymmetry is assumed to be either softly or spontaneously broken, thereby imposing a number of restrictions on the Higgs boson parameters. We elucidate the Higgs boson masses and present Feynman rules for their couplings to the gauge bosons, fermions and scalars of the theory. We also present Feynman rules for vertices which are related by supersymmetry to the above couplings. Exact analytic expressions are given in two useful limits — one corresponding to the absence of the gauge-singlet Higgs field and the other corresponding to the absence of a supersymmetric Higgs mass term.     

Conformal invariance and spontaneous symmetry breaking

We study the spontaneous symmetry breaking in a conformally invariant gravitational theory. We particularly emphasize on the nonminimal coupling of matter fields to gravity. By the nonminimal coupling we consider a local distinction between the conformal frames of metric of matter fieldsand the metric explicitly entering the vacuum sector. We suppose that these two frames are conformally related by a dilaton field. We show that the imposition of a condition on the variable mass term of a scalar field may lead to the spontaneous symmetry breaking. In this way the scalar field may imitate the Higgs field behavior. Attributing a constant configuration to the ground state of the Higgs field, a Higgs conformal frame is specified. We define the Higgs conformal frame as a cosmological frame which describes the large scale characteristics of the observed universe. In the cosmological frame the gravitational coupling acquires a correct value and one no longer deals with the vacuum energy problem. We then study a more general case by considering a variable configuration for the ground state of Higgs field. In this case we introduce a cosmological solution of themodel.     

Self duality solution with a Higgs field

The self-duality concept for the Higgs field is handled in the presence of contact geometry in 5 dimensions.A non-trivial SO(3) Higgs field lives only on the fifth dimension of the contact manifold because of the contact structure, while the SD Yang-Mills field lives in the 4-dimensional hyperplane of the contact manifold. The Higgs and SD Yang-Mills fields do not interact with one another.     

What can we learn from the total width of the Higgs boson?

As one of the key properties of the Higgs boson, the Higgs total width is sensitive to the global profile of the Higgs boson couplings, and thus new physics would modify the Higgs width. We investigate the total width in various new physics models, including various scalar extensions, composite Higgs models, and the fraternal twin Higgs model. Typically, the Higgs width is smaller than the standard model value due to mixture with other scalars if the Higgs is elementary, or curved Higgs field space for the composite Higgs. On the other hand, except for the possible invisible decay mode, the enhanced Yukawa coupling in the two Higgs doublet model or the exotic fermion embeddings in the composite Higgs could enhance the Higgs width greatly. The precision measurement of the Higgs total width at the high-luminosity LHC can be used to discriminate certain new physics models.     

THE PHASE STRUCTURE OF 4-d U(1) HIGGS MODEL WITH RADIAL EXCITATION

On 4⁴ regular lattice, the phase structure of U(1) Higgs model-a U(1) lattice gauge theory coupled to a scalar (Higgs) field-has been studied by using modified Metropolis algorithm without freezing the radial excitation of the Higgs field carrying fundamental charge. The result shows that Higgs and confined regions are completelg separated by a first-order phase transition line and the phase diagram of our model.consists of three distinct phases. This feature greatly differs from that of the model with radially frozen Higgs field discussed by D.J.E.Callaway and L.J. Carson.^[1]     

Higgs-field gravity

It is shown that any excited Higgs field mediates an attractive scalar gravitational interaction of Yukawa type between the elementary particles, which become massive by the ground state of the Higgs field.     

Nuclear pions and the Gottfried and Bjorken sum rules

The thermodynamic potential (TDP) of the boson sector of the Weinberg-Salam model in an external uniform magnetic field at finite temperature and nonzero chemical potential is calculated in one-loop approximation. In the high temperature limit with the use of Mellin summation technique explicit expressions for the thermodynamic potential are obtained to analyze its new minimum, different from the ordinary Higgs one. This new minimum is due to the root singularity in the oneloop expression for the TDP, originating as a consequence of the tachyonic mode in the spectrum of gauge boson in the magnetic field. It is demonstrated that in the high temperature limit the Higgs minimum possesses properties common with the ordinary superconductors and Abelian Higgs model. The influence of the magnetic field on the Higgs minimum is indirect and has a sufficiently complicated character. The presence of the non-zero chemical potential lowers the critical temperature leading to the disappearance of the Higgs minimum.     

Signature change, vacuum condensation and cosmological constant

We proposes an alternative model of duality symmetry, based on the previously obtained divergence theory, including an scalar field, an internal vector and a metric signature. At some small scale an effective scalar field equation has appeared whose potential acts like a Higgs one, where the metric signature plays the role of an order parameter. Non-vanishing Vacuum condensation of this Higgs field occurs once a signature change from Euclidean to Lorentzian is formed. The mass scale of Higgs field excitations around this vacuum may contribute, in the Lorentzian sector, to the cosmological constant, in agreement with observations.     

An algorithm for detecting abelian monopoles inSU 2-valued lattice gauge-Higgs systems

We present an algorithm which calculates the monopole number of anSU ₂-valued lattice gauge field, together with a lattice Higgs field, on a simplicial lattice of dimension ≧3. The calculation is gauge invariant. The expected value of the monopole density (for a fixed Higgs field) does not depend on the Higgs field. Partially supported by NSF grants DMS 8607168 and DMS 8907753 Partially supported by PSC-CUNY and by NSF grant DMS 8805485     

Vector Higgs portal dark matter and the invisible Higgs

The Higgs sector of the Standard Model offers a unique probe of the hidden sector. In this work, we explore the possibility of renormalizable Higgs couplings to the hidden sector vector fields which can constitute dark matter (DM). Abelian gauge sectors with minimal field content, necessary to render the gauge fields massive, have a natural Z₂ parity. This symmetry ensures stability of the vector fields making them viable dark matter candidates, while evading the usual electroweak constraints. We illustrate this idea with the Stückelberg and Higgs mechanisms. Vector DM is consistent with the WMAP, XENON100, and LHC constraints, while it can affect significantly the invisible Higgs decay. Due to the enhanced branching ratio for the Higgs decay into the longitudinal components of the vector field, the vector Higgs portal provides an efficient way to hide the Higgs at the LHC. This could be the reason why the latest combined ATLAS/CMS data did not bring evidence for the existence of the Higgs boson.     

Singularities in Einstein–conformally coupled Higgs cosmological models

The dynamics of Einstein–conformally coupled Higgs field (EccH) system is investigated near the initial singularities in the presence of Friedman–Robertson–Walker symmetries. We solve the field equations asymptotically up to fourth order near the singularities analytically, and determine the solutions numerically as well. We found all the asymptotic, power series singular solutions, which are (1) solutions with a scalar polynomial curvature singularity but the Higgs field is bounded (‘Small Bang’), or (2) solutions with a Milne type singularity with bounded spacetime curvature and Higgs field, or (3) solutions with a scalar polynomial curvature singularity and diverging Higgs field (‘Big Bang’). Thus, in the present EccH model there is a new kind of physical spacetime singularity (‘Small Bang’). We also show that, in a neighbourhood of the singularity in these solutions, the Higgs sector does not have any symmetry breaking instantaneous vacuum state, and hence then the Brout–Englert–Higgs mechanism does not work. The large scale behaviour of the solutions is investigated numerically as well. In particular, the numerical calculations indicate that there are singular solutions that cannot be approximated by power series.     

TWO-DIMENSIONAL GRAVITATION AND NONSTATIONARY HIGGS FIELD SOLITONS

Some aspects of two-dimensional gravity coupled to nonstationary Higgs field solitons are examined.General properties of the nonstationary Higgs field model in flat space-time and their generalization to curved space-time are discussed.A solution which corresponds to cosmology is arrived at.     

Quadrupole moments of hadrons

We study an Abelian Higgs model in three, four and five dimensions using the mean field perturbation expansion with covariant gauge fixing. In four and five dimensions the mean field analysis shows three phases; a confined phase, a Coulomb phase with massless spin waves, and a Higgs phase in which the spin waves aquire a mass. The Higgs and confined phases are shown to be connected. In three dimensions we find a single phase.     

A Definition of Time

We present a definition of time based on a particle’s interaction with the Higgs field. Just as a particle acquires mass by interacting with the Higgs field our model proposes that time is acquired via the energy of virtual particles participating in the quantum exchange interactions with Higgs particles. We show that, for macroscopic time, this definition accords with the Lorentz transformation of special relativity. The research of the authors was supported by NSERC grants.     

Higgs mechanism without Higgs particle

Until now there has been no empirical evidence for the existence of the Higgs particle, although the Higgs mechanism of symmetry breaking is very successful. We propose a scalar-tensor theory of gravity with the Higgs field of theSU(3)×SU(2)×U(1) standard model of the elementary particles as scalar field, which results finally in Einstein's gravity and in theSU(3)×SU(2)×U(1) standard model without any influence of the excited Higgs field.     

Topology Change in (2+1)-Dimensional Gravity with Non-Abelian Higgs Field

We study topology change in (2+1)D gravity coupling with non-Abelian SO(2, 1) Higgs field from the point of view of Morse theory. It is shown that the Higgs potential can be identified as a Morse function. The critical points of the latter (i.e. loci of change of the spacetime topology) coincide with zeros of the Higgs field. In these critical points the two-dimensional metric becomes degenerate, but the curvature remains bounded.     

Multivortex Solutions in (2+1)-Dimensional Abelian Higgs Model with a Chern-Simons Term

The multivortex solutions of (2+l)-dimensional Abelian Higgs model with a Chern-Simons term are stlrrlied. The Bogomol'nyi-type equations and corresponding Weinberg's index theorem have been derived for a sixth-order Higgs potential. The magnetic field is different from that of the Abelian Chern-Simons Higgs model which has no Maxwell term, and has a maximum at the center of the vortex.     

Electroweak Chiral Lagrangian for Neutral Higgs Boson

A neutral Higgs boson is added into the traditional electroweak chiral Lagrangian by writing down all possible high dimension operators. The matter part of the Lagrangian is investigated in detail. We find that if Higgs field dependence of Yukawa couplings can be factorized out, there will be no flavour changing neutral couplings; neutral Higgs can induce coupling between light and heavy neutrinos.