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.     

Higgs couplings in the integer-charge quark model

Colour SU(3) symmetry is broken spontaneously by the introduction of coloured Higgs scalars in the standard SU(3)×SU(2)×U(1) model, so as to make the quarks integrally charged. The resulting couplings of the Higgs bosons with the gauge bosons are worked out.     

Mini little Higgs and dark matter

We construct a little Higgs model with the most minimal extension of the standard model gauge group by an extra U(1)$U(1)$ gauge symmetry. For specific charge assignments of scalars, an approximate U(3)$U(3)$ global symmetry appears in the cutoff-squared scalar mass terms generated from gauge bosons at one-loop level. Hence, the Higgs boson, identified as a pseudo-Goldstone boson of the broken global symmetry, has its mass radiatively protected up to scales of 5–10 TeV. In this model, a Z₂$Z_2$ symmetry, ensuring the two U(1)$U(1)$ gauge groups to be identical, also makes the extra massive neutral gauge boson stable and a viable dark matter candidate with a promising prospect of direct detection.     

Finite-temperature behavior of the lattice abelian Higgs model

We study phase transitions in the lattice version of the abelian Higgs model, a model which can exhibit both spontaneous symmetry breaking and confinement. When the Higgs charge is the basic U(1) unit, we find that the Higgs and confinement regions are not separated by a phase transition and form a single homogenous phase which we call the total screening phase. The model does not undergo a symmetry restoring phase transition at finite temperature.If the Higgs charge is some multiple of the basic unit the model follows the conventional wisdom: there are 3 phases (normal, Higgs and confinement) at zero temperature, two of which disappear above some critical point. We apply the lessons learned from the lattice Higgs model to understand the behavior of the weak interactions at high temperature.In a long appendix we give an intuitive physical picture for the Polyakov-Susskind quark liberating phase transition and show that it is related to the Hagedorn spectrum of a confining model. We end with a collection of effective field theory approximations to various lattice theories.     

Neutral currents and the Higgs mechanism

The consequences of assuming (i) weak and e.m. forces constitute a gauge field theory, and (ii) there are no heavy leptons, are investigated. Relative to the Weinberg model, introduction of a general spontaneous symmetry breaking system leads to a theory with one extra free parameter, namely the neutral vector boson mass. Experimental consequences are indicated. A particular Higgs system containing two multiplets is studied in detail. It is noted that parameters may be chosen such that the cosmological constant is zero before as well as after spontaneous symmetry breakdown.     

In Search of Alternatives to Higgs Fields

Field equations of the S² sigma model (“the A3 model”) with spontaneously broken Z(2) symmetry are presented for (D+1)-dimensional space–time. The A3 model is an extension of the sine-Gordon equation (SGE) and supports kink-like U(1) charged solitons which are a generalization of neutral solitons of the SGE. The natural question arises — is the A3 model completely integrable in (1+1)-dimensional space–time? The Lorentz-invariant scalar A3 field can be viewed as a promising alternative to the Higgs field.     

Higgs as a pseudo-Goldstone boson, the mu problem and gauge-mediated supersymmetry breaking

We study the interplay between the spontaneous breaking of a global symmetry of the Higgs sector and gauge-mediated supersymmetry breaking, in the framework of a supersymmetric model with global SU(3) symmetry. In addition to solving the supersymmetric flavor problem and alleviating the little hierarchy problem, this scenario automatically triggers the breaking of the global symmetry and provides an elegant solution to the μ/Bμ problem of gauge mediation. We study in detail the processes of global symmetry and electroweak symmetry breaking, including the contributions of the top/stop and gauge-Higgs sectors to the one-loop effective potential of the pseudo-Goldstone Higgs boson. While the joint effect of supersymmetry and of the global symmetry allows in principle the electroweak symmetry to be broken with little fine-tuning, the simplest version of the model fails to bring the Higgs mass above the LEP bound due to a suppressed tree-level quartic coupling. To cure this problem, we consider the possibility of additional SU(3)-breaking contributions to the Higgs potential, which results in a moderate fine-tuning. The model predicts a rather low messenger scale, a small tanβ value, a light Higgs boson with Standard Model-like properties, and heavy higgsinos.     

Induced-gravity GUT-scale Higgs inflation in supergravity

Models of induced-gravity inflation are formulated within Supergravity employing as inflaton the Higgs field which leads to a spontaneous breaking of a \(U(1)_{B-L}\) symmetry at \(M_\mathrm{GUT}=2\cdot 10^{16}~{\mathrm{GeV}}\). We use a renormalizable superpotential, fixed by a U(1) R symmetry, and Kähler potentials which exhibit a quadratic non-minimal coupling to gravity with or without an independent kinetic mixing in the inflaton sector. In both cases we find inflationary solutions of Starobinsky type whereas in the latter case, others (more marginal) which resemble those of linear inflation arise too. In all cases the inflaton mass is predicted to be of the order of \(10^{13}~{\mathrm{GeV}}\). Extending the superpotential of the model with suitable terms, we show how the MSSM \(\mu \) parameter can be generated. Also, non-thermal leptogenesis can be successfully realized, provided that the gravitino is heavier than about \(10~{\mathrm{TeV}}\).     

A Three Higgs Doublet Model for Fermion Masses

In this paper we propose a possible explanation to the Fermion mass hierarchy problem by fitting the type-II seesaw mechanism into the Higgs doublet sector, such that their vacuum expectation values are hierarchal. We extend the Standard Model with two extra Higgs doublets as well as a spontaneously broken U_X(1) gauge symmetry. All the fermion Yukawa couplings except that of the top quark are of O(10^-2) in our model. Constraints on the parameter space of the model from low energy processes are studied. Besides, the lightest one of the neutral fermion fields, which is introduced to cancel the anomalies of the U(1)_X gauge symmetry can be the cold dark matter candidate. We investigate its signature in the dark matter direct detection.     

Salam-Weinberg symmetry breaking with superheavy Higgs particles

We discuss here the possibility of the breaking of Salam-Weinberg symmetry by Higgs particles which are superheavy. The symmetry breaking is associated with a nonzero vacuum expectation value of fermion condensates. This mechanism, if operative in nature, will imply the absence of Higgs particles at the weak scale.     

Argyres-Seiberg Duality and the Higgs Branch

We demonstrate the agreement between the Higgs branches of two ${\mathcal{N}=2}We demonstrate the agreement between the Higgs branches of two N=2{\mathcal{N}=2} theories proposed by Argyres and Seiberg to be S-dual, namely the SU(3) gauge theory with six quarks, and the SU(2) gauge theory with one pair of quarks coupled to the superconformal theory with E ₆ flavor symmetry. In mathematical terms, we demonstrate the equivalence between a hyperk?hler quotient of a linear space and another hyperk?hler quotient involving the minimal nilpotent orbit of E ₆, modulo the identification of the twistor lines.     

Quantum gauge models without (classical) Higgs mechanism

We examine the status of massive gauge theories, such as those usually obtained by spontaneous symmetry breakdown, from the viewpoint of causal (Epstein–Glaser) renormalization. The BRST formulation of gauge invariance in this framework, starting from canonical quantization of massive (as well as massless) vector bosons as fundamental entities, and proceeding perturbatively, allows one to rederive the reductive group symmetry of interactions, the need for scalar fields in gauge theory, and the covariant derivative. Thus the presence of higgs particles is understood without recourse to a Higgs(–Englert–Brout–Guralnik–Hagen–Kibble) mechanism. Along the way, we dispel doubts about the compatibility of causal gauge invariance with grand unified theories.     

Charge quantization in theories with an adjoint representation Higgs mechanism

Gauge theories are considered in which an overall simple gauge symmetry group G is broken, by a Higgs field in the adjoint representation, to an exact symmetry with a structure locally of the form U(1)×K. Necessary and sufficient conditions on the Higgs field for K to be semisimple are given, together with an algorithm for determining K from the Dynkin diagram. The theory of weight lattices is used to show that both the electric and magnetic charges are multiples of certain basic units. These are calculated and related to each other by formulae more precise than quantization conditions given previously. It is shown that globally the exact symmetry group has the form $\text{H}\text{=(}\text{U}\text{(1)×}\text{K}\text{)/}\text{Z}$, where $\text{K}$ is simply connected (assuming G is) and Z is a cyclic group whose order can be calculated from the Dynkin diagram.     

Higgs models

This lecture presented at the Baikal summer school on physics of elementary particles and astrophysics in 2011 is devoted to the Higgs mechanism of the electroweak symmetry breaking within the Standard Model and in some models beyond it.     

Left-Right Non-Linear Dynamical Higgs

All the possible CP-conserving non-linear operators up to the p⁴-order in the Lagrangian expansion are analysed here for the left-right symmetric model in the non-linear electroweak chiral context coupled to a light dynamical Higgs. The low energy effects will be triggered by an emerging new physics field content in the nature, more specifically, from spin-1 resonances sourced by the straightforward extension of the SM local gauge symmetry to the larger local group SU(2)_L×SU(2)_R×U(1)_B-L. Low energy phenomenology will be altered by integrating out the resonances from the physical spectrum, being manifested through induced corrections onto the left handed operators. Such modifications are weighted by powers of the scales ratio implied by the symmetries of the model and will determine the size of the effective operator basis to be used. The recently observed diboson excess around the invariant mass 1.8 TeV-2 TeV entails a scale suppression that suggests to encode the low energy effects via a much smaller set of effective operators.     

Doubly charged Higgs bosons

We explore through two simple models, the first in which scalars are treated as fundamental and the second in which they are composite objects, the possibility that representations containing doubly charged scalars may participate in the spontaneous breakdown of the SU(2) × U(1) symmetry of electroweak interactions. We show that such exotic Higgs bosons may posses unsuppressed coupling to pairs of gauge vector bosons and comment on the observability of these charged Higgs bosons through the Cahn-Dawson mechanism in high-energy hadron colliders.     

Higgs–matter splitting in quasi-realistic orbifold string GUTs

E₆ grand unification combines the standard model matter and Higgs states in the single 27 representation. I discuss how the E₆ structure underlies the quasi-realistic free fermion heterotic-string models. E₆→SO(10)×U(1) breaking is obtained by a GSO phase in the N=1 partition function. The equivalence of this symmetry breaking phase with a particular choice of boundary condition basis vectors, which is used in the quasi-realistic models, is demonstrated in several cases. As a result, matter states in the spinorial 16 representation of SO(10) arise from the twisted sectors, whereas the Higgs states arise from the untwisted sector. Possible additional phenomenological implications of this E₆ symmetry breaking pattern are discussed.     

Analyses of Complementarity and Critical Coupling Higgs Phase

We introduce a simple dynamical scheme to supplement the complementarity and Higgs phase analyses of composite model with semi-simple group and determine the order of appearance of the condensates of the simple groups.Together with the Higgs phase analysis,it can help to determine the global symmetry of the fermion composite.The global symmetry group can be gauged to form the low energy dynamical symmetry group of the composite.     

Higgs fields,curved space,and hadron structure

We show that in completely unified Yang-Mills-Einstein-Higgs-type gauge theories with spontaneous symmetry breaking there exists the possibility that hadrons can be visualized as microuniverses where the large curvature within a region of about 0.7×10^–13 cm arises from a large negative value of the VEV of the Hamiltonian. The low-lying collective excitations of the system have Hooke group symmetry and can be described as multiquasiparticle systems with oscillator-like energy spectra. The lowest states span reducible representations ofSU(3) and correspondence with the naive nonrelativistic quark model can be established. Confinement and absence of nonzero triality excitations can be explained in a natural way.     

Composite antisymmetric-tensor Nambu-Goldstone bosons in a four-fermion interaction model and the Higgs mechanism

Starting from the Fierz transform of the two-flavour 't Hooft interaction (a four-fermion Lagrangian with antisymmetric Lorentz tensor interaction terms augmented by an NJL type Lorentz scalar interaction responsible for dynamical symmetry breaking and quark mass generation), we show that: (1) antisymmetric tensor Nambu-Goldstone bosons appear provided that the scalar and tensor couplings stand in the proportion of two to one, which ratio appears naturally in the Fierz transform of the two-flavour 't Hooft interaction; (2) non-Abelian vector gauge bosons coupled to this system acquire a non-zero mass. Axial-vector fields do not mix with antisymmetric tensor fields, so there is no mass shift there. Received: 3 September 1999 / Revised Version: 3 November 1999 / Published online: 6 April 2000