Three-band Extension for the Glashow–Weinberg–Salam Model

The concept of covariant derivatives for quark and lepton fields is generalized on algebras of internal symmetries and the Dirac matrices. Commutators of the covariant derivatives define field strengths for both the gauge fields and the Higgs field. The bosonic part of the Lagrangian is determined using a symmetric combination of quadratic invariants of the gauge and Higgs field strengths. The new version of the standard model thus formulated predicts the Higgs boson mass in terms of the top quark mass as mu'=f2m, at low energies and the Weinberg angle sin 2 In this article, we formulate a new unified theory of the gauge and Higgs fields without changing the notion of the ordinary Minkowski spacetime by generalizing the covariant derivative Dp. (rather than the Dirac operator l/J) on algebras of internal symmetries and the Dirac matrices in a Lorentz and gauge covariant way. Taking commutators of the covariant derivatives, field strengths are defined for both the gauge fields and the Higgs field. The bosonic part of the Lagrangian is determined by a symmetric combination of quadratic invariants of the gauge and Higgs field strengths. Essential results of the Connes theory are reproducible in this version of the standard model, where a strong parallelism is imposed between the gauge and Higgs field strengths. Three generations of leptons are represented by the chiral fields of the electr­ oweak doublets and singlets as t/Jlj=rh j (j=1, 2, 3). Similarly, those of quarks are described by the colored chiral fields of electroweak doublets t/Jqj= tPL (qJj, and the singlets t/Jw=t/JR j and t/Jdi=t/JR i. With these chiral fields, the fermionic part of the Lagrangian density of the standard model is given by ..( ~ ' ;r. ~'(·a + A ca>a 1 1 + A c2>a 1 + A co 1 y)-'· .

How does Clifford algebra show the way to the second quantized fermions with unified spins, charges and families, and with vector and scalar gauge fields beyond the standard model

We point out that the Higgs scalar field introduced as a gauge field associated with the z. discrete symmetry plays a role of the gauge transformation function for Yang-Mills fields and for fermion fields. We show that the Higgs potential identically vanishes and the Yukawa couplings between fermions and the Higgs field are gauged away. We are left with a massless fermion and a massive fermion both interacting with the Yang-Mills field. They are exchanged with each other by another massive vector field. We obtain such a massive vector field without the Higgs potential and hence without any spontaneous-symmetry breaking. This phenomenon is specially characteristic in this model.

We point out that the Higgs scalar field introduced as a gauge field associated with the Z2 discrete symmetry plays a role of the gauge transformation function for Yang-Mills fields and for fermion fields. We show that the Higgs potential identically vanishes and the Yukawa couplings between fermions and the Higgs field are gauged away. We are left with a massless fermion and a massive fermion both interacting with the Yang-Mills field. They are exchanged with each other by another massive vector field. We obtain such a massive vector field without the Higgs potential and hence without any spontaneous-symmetry breaking. This phenomenon is specially characteristic in this model.

We explore the Higgs sector in the supersymmetric economical 3–3–1 model and find new features in this sector. The charged Higgs sector is revised, i.e., in difference of the previous work, the exact eigenvalues and states are obtained without any approximation. In this model, there are three Higgs bosons having masses equal to that of the gauge bosons—the W and extra X and Y. There is one scalar boson with mass of 91.4 GeV, which is closed to the Z boson mass and in good agreement with present limit: 89.8 GeV at 95% CL. The condition of eliminating for charged scalar tachyon leads to splitting of VEV at the first symmetry breaking, namely, w ≃ w ′ . The interactions among the Standard Model gauge bosons and scalar fields in the framework of the supersymmetric economical 3–3–1 model are presented. From these couplings, at some limit, almost scalar Higgs fields can be recognized in accordance with the Standard Model. The hadronic cross section for production of the bilepton charged Higgs boson at the CERN LHC in the effective vector boson approximation is calculated. Numerical evaluation shows that the cross section can exceed 35.8 fb.

We study the phase diagram of lattice gauge theories coupled to fixed-length scalar (Higgs) fields. We consider several gauge groups: ${Z}_{2}$, U(1), and $\mathrm{SU}(N)$. We find that when the Higgs fields transform like the fundamental representation of the gauge group the Higgs and confining phases are smoothly connected, i.e., they are not separated by a phase boundary. When the Higgs fields transform like some representation other than the fundamental, a phase boundary may exist. This is the case for $\mathrm{SU}(N)$ with all the Higgs fields in the adjoint representation and for U(1) with all the Higgs fields in the charge-$N(N>1)$ representation. We present an argument due to Wegner that indicates the stability of the pure gauge transition. Another phase, free charge or Coulomb, is generally present. In this regime, the spectrum of the theory contains massless gauge bosons (for continuous groups) and finite-energy states that represent free charges.

A geometrical unification of gauge and Higgs fields is suggested in a high-dimensional framework. The internal dimensions characterise the gauge group as a manifold; as a result of gauge invariance they do not appear in the Lagrangian. The inhomogeneous transformation behaviour of the physical Higgs field and the gauge field under gauge transformations is derived from the same principle; the actual differences in the transformation behaviour are attributed to the geometrical structure of the high-dimensional space. Mass spectra originate in the known dependence of gauge and Higgs fields on the internal coordinates. An explicit model is given where the gauge group is SU(2) and the Higgs field is in the adjoint representation and proposals are made for more general models. The model given here is equivalent to the corresponding hidden gauge symmetry model. Moreover, the Higgs mass and self-coupling of the Higgs field are predicted in terms of the vector boson mass and self-coupling of the gauge field respectively.

We prove the existence of maximal condensates for the relativistic Abelian Chern-Simons equations involving two Higgs particles and two gauge fields on a torus. After a change of variable, we obtain a variational formulation of the problem whose critical points are equivalent to the original system of the equation. We prove existence of a local minimizer for this functional as well as the existence of a second mountain-pass critical point.

We discuss Preheating after an inflationary stage driven by the Standard Model (SM) Higgs field non-minimally coupled to gravity. We find that Preheating is driven by a complex process in which perturbative and non-perturbative effects occur simultaneously. The Higgs field, initially an oscillating coherent condensate, produces non-perturbatively W and Z gauge fields. These decay very rapidly into fermions, thus preventing gauge bosons to accumulate and, consequently, blocking the usual parametric resonance. The energy transferred into the fermionic species is, nevertheless, not enough to reheat the Universe, and resonant effects are eventually developed. Soon after resonance becomes effective, also backreaction from the gauge bosons into the Higgs condensate becomes relevant. We have determined the time evolution of the energy distribution among the remnant Higgs condensate and the non-thermal distribution of the SM fermions and gauge fields, until the moment in which backreaction becomes important. Beyond backreaction our approximations break down and numerical simulations and theoretical considerations beyond this work are required, in order to study the evolution of the system until thermalization.

We introduce a simple scenario where, by starting with a five-dimensional $SU(3)$ gauge theory, we end up with several 4-D parallel branes with localized fermions and gauge fields. Similar to the split fermion scenario, the confinement of fermions is generated by the nontrivial topological solution of a $SU(3)$ scalar field. The 4-D fermions are found to be chiral, and to have interesting properties coming from their 5-D group representation structure. The gauge fields, on the other hand, are localized by loop corrections taking place at the branes produced by the fermions. We show that these two confining mechanisms can be put together to reproduce the basic structure of the electroweak model for both leptons and quarks. A few important results are: Gauge and Higgs fields are unified at the 5-D level; and new fields are predicted: One left-handed neutrino with zero-hypercharge, and one massive vector field coupling together the new neutrino with other left-handed leptons. The hierarchy problem is also addressed.

The triviality of four-dimensional scalar quantum field theories poses challenging problems to the usually adopted perturbative implementation of the Higgs mechanism. In the first part of the paper, we compare the triviality scenario and the renormalized two-loop perturbation theory to precise and extensive results from nonperturbative numerical simulations of the real scalar field theory on the lattice. The proposal of triviality and spontaneous symmetry breaking turns out to be in good agreement with numerical simulations, while the renormalized perturbative approach seems to suffer significant deviations from the numerical simulation results. In the second part of the paper, we try to illustrate how the triviality of four-dimensional scalar field theory leads, nevertheless, to the spontaneous symmetry breaking in the scalar sector of the Standard Model. We show how triviality allows us to develop a physical picture of the Higgs mechanism in the Standard Model. We suggest that the Higgs condensate behaves like a relativistic quantum liquid leading to the prevision of two Higgs bosons. The light Higgs boson resembles closely the new LHC narrow resonance at 125 GeV. The heavy Higgs boson is a rather broad resonance with mass of about 730 GeV. We critically compare our proposal to the complete LHC Run 2 data collected by the ATLAS and CMS Collaborations. We do not find convincingly evidences of the heavy Higgs boson in the ATLAS datasets. On the other hand, the CMS full Run 2 data display evidences of a heavy Higgs boson in the main decay modes [Formula: see text], while in the preliminary Run 2 data there are hints of the decays [Formula: see text] in the golden channel. We also critically discuss plausible reasons for the discrepancies between the two LHC experiments.

The spin-charge-family theory, in which spinors carry besides the Dirac spin also the second kind of the Clifford object, no charges, is a kind of the Kaluza-Klein theories. The Dirac spinors of one Weyl representation in $d=(13+1)$ manifest in $d=(3+1)$ at low energies all the properties of quarks and leptons assumed by the standard model. The second kind of spins explains the origin of families. Spinors interact with the vielbeins and the two kinds of the spin connection fields, the gauge fields of the two kinds of the Clifford objects, which manifest in $d=(3+1)$ besides the gravity and the known gauge vector fields also several scalar gauge fields. Scalars with the space index $s\in (7,8)$ carry the weak charge and the hyper charge ($\mp \frac{1}{2}, \pm \frac{1}{2}$, respectively), explaining the origin of the Higgs and the Yukawa couplings. It is demonstrated in this paper that the scalar fields with the space index $t\in (9,10,\dots,14)$ carry the triplet colour charges, causing transitions of antileptons and antiquarks into quarks and back, enabling the appearance and the decay of baryons. These scalar fields are offering in the presence of the right handed neutrino condensate, which breaks the ${\cal C}{\cal P}$ symmetry, the answer to the question about the matter-antimatter asymmetry.

A novel model of charged leptons is presented, which contains two basics hypotheses. The first hypothesis is that the Yukawa coupling between Higgs field and charged leptons is the weak interaction, the Higgs field is a scalar intermediate boson which changes the chirality of charged leptons in the weak interaction. The other hypothesis is that the flavor eigenstates of charged leptons are the superposition states of left-handed and right-handed elementary Weyl spinors before the electroweak symmetry breaking. According to this model, the Yukawa coupling constants between Higgs field and three generations of charged leptons are considered to be a universal constant, and the difference of the masses of different charged leptons is due to the different left-right mixing angles of their flavor eigenstates.

We present a gauge and Lorentz invariant effective field theory model for the interaction of a charged scalar matter field with a magnetic monopole source, described by an external magnetic current. The quantum fluctuations of the monopole field are described effectively by a strongly coupled “dual” Ud(1) gauge field, which is independent of the electromagnetic Uem(1) gauge field. The effective interactions of the charged matter with the monopole source are described by a gauge invariant mixed Chern-Simons-like (Pontryagin-density) term between the two U(1) gauge fields. The latter interaction coupling is left free, and a lattice study of the system is performed with the aim of determining the phase structure of this effective theory. Our study shows that, in the spontaneously broken-symmetry phase, the monopole source triggers, via the mixed Chern-Simons term, which is nontrivial in its presence, the generation of a dynamical singular configuration (magnetic-monopolelike) for the respective gauge fields. The scalar field also behaves in the broken phase in a way similar to that of the scalar sector of the ’t Hooft-Polyakov monopole. Moreover, we show that the modest size of the lattices involved does not have significant effects on the main conclusions of our analysis. Published by the American Physical Society 2024

We constrain the Higgs boson (Yukawa) coupling to quarks in the first two generations in the $H\to ZZ$ final states. Deviation of these couplings from the Standard Model values leads to change in the Higgs boson width and in the cross sections of relevant processes. In the Higgs boson resonance region, an increased light Yukawa coupling leads to an increased Higgs boson width, which in turn leads to a decreased cross section. In the off-shell region, increased Yukawa couplings result in an enhancement of the Higgs boson signal through $q\bar{q}$ annihilation. With the assumption of scaling one Yukawa coupling at a time, this study is conceptually simple and yields results with the same order of magnitude as the tightest in the literature. The study is based on results published by the CMS experiment at the LHC in 2014, corresponding to integrated luminosities of $5.1\ifb$ at a centre-of-mass energy $\sqrt{s}=7\tev$ and $19.7\ifb$ at $8\tev$.