higgs field
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2022 ◽  
Vol 2022 (1) ◽  
Teerthal Patel ◽  
Tanmay Vachaspati

Abstract The vacuum manifold of the standard electroweak model is a three-sphere when one considers homogeneous Higgs field configurations. For inhomogeneous configurations we argue that the vacuum manifold is the Hopf fibered three sphere and that this viewpoint leads to general criteria to detect electroweak monopoles and Z-strings. We extend the Kibble mechanism to study the formation of electroweak monopoles and strings during electroweak symmetry breaking. The distribution of magnetic monopoles produces magnetic fields that have a spectrum Bλ ∝ λ−2, where λ is a smearing length scale. Even as the magnetic monopoles annihilate due to the confining Z-strings, the magnetic field evolves with the turbulent plasma and may be relevant for cosmological observations.

2022 ◽  
Vol 82 (1) ◽  
D. M. Ghilencea

AbstractWe study the Standard Model (SM) in Weyl conformal geometry. This embedding is truly minimal with no new fields beyond the SM spectrum and Weyl geometry. The action inherits a gauged scale symmetry D(1) (known as Weyl gauge symmetry) from the underlying geometry. The associated Weyl quadratic gravity undergoes spontaneous breaking of D(1) by a geometric Stueckelberg mechanism in which the Weyl gauge field ($$\omega _\mu $$ ω μ ) acquires mass by “absorbing” the spin-zero mode of the $${\tilde{R}}^2$$ R ~ 2 term in the action. This mode also generates the Planck scale and the cosmological constant. The Einstein-Proca action emerges in the broken phase. In the presence of the SM, this mechanism receives corrections (from the Higgs) and it can induce electroweak (EW) symmetry breaking. The EW scale is proportional to the vev of the Stueckelberg field. The Higgs field ($$\sigma $$ σ ) has direct couplings to the Weyl gauge field ($$\sigma ^2\omega _\mu \omega ^\mu $$ σ 2 ω μ ω μ ). The SM fermions only acquire such couplings for non-vanishing kinetic mixing of the gauge fields of $$D(1)\times U(1)_Y$$ D ( 1 ) × U ( 1 ) Y . If this mixing is present, part of the mass of Z boson is not due to the usual Higgs mechanism, but to its mixing with massive $$\omega _\mu $$ ω μ . Precision measurements of Z mass then set lower bounds on the mass of $$\omega _\mu $$ ω μ which can be light (few TeV). In the early Universe the Higgs field can have a geometric origin, by Weyl vector fusion, and the Higgs potential can drive inflation. The dependence of the tensor-to-scalar ratio r on the spectral index $$n_s$$ n s is similar to that in Starobinsky inflation but mildly shifted to lower r by the Higgs non-minimal coupling to Weyl geometry.

R. Cartas-Fuentevilla ◽  
A. Herrera-Aguilar ◽  
J. Berra-Montiel

Using Perelman’s approach for geometrical flows in terms of an entropy functional, the Higgs mechanism is studied dynamically along flows defined in the space of parameters and in fields space. The model corresponds to two-dimensional gravity that incorporates torsion as the gradient of a Higgs field, and with the reflection symmetry to be spontaneously broken. The results show a discrete mass spectrum and the existence of a mass gap between the Unbroken Exact Symmetry and the Spontaneously Broken Symmetry scenarios. In the latter scenario, the geometries at the degenerate vacua correspond to conformally flat manifolds without torsion; twisted two-dimensional geometries are obtained by building perturbation theory around a ground state; the tunneling quantum probability between vacua is determined along the flows.

2021 ◽  
Vol 34 (4) ◽  
pp. 429-463
Harry Ian Epstein

A novel quantum mechanical framework in discrete space and time leads to the derivation of the relativistic energy equation and a potential path toward quantum gravity. A unique approach to geometry is also derived where pregeometric points containing intrinsic compactified geometries generate a topologically 4D cosmos with a local dynamical 3D geometry. An interpretation of the quantum mechanics wavefunction is considered as longitudinal density waves traveling through dynamical pregeometric points. Similarly, general relativity can be described as density variations of the pregeometric points caused by matter-energy distribution. A primordial quantum (Higgs) field emerging at the big bang that generates all the other quantum fields is considered. A four-dimensional structure of black holes, and dark matter and energy are discussed.

2021 ◽  
Vol 36 (38) ◽  
T. B. Watson ◽  
Z. E. Musielak

A generalization of the original Bargmann–Wigner equations for spin-1 massive fields is employed, taking fully into account all internal degrees of freedom associated with the underlying chiral bases of the constituent spin-1/2 representations. Through the specification of a chiral basis, the chiral Bargmann–Wigner equations are reduced to a Proca-like form coupled by chirality to an auxiliary equation for a spin-0 massive field. The coupling derived is a new phenomenon whose physical implications are discussed in the context of identification of this field with the Higgs field and dark matter.

2021 ◽  
Vol 2021 (12) ◽  
Timothy Cohen ◽  
Nathaniel Craig ◽  
Xiaochuan Lu ◽  
Dave Sutherland

Abstract We derive the scale of unitarity violation from the geometry of Effective Field Theory (EFT) extensions of the Standard Model Higgs sector. The high-energy behavior of amplitudes with more than four scalar legs depends on derivatives of geometric invariants with respect to the physical Higgs field h, such that higher-point amplitudes begin to reconstruct the scalar manifold away from our vacuum. In theories whose low-energy limit can be described by the Higgs EFT (HEFT) but not the Standard Model EFT (SMEFT), non-analyticities in the vicinity of our vacuum limit the radius of convergence of geometric invariants, leading to unitarity violation at energies below 4πv. Our results unify approaches to the HEFT/SMEFT dichotomy based on unitarity, analyticity, and geometry, and more broadly illustrate the sense in which observables probe the geometry of an EFT. Along the way, we provide novel basis-independent results for Goldstone/Higgs boson scattering amplitudes expressed in terms of geometric covariant quantities.

Ole Lynnerup Trinhammer ◽  
Henrik G. Bohr

Abstract We calculate the pion mass from Goldstone modes in the Higgs mechanism related to the neutron decay. The Goldstone pion modes acquire mass by a vacuum misalignment of the Higgs field. The size of the misalignment is controlled by the ratio between the electronic and the nucleonic energy scales. The nucleonic energy scale is involved in the neutron to proton transformation and the electronic scale is involved in the related creation of the electronic state in the course of the electroweak neutron decay. The respective scales influence the mapping of the intrinsic configuration spaces used in our description. The configuration spaces are the Lie groups U(3) for the nucleonic sector and U(2) for the electronic sector. These spaces are both compact and lead to periodic potentials in the Hamiltonians in coordinate space. The periodicity and strengths of these potentials control the vacuum misalignment and leads to a pion mass of 135.2(1.5) MeV with an uncertainty mainly from the fine structure coupling at pionic energies. The pion decay constant 92 MeV results from comparing the fourth order self-coupling in an effective pion field theory with the corresponding fourth order term in the Higgs potential. We suggest analogies with the Goldberger-Treiman relation.

2021 ◽  
Vol 2021 (11) ◽  
Gui-Jun Ding ◽  
Stephen F. King ◽  
Jun-Nan Lu

Abstract We combine SO(10) Grand Unified Theories (GUTs) with A4 modular symmetry and present a comprehensive analysis of the resulting quark and lepton mass matrices for all the simplest cases. We focus on the case where the three fermion families in the 16 dimensional spinor representation form a triplet of Γ3 ≃ A4, with a Higgs sector comprising a single Higgs multiplet H in the 10 fundamental representation and one Higgs field $$ \overline{\Delta } $$ ∆ ¯ in the $$ \overline{\mathbf{126}} $$ 126 ¯ for the minimal models, plus one Higgs field Σ in the 120 for the non-minimal models, all with specified modular weights. The neutrino masses are generated by the type-I and/or type II seesaw mechanisms and results are presented for each model following an intensive numerical analysis where we have optimized the free parameters of the models in order to match the experimental data. For the phenomenologically successful models, we present the best fit results in numerical tabular form as well as showing the most interesting graphical correlations between parameters, including leptonic CP phases and neutrinoless double beta decay, which have yet to be measured, leading to definite predictions for each of the models.

Engel Roza

It is shown that the four fundamental physical forces, i.e. weak interaction, strong interaction, electromagnetism and gravity, all have their origin in the quark as the single true elementary particle.This requires conceiving the quark as a Dirac particle in a pseudo-tachyon mode, which possesses two real dipole moments: the common one associated with its angular momentum and a second one that is polarisable in a scalar field. This Dirac particle carries a regular charge magnetic monopole without Dirac’s string, theorized by Comay. The boson carrier of its field of energy is the gluon showing an exponential decay of its spatial range because of the influence of an omni-present energetic background field, known as the Higgs field, in this article interpreted as the Lambda in Einstein’s Field Equation.

Christopher Pilot

Assuming a two component, positive and negative mass, superfluid/supersolid for space (the Winterberg model), we model the Higgs field as a condensate made up of a positive and a negative mass, planckion pair. The connection is shown to be consistent (compatible) with the underlying field equations for each field, and the continuity equation is satisfied for both species of planckions, as well as for the Higgs field. An inherent length scale for space (the vacuum) emerges, which we estimate from previous work to be of the order of,

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