scholarly journals Standard Model in Weyl conformal geometry

2022 ◽  
Vol 82 (1) ◽  
Author(s):  
D. M. Ghilencea
Keyword(s):  
Standard Model ◽  
Gauge Field ◽  
Conformal Geometry ◽  
Planck Scale ◽  
Higgs Field ◽  
Spontaneous Breaking ◽  
Weyl Geometry ◽  
Quadratic Gravity ◽  
Geometric Origin ◽  
Present Part

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.

scholarly journals Gauging scale symmetry and inflation: Weyl versus Palatini gravity

2021 ◽  
Vol 81 (6) ◽  
Author(s):  
D. M. Ghilencea
Keyword(s):  
Ad Hoc ◽  
Scalar Potential ◽  
Planck Scale ◽  
Spontaneous Breaking ◽  
Similar Action ◽  
Quadratic Gravity ◽  
Higher Dimensional ◽  
Weyl Theory ◽  
Geometric Origin ◽  
Quadratic Action

AbstractWe present a comparative study of inflation in two theories of quadratic gravity with gauged scale symmetry: (1) the original Weyl quadratic gravity and (2) the theory defined by a similar action but in the Palatini approach obtained by replacing the Weyl connection by its Palatini counterpart. These theories have different vectorial non-metricity induced by the gauge field ($$w_\mu $$ w μ ) of this symmetry. Both theories have a novel spontaneous breaking of gauged scale symmetry, in the absence of matter, where the necessary scalar field is not added ad-hoc to this purpose but is of geometric origin and part of the quadratic action. The Einstein-Proca action (of $$w_\mu $$ w μ ), Planck scale and metricity emerge in the broken phase after $$w_\mu $$ w μ acquires mass (Stueckelberg mechanism), then decouples. In the presence of matter ($$\phi _1$$ ϕ 1 ), non-minimally coupled, the scalar potential is similar in both theories up to couplings and field rescaling. For small field values the potential is Higgs-like while for large fields inflation is possible. Due to their $$R^2$$ R 2 term, both theories have a small tensor-to-scalar ratio ($$r\sim 10^{-3}$$ r ∼ 10 - 3 ), larger in Palatini case. For a fixed spectral index $$n_s$$ n s , reducing the non-minimal coupling ($$\xi _1$$ ξ 1 ) increases r which in Weyl theory is bounded from above by that of Starobinsky inflation. For a small enough $$\xi _1\le 10^{-3}$$ ξ 1 ≤ 10 - 3 , unlike the Palatini version, Weyl theory gives a dependence $$r(n_s)$$ r ( n s ) similar to that in Starobinsky inflation, while also protecting r against higher dimensional operators corrections.

scholarly journals Palatini quadratic gravity: spontaneous breaking of gauged scale symmetry and inflation

2020 ◽  
Vol 80 (12) ◽  
Author(s):  
D. M. Ghilencea
Keyword(s):  
Scalar Field ◽  
Gauge Field ◽  
Ad Hoc ◽  
Planck Scale ◽  
Kinetic Term ◽  
Spontaneous Breaking ◽  
Mass Generation ◽  
Quadratic Gravity ◽  
Derivative Term ◽  
Specific Prediction

AbstractWe study quadratic gravity $$R^2+R_{[\mu \nu ]}^2$$ R 2 + R [ μ ν ] 2 in the Palatini formalism where the connection and the metric are independent. This action has a gauged scale symmetry (also known as Weyl gauge symmetry) of Weyl gauge field $$v_\mu = (\tilde{\Gamma }_\mu -\Gamma _\mu )/2$$ v μ = ( Γ ~ μ - Γ μ ) / 2 , with $$\tilde{\Gamma }_\mu $$ Γ ~ μ ($$\Gamma _\mu $$ Γ μ ) the trace of the Palatini (Levi-Civita) connection, respectively. The underlying geometry is non-metric due to the $$R_{[\mu \nu ]}^2$$ R [ μ ν ] 2 term acting as a gauge kinetic term for $$v_\mu $$ v μ . We show that this theory has an elegant spontaneous breaking of gauged scale symmetry and mass generation in the absence of matter, where the necessary scalar field ($$\phi $$ ϕ ) is not added ad-hoc to this purpose but is “extracted” from the $$R^2$$ R 2 term. The gauge field becomes massive by absorbing the derivative term $$\partial _\mu \ln \phi $$ ∂ μ ln ϕ of the Stueckelberg field (“dilaton”). In the broken phase one finds the Einstein–Proca action of $$v_\mu $$ v μ of mass proportional to the Planck scale $$M\sim \langle \phi \rangle $$ M ∼ ⟨ ϕ ⟩ , and a positive cosmological constant. Below this scale $$v_\mu $$ v μ decouples, the connection becomes Levi-Civita and metricity and Einstein gravity are recovered. These results remain valid in the presence of non-minimally coupled scalar field (Higgs-like) with Palatini connection and the potential is computed. In this case the theory gives successful inflation and a specific prediction for the tensor-to-scalar ratio $$0.007\le r\le 0.01$$ 0.007 ≤ r ≤ 0.01 for current spectral index $$n_s$$ n s (at $$95\%$$ 95 % CL) and $$N=60$$ N = 60 efolds. This value of r is mildly larger than in inflation in Weyl quadratic gravity of similar symmetry, due to different non-metricity. This establishes a connection between non-metricity and inflation predictions and enables us to test such theories by future CMB experiments.

scholarly journals HIGGS FIELD AS THE GAUGE FIELD CORRESPONDING TO PARITY IN THE USUAL SPACE–TIME

1998 ◽  
Vol 13 (06) ◽  
pp. 465-478 ◽  
Author(s):  
RECAI ERDEM
Keyword(s):  
Field Theory ◽  
Standard Model ◽  
Gauge Field ◽  
Higgs Field ◽  
Space Time ◽  
Degree Of Freedom ◽  
Local Character ◽  
Fifth Dimension ◽  
Local Description ◽  
The Standard Model

We find that the local character of field theory requires the parity degree of freedom of the fields to be considered as an additional discrete fifth dimension which is an artifact emerging due to the local description of space–time. Higgs field can be interpreted as the gauge field corresponding to this discrete dimension. Hence the noncommutative geometric derivation of the standard model follows as a manifestation of the local description of the usual space–time.

scholarly journals Super-soft CP violation

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Alessandro Valenti ◽  
Luca Vecchi
Keyword(s):  
Cp Violation ◽  
Standard Model ◽  
A Priori ◽  
Planck Scale ◽  
Higgs Doublet ◽  
Spontaneous Breaking ◽  
Beyond The Standard Model ◽  
Dark Sector ◽  
Generic Structure ◽  
The Standard Model

Abstract Solutions of the Strong CP Problem based on the spontaneous breaking of CP must feature a non-generic structure and simultaneously explain a coincidence between a priori unrelated CP-even and CP-odd mass scales. We show that these properties can emerge from gauge invariance and a CP-conserving, but otherwise generic, physics at the Planck scale. In our scenarios no fundamental scalar is introduced beyond the Standard Model Higgs doublet, and CP is broken at naturally small scales by a confining non-abelian dynamics. This approach is remarkably predictive: robustness against uncontrollable UV corrections to the QCD topological angle requires one or more families of vector-like quarks below a few 10’s of TeV, hence potentially accessible at colliders. Because CP violation is communicated to the SM at these super-soft scales, our solution of the Strong CP Problem is not spoiled by the presence of heavy new states motivated by other puzzles in physics beyond the Standard Model. In addition, these models generically predict a dark sector that may lead to interesting cosmological signatures.

scholarly journals Renormalization group equations of Higgs-R2 inflation

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Yohei Ema ◽  
Kyohei Mukaida ◽  
Jorinde van de Vis
Keyword(s):  
Renormalization Group ◽  
Standard Model ◽  
Planck Scale ◽  
Energy Scale ◽  
Einstein Frame ◽  
Ricci Scalar ◽  
Minimal Coupling ◽  
Renormalization Group Equations ◽  
The Standard Model

Abstract We derive one- and two-loop renormalization group equations (RGEs) of Higgs-R2 inflation. This model has a non-minimal coupling between the Higgs and the Ricci scalar and a Ricci scalar squared term on top of the standard model. The RGEs derived in this paper are valid as long as the energy scale of interest (in the Einstein frame) is below the Planck scale. We also discuss implications to the inflationary predictions and the electroweak vacuum metastability.

scholarly journals Planck Neutrinos as Ultra High Energy Cosmic Rays

2020 ◽  
Vol 29 (1) ◽  
pp. 40-46
Author(s):  
Dmitri L. Khokhlov
Keyword(s):  
Black Holes ◽  
Cosmic Rays ◽  
Standard Model ◽  
Active Galactic Nuclei ◽  
Planck Scale ◽  
Galactic Nuclei ◽  
High Energy ◽  
Ultra High Energy ◽  
High Energy Cosmic Rays ◽  
The Standard Model

AbstractThe studied conjecture is that ultra high energy cosmic rays (UHECRs) are hypothetical Planck neutrinos arising in the decay of the protons falling onto the gravastar. The proton is assumed to decay at the Planck scale into positron and four Planck neutrinos. The supermassive black holes inside active galactic nuclei, while interpreted as gravastars, are considered as UHECR sources. The scattering of the Planck neutrinos by the proton at the Planck scale is considered. The Planck neutrinos contribution to the CR events may explain the CR spectrum from 5 × 1018 eV to 1020 eV. The muon number in the Planck neutrinos-initiated shower is estimated to be larger by a factor of 3/2 in comparison with the standard model that is consistent with the observational data.

scholarly journals Dark matter spectra from the electroweak to the Planck scale

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Christian W. Bauer ◽  
Nicholas L. Rodd ◽  
Bryan R. Webber
Keyword(s):  
Dark Matter ◽  
Standard Model ◽  
Symmetry Breaking ◽  
Planck Scale ◽  
Electroweak Symmetry Breaking ◽  
Indirect Detection ◽  
Electroweak Symmetry ◽  
Stable States ◽  
Decay Spectrum ◽  
Crucial Ingredient

Abstract We compute the decay spectrum for dark matter (DM) with masses above the scale of electroweak symmetry breaking, all the way to the Planck scale. For an arbitrary hard process involving a decay to the unbroken standard model, we determine the prompt distribution of stable states including photons, neutrinos, positrons, and antiprotons. These spectra are a crucial ingredient in the search for DM via indirect detection at the highest energies as being probed in current and upcoming experiments including IceCube, HAWC, CTA, and LHAASO. Our approach improves considerably on existing methods, for instance, we include all relevant electroweak interactions.

scholarly journals Weak scale from Planck scale: Mass scale generation in a classically conformal two-scalar system

2020 ◽  
Vol 2020 (3) ◽  
Author(s):  
Junichi Haruna ◽  
Hikaru Kawai
Keyword(s):  
Scalar Field ◽  
Standard Model ◽  
Planck Scale ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
The Other ◽  
Expectation Value ◽  
Weak Scale ◽  
The Standard Model ◽  
The One

Abstract In the standard model, the weak scale is the only parameter with mass dimensions. This means that the standard model itself cannot explain the origin of the weak scale. On the other hand, from the results of recent accelerator experiments, except for some small corrections, the standard model has increased the possibility of being an effective theory up to the Planck scale. From these facts, it is naturally inferred that the weak scale is determined by some dynamics from the Planck scale. In order to answer this question, we rely on the multiple point criticality principle as a clue and consider the classically conformal $\mathbb{Z}_2\times \mathbb{Z}_2$ invariant two-scalar model as a minimal model in which the weak scale is generated dynamically from the Planck scale. This model contains only two real scalar fields and does not contain any fermions or gauge fields. In this model, due to a Coleman–Weinberg-like mechanism, the one-scalar field spontaneously breaks the $ \mathbb{Z}_2$ symmetry with a vacuum expectation value connected with the cutoff momentum. We investigate this using the one-loop effective potential, renormalization group and large-$N$ limit. We also investigate whether it is possible to reproduce the mass term and vacuum expectation value of the Higgs field by coupling this model with the standard model in the Higgs portal framework. In this case, the one-scalar field that does not break $\mathbb{Z}_2$ can be a candidate for dark matter and have a mass of about several TeV in appropriate parameters. On the other hand, the other scalar field breaks $\mathbb{Z}_2$ and has a mass of several tens of GeV. These results will be verifiable in near-future experiments.

scholarly journals The gravitational condensate of the higgs field

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Higgs Boson ◽  
Standard Model ◽  
Higgs Field ◽  
Higgs Bosons ◽  
Grand Unification ◽  
Gravitational Potential Energy ◽  
Mass Hierarchy ◽  
The Standard Model ◽  
Cell Condensation ◽  
The Difference

This paper analyses a method of producing the Higgs mass via the gravitational field. This approach has become very popular in recent years, as the consideration of other forces do not help in solving the problem of mass hierarchy. Not understand the difference between scales of the standard model and Grand unification theory. Here, we present a heuristic mechanism which eliminated this difference. The idea is that the density of the condensate of the Higgs is increased so that it is necessary to take into account self gravitational potential energy of the Higgs boson. The result is as follows. The mass of the Higgs is directly proportional to the cell density of the Higgs bosons. Or else the mass of the Higgs is inversely proportional to the cell volume, which is the Higgs boson in the condensate. The most interesting dimension of this cell condensation is equal to the scale of Grand unification. This formula naturally combines the scale of the standard model and Grand unification through gravitational condensation.

scholarly journals Testing the mechanism of lepton compositeness

2021 ◽  
Vol 10 (3) ◽  
Author(s):  
Vincenzo Afferrante ◽  
Axel Maas ◽  
René Sondenheimer ◽  
Pascal Törek
Keyword(s):  
Gauge Theory ◽  
Standard Model ◽  
Gauge Invariance ◽  
Bound States ◽  
Lattice Gauge Theory ◽  
Higgs Field ◽  
Left Handed ◽  
Lattice Gauge ◽  
The Standard Model ◽  
Weyl Fermions

Strict gauge invariance requires that physical left-handed leptons are actually bound states of the elementary left-handed lepton doublet and the Higgs field within the standard model. That they nonetheless behave almost like pure elementary particles is explained by the Fr"ohlich-Morchio-Strocchi mechanism. Using lattice gauge theory, we test and confirm this mechanism for fermions. Though, due to the current inaccessibility of non-Abelian gauged Weyl fermions on the lattice, a model which contains vectorial leptons but which obeys all other relevant symmetries has been simulated.

Sign in / Sign up

Export Citation Format

Share Document