Implications of the complex singlet field for noncommutative geometry model

Karimi, Hamid

doi:10.1007/jhep12(2017)040

Cited by 4 publications

(5 citation statements)

References 20 publications

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“…In the Standard Model the Higgs coupling will become negative at some high energy scale of the order of 10 11 Gev. Remarkably, this field σ plays a very important role in stabilizing the Higgs coupling which will not become negative at very high energies as well as being consistent with a low Higgs mass of 125 Gev [13], [14]. The form of the gauge and Higgs kinetic terms and potential implies unification of the gauge couplings and the Higgs coupling.…”

Section: Classification and Why The Standard Modelmentioning

confidence: 89%

“…We can show using elementary algebra, that the structure of the connection A is such that the block diagonal elements are of the form γ µ tensored with the gauge vectors of U (1)×SU ( 2)×SU (3) while the off-diagonal block elements are of the form γ 5 tensored with the Higgs doublet complex scalar field. There is, in addition, one singlet scalar field σ (real, or complex) [13], [14], not present in the Standard Model whose vev gives mass to the right-handed neutrinos [9]. Dynamics of all the fermion fields is then governed by the Dirac action [8] (JΨ, D A Ψ) .…”

Section: Classification and Why The Standard Modelmentioning

confidence: 99%

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Noncommutative geometry and structure of space–time

Chamseddine

2018

Afr. Mat.

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I give a summary review of the research program using noncommutative geometry as a framework to determine the structure of space-time. Classification of finite noncommutative spaces under few assumptions reveals why nature chose the Standard Model and the reasons behind the particular form of gauge fields, Higgs fields and fermions as well as the origin of symmetry breaking. It also points that at high energies the Standard Model is a truncation of Pati-Salam unified model of leptons and quarks. The same conclusions are arrived at uniquely without making any assumptions except for an axiom which is a higher form of Heisenberg commutation relations quantizing the volume of space-time. We establish the existence of two kinds of quanta of geometry in the form of unit spheres of Planck length. We provide answers to many of the questions which are not answered by other approaches, however, more research is needed to answer the remaining challenging questions.

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Section: Classification and Why The Standard Modelmentioning

confidence: 89%

Section: Classification and Why The Standard Modelmentioning

confidence: 99%

Noncommutative geometry and structure of space–time

Chamseddine

2018

Afr. Mat.

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“…For the renormalization group predictions it could simply mean that the big desert hypothesis is not correct. In fact it turns out that a single scalar field is enough to "cure" the prediction [5,30,36].…”

Section: Pos(corfu2019)216mentioning

confidence: 99%

Noncommutative Geometry, background independence, and $B-L$ extension of the Standard Model

Besnard¹

2020

Proceedings of Corfu Summer Institute 2019 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2019)

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In these notes we present a new framework, called "algebraic backgrounds", which is a slight modification of Connes' Spectral Triples theory which allows for a transparent representation of diffeomorphisms and spin structure equivalences. In an algebraic background there is no fixed Dirac operator but, instead, a bimodule of noncommutative 1-forms which plays the role of the differential structure of the manifold. The configuration space is the space of Dirac operators which are compatible with this bimodule. They play the role of metrics compatible with the differential structure. We present the cases of manifolds and finite graphs as motivations. The symmetry group of the algebraic background associated to a manifold turns out to be exactly that of the tetradic formulation of General Relativity, but the configuration space contains extra fields, not associated with a metric. However the projection on metric fields is diffeomorphism invariant so that they can be safely removed. The same framework adapted to the Standard Model automatically gauge the B-L symmetry. The resulting Kaluza-Klein theory contains many non-SM fields, most of them only acting on flavour space. They can be removed like in the GR case. What remains is a B-L extension of the Standard Model with a complex scalar breaking the new symmetry.

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“…The two latter solutions allow the introduction of a new field σ which not only fixes the mass of the Higgs making it compatible with 126 GeV, but also solves the possible instability of the theory. The last solution points decidedly to a version of the Pati-Salam model [66], an avenue also investigated from a phenomenological angle in [67][68][69][70][71][72].…”

Section: Beyond Standardmentioning

confidence: 99%

Noncommutative Geometry and Particle Physics

Lizzi¹

2018

Proceedings of Corfu Summer Institute 2017 "Schools and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2017)

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We review the noncommutative approach to the standard model. We start with the introduction if the mathematical concepts necessary for the definition of noncommutative spaces, and manifold in particular. This defines the framework of spectral geometry. This is applied to the standard model of particle interaction, discussing the fermionic and bosonic spectral action. The issues relating to the calculation of the mass of the Higgs are discussed, as well as the role of neutrinos and Wick rotations. Finally, we present the possibility of solving the problem of the Higgs mass by considering a pregeometric grand symmetry.

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Implications of the complex singlet field for noncommutative geometry model

Cited by 4 publications

References 20 publications

Noncommutative geometry and structure of space–time

Noncommutative geometry and structure of space–time

Noncommutative Geometry, background independence, and $B-L$ extension of the Standard Model

Noncommutative Geometry and Particle Physics

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