Complexification of the Exceptional Jordan Algebra and Its Application to Particle Physics

2021 ◽  
Vol 61 ◽  
pp. 1-16
Author(s):  
Daniele Corradetti ◽  
Keyword(s):  
Standard Model ◽  
Gauge Group ◽  
Jordan Algebra ◽  
Particle Physics ◽  
Compact Form ◽  
Symmetric Extension ◽  
Grand Unified Theories ◽  
The Standard Model ◽  
Unified Theories ◽  
Standard Model Gauge Group

Recent papers contributed revitalizing the study of the exceptional Jordan algebra $\mathfrak{h}_{3}(\mathbb{O})$ in its relations with the true Standard Model gauge group $\mathrm{G}_{SM}$. The absence of complex representations of $\mathrm{F}_{4}$ does not allow $\Aut\left(\mathfrak{h}_{3}(\mathbb{O})\right)$ to be a candidate for any Grand Unified Theories, but the automorphisms of the complexification of this algebra, i.e., $\mathfrak{h}_{3}^{\mathbb{C}}(\mathbb{O})$, are isomorphic to the compact form of $\mathrm{E}_{6}$ and similar constructions lead to the gauge group of the minimal left-right symmetric extension of the Standard Model.

scholarly journals the complexification of the exceptional Jordan algebra and applications to particle physics

2021 ◽  
Author(s):  
Daniele Corradetti
Keyword(s):  
Standard Model ◽  
Gauge Group ◽  
Jordan Algebra ◽  
Particle Physics ◽  
Proper Subgroup ◽  
Group Of Automorphisms ◽  
Grand Unified Theories ◽  
The Standard Model ◽  
Unified Theories ◽  
Standard Model Gauge Group

Abstract Recent papers of Todorov and Dubois-Violette[4] and Krasnov[7] contributed revitalizing the study of the exceptional Jordan algebra h3(O) in its relations with the true Standard Model gauge group GSM. The absence of complex representations of F4 does not allow Aut (h3 (O)) to be a candidate for any Grand Unified Theories, but the group of automorphisms of the complexification of this algebra isisomorphic to the compact form of E6. Following Boyle in [12], it is then easy to show that the gauge group of the minimal left-right symmetric extension of the Standard Model is isomorphic to a proper subgroup of Aut(C⊗h3(O))

scholarly journals SPARTICLE MASS SPECTRUM IN GRAND UNIFIED THEORIES

2007 ◽  
Vol 22 (19) ◽  
pp. 3229-3259 ◽  
Author(s):  
B. ANANTHANARAYAN ◽  
P. N. PANDITA
Keyword(s):  
Mass Spectrum ◽  
Gauge Group ◽  
Gauge Groups ◽  
Grand Unified Theories ◽  
Renormalization Group Equations ◽  
The Standard Model ◽  
Unified Theories ◽  
The One ◽  
The Impact ◽  
Standard Model Gauge Group

We carry out a detailed analysis of sparticle mass spectrum in supersymmetric grand unified theories. We consider the spectroscopy of the squarks and sleptons in SU (5) and SO (10) grand unified theories, and show how the underlying supersymmetry breaking parameters of these theories can be determined from a measurement of different sparticle masses. This analysis is done analytically by integrating the one-loop renormalization group equations with appropriate boundary conditions implied by the underlying grand unified gauge group. We also consider the impact of nonuniversal gaugino masses on the sparticle spectrum, especially the neutralino and chargino masses which arise in supersymmetric grand unified theories with nonminimal gauge kinetic function. In particular, we study the interrelationships between the squark and slepton masses which arise in grand unified theories at the one-loop level, which can be used to distinguish between the different underlying gauge groups and their breaking pattern to the Standard Model gauge group. We also comment on the corrections that can affect these one-loop results.

scholarly journals Testable SUSY spectra from GUTs at a 100 TeV pp collider

2016 ◽  
Vol 31 (33) ◽  
pp. 1644011 ◽  
Author(s):  
Stefan Antusch ◽  
Constantin Sluka
Keyword(s):  
Elementary Particle ◽  
Standard Model ◽  
Gauge Group ◽  
Charged Lepton ◽  
Experimental Results ◽  
Recent Analysis ◽  
Grand Unified Theories ◽  
The Standard Model ◽  
Unified Theories ◽  
Different Types

Grand Unified Theories (GUTs) are attractive candidates for more fundamental elementary particle theories. They cannot only unify the Standard Model (SM) interactions but also different types of SM fermions, in particular quarks and leptons, in joint representations of the GUT gauge group. We discuss how comparing predictive supersymmetric GUT models with the experimental results for quark and charged lepton masses leads to constraints on the SUSY spectrum. We show an example from a recent analysis where the resulting superpartner masses where found just beyond the reach of LHC Run 1, but fully within the reach of a 100 TeV [Formula: see text] collider.

scholarly journals Leptoquarks in oblique corrections and Higgs signal strength: status and prospects

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Andreas Crivellin ◽  
Dario Müller ◽  
Francesco Saturnino
Keyword(s):  
Standard Model ◽  
Signal Strength ◽  
Grand Unified Theories ◽  
The Standard Model ◽  
Unified Theories ◽  
Discovery Potential ◽  
Weak Constraints ◽  
The Impact ◽  
Standard Model Gauge Group ◽  
Higgs Signal

Abstract Leptoquarks (LQs) are predicted within Grand Unified Theories and are well motivated by the current flavor anomalies. In this article we investigate the impact of scalar LQs on Higgs decays and oblique corrections as complementary observables in the search for them. Taking into account all five LQ representations under the Standard Model gauge group and including the most general mixing among them, we calculate the effects in h → γγ, h → gg, h → Zγ and the Peskin-Takeuchi parameters S, T and U. We find that these observables depend on the same Lagrangian parameters, leading to interesting correlations among them. While the current experimental bounds only yield weak constraints on the model, these correlations can be used to distinguish different LQ representations at future colliders (ILC, CLIC, FCC-ee and FCC-hh), whose discovery potential we are going to discuss.

scholarly journals Beyond the Standard Model at LEP

1991 ◽  
Vol 336 (1642) ◽  
pp. 247-259 ◽  
Keyword(s):  
Dark Matter ◽  
Standard Model ◽  
Beyond The Standard Model ◽  
Grand Unified Theories ◽  
The Standard Model ◽  
Unified Theories ◽  
Massive Neutrinos ◽  
Supersymmetric Particles ◽  
The Universe

LEP data constrain severely many proposed extensions of the Standard Model. These include: massive neutrinos, which are now largely excluded as candidates for the dark matter of the Universe; supersymmetric particles, the lightest of which would still constitute detectable dark matter; technicolour, of which many favoured versions are now excluded by precision electroweak measurements; and grand unified theories, of which LEP data favour supersymmetric versions.

scholarly journals PROBING SO(10) SYMMETRY BREAKING PATTERNS THROUGH SFERMION MASS RELATIONS

2005 ◽  
Vol 20 (18) ◽  
pp. 4241-4257 ◽  
Author(s):  
B. ANANTHANARAYAN ◽  
P. N. PANDITA
Keyword(s):  
Standard Model ◽  
Supersymmetry Breaking ◽  
Gauge Group ◽  
Low Energy ◽  
Grand Unification ◽  
The Standard Model ◽  
Scalar Mass ◽  
Mass Terms ◽  
Standard Model Gauge Group ◽  
Slepton Mass

We consider supersymmetric SO(10) grand unification where the unified gauge group can break to the Standard Model gauge group through different chains. The breaking of SO(10) necessarily involves the reduction of the rank, and consequent generation of nonuniversal supersymmetry breaking scalar mass terms. We derive squark and slepton mass relations, taking into account these nonuniversal contributions to the sfermion masses, which can help distinguish between the different chains through which the SO(10) gauge group breaks to the Standard Model gauge group. We then study some implications of these nonuniversal supersymmetry breaking scalar masses for the low energy phenomenology.

scholarly journals E6 inspired SUSY models with custodial symmetry

2018 ◽  
Vol 33 (31) ◽  
pp. 1844007 ◽  
Author(s):  
R. Nevzorov
Keyword(s):  
Gauge Symmetry ◽  
Standard Model ◽  
Supersymmetric Standard Model ◽  
Exotic States ◽  
Grand Unified Theories ◽  
The Standard Model ◽  
Unified Theories ◽  
Low Energies ◽  
Custodial Symmetry ◽  
Susy Models

The breakdown of [Formula: see text] within the supersymmetric (SUSY) Grand Unified Theories (GUTs) can result in SUSY extensions of the standard model (SM) based on the SM gauge group together with extra [Formula: see text] gauge symmetry under which right-handed neutrinos have zero charge. In these [Formula: see text] extensions of the minimal supersymmetric standard model (MSSM) a single discrete [Formula: see text] symmetry may be used to suppress the most dangerous operators, that give rise to proton decay as well as nondiagonal flavour transitions at low energies. The SUSY models under consideration involves [Formula: see text] and extra exotic matter beyond the MSSM. We discuss leptogenesis within this SUSY model and argue that the extra exotic states may lead to the nonstandard Higgs decays.

scholarly journals Dark matter and baryogenesis from non-Abelian gauged lepton number

2017 ◽  
Vol 32 (19) ◽  
pp. 1730018 ◽  
Author(s):  
Bartosz Fornal
Keyword(s):  
Dark Matter ◽  
Gauge Symmetry ◽  
Simple Model ◽  
Standard Model ◽  
Gauge Group ◽  
Lepton Number ◽  
Dark Matter Candidate ◽  
The Standard Model ◽  
The Right ◽  
Standard Model Gauge Group

A simple model is constructed based on the gauge symmetry [Formula: see text], with only the leptons transforming nontrivially under [Formula: see text]. The extended symmetry is broken down to the Standard Model gauge group at TeV-scale energies. We show that this model provides a mechanism for baryogenesis via leptogenesis in which the lepton number asymmetry is generated by [Formula: see text] instantons. The theory also contains a dark matter candidate — the [Formula: see text] partner of the right-handed neutrino.

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