Generations Of Fermions Research Articles

Proton Decay and Gauge Coupling Unification in an Extended SU(5) GUT with 45D Higgs

Abstract We present a comprehensive study of an extended SU(5) grand unified theory (GUT) that incorporates a 45D Higgs representation to address the shortcomings of the minimal SU(5) GUT, such as the inability to generate realistic fermion mass hierarchies and insufficient proton stability. By considering a hierarchical mass spectrum for the scalar components of the 45D Higgs, we demonstrate that successful gauge coupling unification (GCU) can be achieved. The color octet scalar, color triplet scalar, and color antitriplet scalar play crucial roles in realizing GCU when their masses are significantly lighter than other components of the 45D Higgs. We focus on the proton decay channels mediated by the exchange of the color antitriplet scalar. Assuming that the 45D Higgs couples to all three generations of fermions, we determine the 45D Higgs Yukawa couplings with which the observed fermion mass matrices at low energies are realized. We calculate proton decay rates using the Yukawa couplings obtained from renormalization group evolutions and matching conditions at the GUT scale, thereby exploring the dependence of proton decay rates on model parameters. We find that the $p \rightarrow \nu \pi$ mode imposes the most stringent constraint on the mass of the color antitriplet scalar $M_{S_1}$. We also study the correlations between the lower bounds on $M_{S_1}$ derived from different proton decay modes.

Probing bottom-associated production of a TeV scale scalar decaying to a top quark and dark matter at the LHC

A minimal non-thermal dark matter model that can explain both the existence of dark matter and the baryon asymmetry in the universe is studied. It requires two color-triplet, iso-singlet scalars with OTeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O}\\left(\ extrm{TeV}\\right) $$\\end{document} masses and a singlet Majorana fermion with a mass of OGeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O}\\left(\ extrm{GeV}\\right) $$\\end{document}. The fermion becomes stable and can play the role of the dark matter candidate. We consider the fermion to interact with a top quark via the exchange of QCD-charged scalar fields coupled dominantly to third generation fermions. The signature of a single top quark production associated with a bottom quark and large missing transverse momentum opens up the possibility to search for this type of model at the LHC in a way complementary to existing monotop searches.

A common framework for fermion mass hierarchy, leptogenesis and dark matter

In this work, we explore an extension of the Standard Model designed to elucidate the fermion mass hierarchy, account for the dark matter relic abundance, and explain the observed matter-antimatter asymmetry in the universe. Beyond the Standard Model particle content, our model introduces additional scalars and fermions. Notably, the light active neutrinos and the first two generations of charged fermions acquire masses at the one-loop level. The model accommodates successful low-scale leptogenesis, permitting the mass of the decaying heavy right-handed neutrino to be as low as 10 TeV. We conduct a detailed analysis of the dark matter phenomenology and explore various interesting phenomenological implications. These include charged lepton flavor violation, muon and electron anomalous magnetic moments, constraints arising from electroweak precision observables, and implications for collider experiments.

Quantum number conservation: a tool in the design and analysis of high energy experiments

The Clifford Unification algebra Cl 7,7 is shown to provide a unified description of all the elementary fermions and hadrons in terms of seven binary quantum numbers. Four of these are defined in existing theories, namely spin-direction, fermion/anti-fermion pairing and the two commuting generators in the SU(3) description of quark colour. A Cl 3,3 sub-algebra integrates the Cl 1,3 space-time and Dirac algebras providing a new definition of time direction and identifying parity as a new quantum number. A further two quantum numbers are related to the commuting generators of an SU(3) description of fermion generations. All seven are conserved in the decays and interactions of charged particles, suggesting that quantum number conservation provides a useful tool in the design and interpretation of high energy experiments. This is especially relevant when neutral particles and parity are involved.

Questions of flavor physics and neutrino mass from a flipped hypercharge

The flavor structure of quarks and leptons is not yet fully understood, but it hints a more fundamental theory of nonuniversal generations. We therefore propose a simple extension of the Standard Model by flipping (i.e., enlarging) the hypercharge U(1)Y to U(1)X⊗U(1)N for which both X and N depend on generations of both quark and lepton. By anomaly cancellation, this extension not only explains the existence of just three fermion generations as observed but also requires the presence of a right-handed neutrino per generation, which motivates seesaw neutrino mass generation. Furthermore, in its minimal version with a scalar doublet and two scalar singlets, the model naturally generates the measured fermion-mixing matrices while it successfully accommodates several flavor anomalies observed in the neutral meson mixings, B-meson decays, lepton-flavor-violating processes of charged leptons, as well as satisfying constraints from particle colliders. Published by the American Physical Society 2024

Lessons from ATLAS and CMS measurements of Higgs boson decays to second generation fermions

There is now experimental evidence for Higgs boson decay into a pair of muons, and significant constraints on the Higgs boson decay into a charm quark-antiquark pair. The data on Higgs boson decays into second generation fermions probes various extensions of the Standard Model. We analyze the implications for the Standard Model effective field theory (SMEFT), without and with minimal flavor violation (MFV), for two Higgs doublet models (2HDM) with natural flavor conservation (NFC), for models with vector-like fermions, and for specific models that predict significant modifications of the Yukawa couplings to the light generations.

Sedenion Algebra Model as an Extension of the Standard Model and Its Link to SU(5)

In the Standard Model, ad hoc hypotheses assume the existence of three generations of point-like leptons and quarks, which possess a point-like structure and follow the Dirac equation involving four anti-commutative matrices. In this work, we consider the sedenion hypercomplex algebra as an extension of the Standard Model and show its close link to SU(5), which is the underlying symmetry group for the grand unification theory (GUT). We first consider the direct-product quaternion model and the eight-element octonion algebra model. We show that neither the associative quaternion model nor the non-associative octonion model could generate three fermion generations. Instead, we show that the sedenion model, which contains three octonion sub-algebras, leads naturally to precisely three fermion generations. Moreover, we demonstrate the use of basis sedenion operators to construct twenty-four 5 × 5 generalized lambda matrices representing SU(5) generators, in analogy to the use of octonion basis operators to generate Gell-Mann’s eight 3 × 3 lambda-matrix generators for SU(3). Thus, we provide a link between the sedenion algebra and Georgi and Glashow’s SU(5) GUT model that unifies the electroweak and strong interactions for the Standard Model’s elementary particles, which obey SU(3)SU(2)U(1) symmetry.

Phenomenology of a Deconstructed Electroweak Force

We study an effective theory of flavour in which the SU(2)L interaction is ‘flavour-deconstructed’ near the TeV scale. This arises, for example, in UV models that unify all three generations of left-handed fermions via an Sp(6)L symmetry. Flavour-universality of the electroweak force emerges accidentally (but naturally) from breaking the ∏i=13SU2L,i\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\prod}_{i=1}^3\ extrm{SU}{(2)}_{L,i} $$\\end{document} gauge group to its diagonal subgroup, delivering hierarchical fermion masses and left-handed mixing angles in the process. The heavy gauge bosons transform as two SU(2)L triplets that mediate new flavour non-universal forces. The lighter of these couples universally to the light generations, allowing consistency with flavour bounds even for a TeV scale mass. Constraints from flavour, high mass LHC searches, and electroweak precision are then highly complementary, excluding masses below 9 TeV. The heavier triplet must instead be hundreds of TeV to be consistent with meson mixing constraints. Because only the lighter triplet couples to the Higgs, we find radiative Higgs mass corrections of a few hundred GeV, meaning this model of flavour is arguably natural. The natural region will, however, be almost completely covered by the planned electroweak programme at FCC-ee. On shorter timescales, significant parameter space will be explored by the High-Luminosity LHC measurements at high-pT, and upcoming lepton flavour violation experiments, principally Mu3e.

Minimal flavour deconstruction

We construct two concrete examples of flavour non-universal gauge theories which, after the inclusion of all d ≤ 4 gauge invariant operators, allow to describe the observed pattern of flavour in the charged fermion sector without any small Yukawa coupling (y ≳ 0.1). Guided by the criterium of minimality, we assume that flavour non universality is confined to the Abelian sector of the gauge group: the universal hypercharge emerges after a sequence of symmetry-breaking steps characterised by two high mass scales, Λ[23]< Λ[12], where the second and the first fermion generations get their mass respectively. At least in one of the two models the smaller of these scales can be in the 10 TeV range, consistently with current bounds from flavour observables. Both models are extended to include as well neutrino masses and mixings.

Towards a Standard Model with six fermion generations and a new breaking scale?

We propose here an enhanced version of the Standard Model based on the same local gauge group SU(3) c ⨂ SU(2) L ⨂ U(1) Y that undergoes a spontaneous symmetry breaking up to SU(3) c ⨂ U(1) em . We prove that it can naturally predict: (i) the electric and weak charges’ quantization, (ii) the muon anomalous magnetic moment discrepancy Δa μ , along with (iii) a realistic Higgs spectrum, (iv) a viable neutrino phenomenology, and (v) FCNCs suppression. This promising outcome—without spoiling any of the experimentally validated predictions of the Standard Model—occurs by simply assuming there are six non-universal fermion generations and two distinct scalar doublets. The latter ones develop different breaking scales, the old Standard Model scale v ≃ 246 GeV and a higher scale V —most likely in 1–100 TeV region, to be tested at LHC.

Asymptotic ultraviolet-safe unification of gauge and Yukawa couplings: The exceptional case

The ultimate dream of unification models consists in combining both gauge and Yukawa couplings into one unified coupling. This is achieved by using a supersymmetric exceptional E6 gauge symmetry together with asymptotic unification in compact five-dimensional space-time. The ultraviolet fixed point requires exactly three fermion generations: one in the bulk, and the two light ones localised on the SO(10) boundary in order to cancel gauge anomalies. A second option allows to preserve baryon number and to lower the compactification scale down to the typical scales of the intermediate Pati-Salam gauge theory.

Theoretically Motivated Dark Electromagnetism as the Origin of Relativistic Modified Newtonian Dynamics

The present paper is a modest attempt to initiate the research program outlined in this abstract. We propose that general relativity and relativistic MOND (RelMOND) are analogues of broken electroweak symmetry. That is, SU(2)R×U(1)YDEM→U(1)DEM (DEM stands for dark electromagnetism), and GR is assumed to arise from the broken SU(2)R symmetry and is analogous to the weak force. RelMOND is identified with dark electromagnetism U(1)DEM, which is the remaining unbroken symmetry after the spontaneous symmetry breaking of the dark electro-grav sector SU(2)R×U(1)YDEM. This sector, as well as the electroweak sector, arises from the breaking of an E8×E8 symmetry in a recently proposed model of unification of the standard model with pre-gravitation, with the latter based on an SU(2)R gauge theory. The source charge for the dark electromagnetic force is the square root of mass, motivated by the experimental fact that the ratio of the square roots of the masses of the electron, up-quark, and down-quark is 1:2:3, which is the opposite of the ratio of their electric charges at 3:2:1. The introduction of the dark electromagnetic force helps us understand the peculiar mass ratios of the second and third generations of charged fermions. We also note that in the deep MOND regime, acceleration is proportional to the square root of mass, which motivates us to propose the relativistic U(1)DEM gauge symmetry as the origin of MOND. We explain why the dark electromagnetic force falls inversely with distance, as in MOND, rather than following the inverse square of distance. We conclude that dark electromagnetism effectively mimics cold dark matter, and the two are essentially indistinguishable in cosmological situations where CDM successfully explains observations, such as CMB anisotropies and gravitational lensing.

Rising through the ranks: flavor hierarchies from a gauged SU(2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\varvec{\\mathrm {SU(2)}}}$$\\end{document} symmetry

We propose an economical model to address the mass hierarchies of quarks and charged leptons. The light generations of the left-handed fermions form doublets under an SU(2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \ extrm{SU}(2) $$\\end{document} flavor symmetry, which is gauged. The generational hierarchies emerge from three independent rank-one contributions to the Yukawa matrices: one is a renormalizable contribution, the second is suppressed by a mass ratio, and the last by an additional loop factor. The model is renormalizable, features only a handful of new fields, and is remarkably simple compared to typical completions of gauged flavor symmetries or Froggatt–Nielsen. The model has a rich phenomenology, and we highlight promising signatures, especially in the context of K and B meson physics. This includes an interpretation of the latest B+→K+νν¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B^+ \\rightarrow K^+ \ u \\bar{\ u }$$\\end{document} measurement from Belle II.

A complete set of the dimension-8 Green’s basis operators in the Standard Model effective field theory

We present a complete and independent off-shell Green’s basis of the dimension 8 operators in the Standard Model effective field theory (SMEFT). We propose an off-shell amplitude formalism such that this new kind of amplitude has a one-to-one correspondence to general operators carrying all kinds of redundancies. The advantage of such formalism is that all kinds of redundancies can be formulated explicitly in terms of the off-shell spinors and thus be removed systematically from the exhaustive list of the general off-shell amplitudes. Following such procedures, redundant operators can be reduced to the ones with the only redundancy from the equation of motion kept, the Green’s basis. We find there are (993+1649) independent (on-shell + off-shell) operators for one generation of fermions and (44807+66197) ones for three generations at dimension 8. This systematic method can be applied to obtain the Green’s basis at any mass dimension for general EFTs.

Effective field theories of axion, ALP and dark photon

With the help of Young tensor technique, we enumerate the complete and independent set of effective operators up to dim-8 for the extension of the standard model with a Goldstone boson by further imposing the Adler’s zero condition in the soft momentum limit. Such basis can be reduced to describe the axion or majoron effective Lagrangian if further (symmetry) constraints are imposed. Then reformulating dark photon as combination of Goldstone boson and transverse gauge boson, the effective operators of the Goldstone boson can be extended to effective chiral Lagrangian description of the dark photon. For the first time we obtain 0 (0), 6 (44), 1 (1), 44 (356), 32 (520) operators in Goldstone effective field theory, and 9 (49), 0 (0), 108 (676), 10 (426), 1904 (40783) operators in dark photon effective field theory at the dimension 4, 5, 6, 7, 8 for one (three) generation of fermions.

A sedenion algebraic representation of three colored fermion generations

Three generations of fermions with SU(3) C symmetry are represented algebraically in terms of the algebra of sedenions, 𝕊, generated from the octonions, 𝕆, via the Cayley-Dickson process. Despite significant recent progress in generating the Standard Model gauge groups and particle multiplets from the four normed division algebras, an algebraic motivation for the existence of exactly three generations has been difficult to substantiate. In the sedenion model, one generation of leptons and quarks with SU(3) C symmetry is represented in terms of two minimal left ideals of ℂℓ(6), generated from a subset of all left actions of the complex sedenions on themselves. Subsequently, the finite group S 3, which are automorphisms of 𝕊 but not of 𝕆, is used to generate two additional generations. The present paper highlight the key aspects and ideas underlying this construction.

On the sensitivity reach of LQ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{LQ}$$\\end{document} production with preferential couplings to third generation fermions at the LHC

Leptoquarks (LQ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{LQ}$$\\end{document}s) are hypothetical particles that appear in various extensions of the Standard Model (SM), that can explain observed differences between SM theory predictions and experimental results. The production of these particles has been widely studied at various experiments, most recently at the Large Hadron Collider (LHC), and stringent bounds have been placed on their masses and couplings, assuming the simplest beyond-SM (BSM) hypotheses. However, the limits are significantly weaker for LQ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{LQ}$$\\end{document} models with family non-universal couplings containing enhanced couplings to third-generation fermions. We present a new study on the production of a LQ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{LQ}$$\\end{document} at the LHC, with preferential couplings to third-generation fermions, considering proton-proton collisions at s=13TeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{s} = 13 \\, \ extrm{TeV}$$\\end{document} and s=13.6TeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{s} = 13.6 \\, \ extrm{TeV}$$\\end{document}. Such a hypothesis is well motivated theoretically and it can explain the recent anomalies in the precision measurements of B\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{B}$$\\end{document}-meson decay rates, specifically the RD(∗)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R_{D^{(*)}}$$\\end{document} ratios. Under a simplified model where the LQ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{LQ}$$\\end{document} masses and couplings are free parameters, we focus on cases where the LQ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{LQ}$$\\end{document} decays to a τ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au $$\\end{document} lepton and a b\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{b}$$\\end{document} quark, and study how the results are affected by different assumptions about chiral currents and interference effects with other BSM processes with the same final states, such as diagrams with a heavy vector boson, Z′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{Z}^{\\prime }$$\\end{document}. The analysis is performed using machine learning techniques, resulting in an increased discovery reach at the LHC, allowing us to probe new physics phase space which addresses the B\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{B}$$\\end{document}-meson anomalies, for LQ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{LQ}$$\\end{document} masses up to 5.00TeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$5.00\\, \ extrm{TeV}$$\\end{document}, for the high luminosity LHC scenario.

Dixon-Rosenfeld lines and the Standard Model

We present three new coset manifolds named Dixon-Rosenfeld lines that are similar to Rosenfeld projective lines except over the Dixon algebra mathbb {C}otimes mathbb {H}otimes mathbb {O}. Three different Lie groups are found as isometry groups of these coset manifolds using Tits’ formula. We demonstrate how Standard Model interactions with the Dixon algebra in recent work from Furey and Hughes can be uplifted to tensor products of division algebras and Jordan algebras for a single generation of fermions. The Freudenthal–Tits construction clarifies how the three Dixon-Rosenfeld projective lines are contained within mathbb {C}otimes mathbb {H}otimes J_{2}(mathbb {O}), mathbb {O}otimes J_{2}(mathbb {C}otimes mathbb {H}), and mathbb {C}otimes mathbb {O}otimes J_{2}(mathbb {H}).

Three generations of colored fermions with S_3 family symmetry from Cayley–Dickson sedenions

An algebraic representation of three generations of fermions with SU(3)_C color symmetry based on the Cayley–Dickson algebra of sedenions {mathbb {S}} is constructed. Recent constructions based on division algebras convincingly describe a single generation of leptons and quarks with Standard Model gauge symmetries. Nonetheless, an algebraic origin for the existence of exactly three generations has proven difficult to substantiate. We motivate mathbb {S} as a natural algebraic candidate to describe three generations with SU(3)_C gauge symmetry. We initially represent one generation of leptons and quarks in terms of two minimal left ideals of mathbb {C}ell (6), generated from a subset of all left actions of the complex sedenions on themselves. Subsequently we employ the S_3 automorphism of order three, which is an automorphism of mathbb {S} but not of mathbb {O}, to generate two additional generations. Given the relative obscurity of sedenions, efforts have been made to present the material in a self-contained manner.

A perturbative production of massive Z bosons and fermion–antifermion pairs from the vacuum in the de Sitter Universe

In this paper we study the problem of neutral electro-weak interactions in a de Sitter geometry. We develop the formalism of reduction for the Proca field with the help of the solutions for the interacting fields and by using perturbative methods we obtain the definition of the transition amplitudes in the first order of perturbation theory. As an application to our formalism we study the generation of massive fermions and Z bosons from vacuum in the expanding de Sitter universe. Our results are the generalization to the curved geometry of the Weinberg–Salam electro-weak theory for the case of Z boson interaction with leptons. The probability is found to be a quantity that depends on the Hubble parameter and we prove that such perturbative processes are possible only for large expansion regime of the early Universe. The total probability and rate of transition are obtained for the case of large expansion and we use the dimensional regularization for extract finite results from the momenta integrals. In the Minkowski limit we obtain that the probability of particle generation from vacuum is vanishing recovering the well known result that forbids particle production in flat space-time due to the momentum-energy conservation.