Related papers: Triality selection rules of Octonion and Quantum M…
We apply the supersymmetric model of \'E. Cartan to the pseudoscalar meson decay into two photons, $\pi_0\to\gamma\gamma$, $\eta\to\gamma\gamma$ and $\eta'\to\gamma\gamma$. In the book of \'E. Cartan published in 1966, Dirac spinors…
We compare the decay of a Higgs boson $H^0(0^+)\to\ell\bar\ell \ell\bar\ell\to\gamma\gamma$, $H^0(0^+)\to W\bar W\to \ell\bar\nu\bar\ell\nu$, and $H^0(0^+)\to Z\bar Z\to\ell\bar\ell\ell\bar\ell$ using Cartan's supersymmetry, that defines…
We apply the Cartan's supersymmetric model to the weak interaction of hadrons. The electromagnetic currents are transformed by $G_{12},G_{123},G_{13},G_{132}$ and the factor$(1-\gamma_5)$ is inserted between $l \bar\nu$ or $\bar l \nu$ when…
A Dirac fermion is expressed by a 4 component spinor which is a combination of two quaternions and which can be treated as an octonion. The octonion possesses the triality symmetry, which defines symmetry of fermion spinors and bosonic…
In these lectures, we discuss some well-known facts about Clifford algebras: matrix representations, Cartan's periodicity of 8, double coverings of orthogonal groups by spin groups, Dirac equation in different formalisms, spinors in $n$…
It is shown that, under a conformal transformation with reference to the Higgs field, the Higgs boson can be completely decoupled from electroweak interactions with no apparent change in known properties of leptons, quarks and vector…
This paper is meant to be an informative introduction to spinor representations of Clifford algebras. In this paper we will have a look at Clifford algebras and the octonion algebra. We begin the paper looking at the quaternion algebra…
We propose a Clifford algebra approach to chiral symmetry breaking and fermion mass hierarchies in the context of composite Higgs bosons. Standard model fermions are represented by algebraic spinors of six-dimensional binary Clifford…
A model is presented of the leptons, quarks and bosons as non-elementary particles being composed of spinons. They are defined as massless fermions obeying the Weyl equations, but in addition are charged and assumed to have two internal…
Multi-spinor fields which behave as triple-tensor products of the Dirac spinors and form reducible representations of the Lorentz group describe three families of ordinary quarks and leptons in the visible sector and an additional family of…
We propose a minimal model for the cosmic coincidence problem $\Omega_{\rm DM}/\Omega_B \sim 5$ and neutrino mass in a type-II seesaw scenario. We extend the standard model of particle physics with a $\rm SU(2)$ singlet leptonic Dirac…
Dark matter is postulated to be a neutral Dirac fermion, charged under a dark $U(1)_D$ gauge symmetry. Scalar partners of the quarks and leptons are also charged under $U(1)_D$. The dark gauge boson $Z_D$ and the dark Higgs boson $h_D$…
Recently, it has been pointed out that two different excesses of events observed at LEP could be interpreted as the CP-even Higgs bosons of the MSSM with masses of approximately 98 and 114 GeV. If this is the case, the entire MSSM Higgs…
This paper discusses the Higgs and spinor fermion terms of the D4-D5-E6 model of a series of papers (hep-ph/9301210, hep-th/9302030, hep-th/9306011, and hep-th/9402003) an 8-dimensional spacetime is reduced to 4-dimensions. The gauge boson…
The paper surveys recent progress in the search for an appropriate internal space algebra for the Standard Model (SM) of particle physics. As a starting point serve Clifford algebras involving operators of left multiplication by octonions.…
We propose a simple scenario which explains the observed matter-antimatter imbalance and the origin of dark matter in the Universe. We use the Einstein-Cartan-Sciama-Kibble theory of gravity which naturally extends general relativity to…
We study the indirect effects of new physics on the phenomenology of the "Higgs-like" particle. Assuming that the recently observed state belongs to a light electroweak doublet scalar and that the SU(2)_L x U(1)_Y symmetry is linearly…
We present a new model of "Stealth Dark Matter": a composite baryonic scalar of an $SU(N_D)$ strongly-coupled theory with even $N_D \geq 4$. All mass scales are technically natural, and dark matter stability is automatic without imposing an…
In the present universe visible and dark matter contribute comparable energy density although they have different properties. This coincidence can be elegantly explained if the dark matter relic density, originating from a dark matter…
The theory of representations of Clifford algebras is extended to employ the division algebra of the octonions or Cayley numbers. In particular, questions that arise from the non-associativity and non-commutativity of this division algebra…