Renovation of the Standard Model with Clifford-Dirac algebras for chiral-triplets

Abstract

Three repetitive chiral fields of quarks and leptons are bundled to form clusters, called chiral-triplets, in the electroweak symmetric regime. Postulating that each chiral-triplets possesses its own Clifford-Dirac algebra with the common Lorentz subalgebra and that the gauge fields and the Higgs field interact with the chiral-triplets, we renovate the Standard Model of elementary particles so that the uncertainties persisted in the Yukawa interactions are reduced. The vertex of the interaction between the Higgs field and the chiral-triplets includes pairs of unipotent matrices and four parameters generating the nine Yukawa coupling constants in the Standard Model. The small masses of light active neutrinos arise from the seesaw mechanism induced from the Majorana mass of the right-handed neutrinos. The Higgs mechanism leads to the Dirac mass matrices which can describe all data of the mass spectra and the flavor mixing matrices in the quark and lepton sectors to high precision.