Gauge Field Theory of Horizontal Symmetry Generated by a Central Extension of the Pauli Algebra

Abstract

The standard model of particle physics is generalized so as to be furnished with a horizontal symmetry generated by an intermediary algebra between simple Lie algebras $\mathfrak{su}(2)$ and $\mathfrak{su}(3)$. Above a certain high energy scale $\breve{\Lambda}$, the horizontal gauge symmetry is postulated to hold so that the basic fermions, quarks and leptons, form its fundamental triplets, and a triplet and singlet of the horizontal gauge fields distinguish generational degrees of freedom. A horizontal scalar triplet is introduced to make the gauge fields super-massive by breaking the horizontal symmetry at $\breve{\Lambda}$. From this scalar triplet, there emerge real scalar fields which do not interact with fermions except for neutrino species and may give substantial influence on evolution of the universe. Another horizontal scalar triplet which breaks the electroweak symmetry at a low energy scale $\Lambda\simeq 2\times 10^2$GeV reproduces all of the results of the Weinberg-Salam theory, produces hierarchical mass matrices with less numbers of unknown parameters in a unified way and predicts six massive scalar particles, some of which might be observed by the future LHC experiment.