Nontrivial Flavor Structure from Noncompact Lie Group in Noncommutative Geometry

Abstract

In this paper, we propose a mechanism which induces nontrivial flavor structure from transformations of a noncompact Lie group SL(3,C) in noncommutative geometry. Matrices $L\in$ SL(3,C) are associated with accompanied by the preon fields as $a_{L,R}(x)\to L_{L,R}{a}_{L,R}(x)$. In order to retain the Hermiticity of the Lagrangian, we assume the same trick when ${\psi }^{†}\psi$ is replaced by $\bar{\psi }\psi$ to construct a Lorentz invariant Lagrangian. As a result, the Dirac Lagrangian has both of flavor-universal gauge interactions and nontrivial Yukawa interactions. Removing the unphysical unitary transformations, Yukawa matrices found to be $Y_{ij}=L_L^{†}k{L}_R\to {\Lambda }_L^{}{U}_L^{†}k{U}_R{\Lambda }_R$. Here, $k$ is a coefficient, $U$ is 3 $\times$ 3 unitary matrix and $\Lambda$ is the eigenvalue matrix $\Lambda =\mathrm{diag}({\lambda }_1,{\lambda }_2,{\lambda }_3)$ with ${\lambda }_1{\lambda }_2{\lambda }_3=1$. If $L_{L,R}$ are originated from a broken symmetry, the hierarchy and mixing of flavor can be interpreted as the "Lorentz boost" and the "rotation" in this space respectively.

This paper has been withdrawn by the author because the paper has several faults

References in corpus (5)

• Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
• Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
• The Minimal Composite Higgs Model
• Tasi 2009 lectures: The Higgs as a Composite Nambu-Goldstone Boson
• Proceedings of the first workshop on Flavor Symmetries and consequences in Accelerators and Cosmology (FLASY2011)