The Spectrum of the 4-Generation Dirac-Kaehler Extension of the SM

TL;DR

This paper analyzes the fermionic mass spectrum of the Dirac-Kaehler extension of the Standard Model, predicting a 4th generation charged lepton mass of 370 GeV and relating neutrino masses through a see-saw mechanism.

Contribution

It introduces a Bogoliubov transformation to relate the DK-SM to a flavor U(4) extension, enabling mass predictions and mixing texture analysis.

Findings

Predicts the 4th charged lepton mass as 370 GeV.

Reproduces near tri-bimaximal and quark mixing textures.

Establishes a see-saw relation between electron neutrino and 4th neutrino masses.

Abstract

We compute the mass spectrum of the fermionic sector of the Dirac-Kaehler extension of the SM (DK-SM) by showing that there exists a Bogoliubov transformation that transforms the DK-SM into a flavor U(4) extension of the SM (SM-4) with a particular choice of masses and mixing textures. Mass relations of the model allow determination of masses of the 4th generation. Tree level prediction for the mass of the 4th charged lepton is 370 GeV. The model selects the normal hierarchy for neutrino masses and reproduces naturally the near tri-bimaximal and quark mixing textures. The electron neutrino and the 4th neutrino masses are related via a see-saw-like mechanism.