Z_2-Bi-Gradings, Majorana Modules and the Standard Model Action

TL;DR

This paper explores the geometric structure of Dirac operators related to the Standard Model, showing how Majorana masses can be incorporated and may influence dark energy through a small cosmological constant.

Contribution

It introduces a geometric framework based on real Dirac operators of simple type to incorporate Majorana masses into the Standard Model action.

Findings

Majorana mass terms can be naturally integrated into the Standard Model geometry.

Majorana masses contribute to a small cosmological constant.

The framework suggests a link between Dirac-Majorana interplay and dark energy.

Abstract

The action functional of the Standard Model of particle physics is intimately related to a specific class of first order differential operators called Dirac operators of Pauli type ("Pauli-Dirac operators"). The aim of this article is to carefully analyze the geometrical structure of this class of Dirac operators on the basis of real Dirac operators of simple type. On the basis of simple type Dirac operators, it is shown how the Standard Model action (STM action) may be viewed as generalizing the Einstein-Hilbert action in a similar way the Einstein-Hilbert action is generalized by a cosmological constant. Furthermore, we demonstrate how the geometrical scheme presented allows to naturally incorporate also Majorana mass terms within the Standard Model. For reasons of consistency these Majorana mass terms are shown to dynamically contribute to the Einstein-Hilbert action by a "true" cosmological constant. Due to its specific form, this cosmological constant can be very small. Nonetheless, this cosmological constant may provide a significant contribution to dark matter/energy. In the geometrical description presented this possibility arises from a subtle interplay between Dirac and Majorana masses.