SO(10) unification in noncommutative geometry revisited

TL;DR

This paper revisits the SO(10) unification model within noncommutative geometry, exploring a complex Higgs structure and confirming standard model predictions like the weak mixing angle and mass relations.

Contribution

It introduces a more general Higgs multiplet structure in the SO(10) noncommutative geometry framework, differing from previous models, and confirms key standard model predictions.

Findings

Standard model predictions are recovered at tree level.

A more complex Higgs multiplet structure is proposed.

The model differs significantly from previous approaches.

Abstract

We investigate the SO(10)-unification model in a Lie algebraic formulation of noncommutative geometry. The SO(10)-symmetry is broken by a 45-Higgs and the Majorana mass term for the right neutrinos (126-Higgs) to the standard model structure group. We study the case that the fermion masses are as general as possible, which leads to two 10-multiplets, four 120-multiplets and two additional 126-multiplets of Higgs fields. This Higgs structure differs considerably from the two Higgs multiplets 16 \otimes 16^* and 16^c \otimes 16^* used by Chamseddine and Fr\"ohlich. We find the usual tree-level predictions of noncommutative geometry m_W=(1/2)m_t, \sin^2\theta_W=(3/8) and g_2=g_3 as well as m_H \leq m_t.