Renormalization Group Running of Fermion Observables in an Extended Non-Supersymmetric SO(10) Model

TL;DR

This paper studies how fermion masses, mixings, and scalar couplings evolve with energy in an extended non-supersymmetric SO(10) GUT model, incorporating gauge group changes and comparing with minimal models to match experimental data.

Contribution

It derives renormalization group equations for fermion and scalar couplings in an extended SO(10) model, demonstrating successful low-energy observable predictions and comparing with minimal models.

Findings

Fermion observables can be matched to experimental values using RG evolution.

Differences up to 80% found when comparing extended and SM-like evolution.

Predictions made for CP-violating phases and neutrino masses.

Abstract

We investigate the renormalization group evolution of fermion masses, mixings and quartic scalar Higgs self-couplings in an ${\it extended}$ non-supersymmetric SO(10) model, where the Higgs sector contains the ${\bf 10}_{\rm H}$, ${\bf 120}_{\rm H}$, and ${\bf 126}_{\rm H}$ representations. The group SO(10) is spontaneously broken at the GUT scale to the Pati-Salam group and subsequently to the Standard Model (SM) at an intermediate scale $M_{\rm I}$. We explicitly take into account the effects of the change of gauge groups in the evolution. In particular, we derive the renormalization group equations for the different Yukawa couplings. We find that the computed physical fermion observables can be successfully matched to the experimental measured values at the electroweak scale. Using the same Yukawa couplings at the GUT scale, the measured values of the fermion observables cannot be reproduced with a SM-like evolution, leading to differences in the numerical values up to around 80 %. Furthermore, a similar evolution can be performed for a ${\it minimal}$ SO(10) model, where the Higgs sector consists of the ${\bf 10}_{\rm H}$ and ${\bf 126}_{\rm H}$ representations only, showing an equally good potential to describe the low-energy fermion observables. Finally, for both the extended and the minimal SO(10) models, we present predictions for the three Dirac and Majorana CP-violating phases as well as three effective neutrino mass parameters.