Yukawa ratio predictions in non-renormalizable $\mathrm{SO}(10)$ GUT models

TL;DR

This paper investigates the predictive power of non-renormalizable SO(10) GUT models for fermion mass ratios, extending previous analyses to more general Higgs representations and vacuum expectation value directions, with a focus on the MSSM Higgs placement.

Contribution

It extends the analysis of fermion mass ratio predictivity in SO(10) GUTs to include larger Higgs representations and general VEV directions, highlighting the importance of MSSM Higgs localization.

Findings

Identified highly predictive GUT operator structures.

Demonstrated the significance of MSSM Higgs placement.

Showed predictive power in simplified fermion mass models.

Abstract

Since $\mathrm{SO}(10)$ GUTs unify all fermions of the Standard Model plus a right-chiral neutrino in a representation $\mathbf{16}$ per family, they have the potential to be maximally predictive regarding the ratios between the masses (or Yukawa couplings) of different fermion types, i.e.~the up-type quarks, down-type quarks, charged leptons and neutrinos. We analyze the predictivity of classes of $\mathrm{SO}(10)$ (SUSY) GUT models for the fermion mass ratios, where the Yukawa couplings for each family are dominated by a single effective GUT operator of the schematic form $\mathbf{16}^2\cdot\mathbf{45}^n\cdot\mathbf{210}^{m}\cdot\mathbf{H}$, for $\mathbf{H}\in\{\mathbf{10},\mathbf{120},\mathbf{\overline{126}}\}$. This extends previous works to general vacuum expectation value directions for GUT-scale VEVs and to larger Higgs representations. In addition, we show that the location of the MSSM Higgses in the space of all doublets is a crucial aspect to consider. We discuss highly predictive cases and illustrate the predictive power in toy models consisting of masses for the 3rd and 2nd fermion family.