Babel on the Petaplex site: On Rival Calculational methods in SO(10) MSGUTs

TL;DR

This paper compares different computational methods for deriving spectra and Yukawa couplings in SO(10) GUT models, emphasizing a unified approach that simplifies calculations and enhances understanding of fermion mass generation.

Contribution

It advocates for a unified, component-free methodology based on group-theoretic principles to improve the accuracy and clarity of SO(10) GUT computations.

Findings

Explicit component-based methods can compromise the symmetry structure.

A simple prescription for MSSM Yukawas avoids complex calculations.

Unified notation and descent from SO(10) streamline the analysis.

Abstract

We compare and contrast the computations that lead to the NMSGUT spectra and Yukawa couplings that appeared\cite{nmsgut} in 2006 and a recent recalculation of the same\cite{malinsky}. We argue that an explicit component based method of computation jeopardizes the power of SO(10) and its sub-groups to organize, in a unified and automatically phase correlated way, computations of dynamics beyond the basic mass matrix computation. The correct (one line) prescription for generating MSSM Yukawas from SO(10) ones was given in \cite{ag2} and requires no computation beyond the identification of null vectors of the Higgs doublet mass matrix and the Clebsches given in \cite{ag1,ag2}. It was already used to derive all fermion Yukawas and Majorana masses in \cite{ag2,nmsgut}. We thus urge the adoption of a uniform notation and methodology based on descent from SO(10) to the SM through the Pati-Salam maximal subgroup of SO(10) to avoid Babel in this rapidly developing and highly promising subject.