Good flavor search in SU(5): a machine learning approach

TL;DR

This paper uses machine learning to evaluate and compare modifications of the SU(5) grand unified theory, identifying the most aesthetically pleasing model based on proximity to the original Georgi-Glashow model.

Contribution

It introduces a machine learning framework to assess the 'beauty' of SU(5) model modifications, quantifying their closeness to the original model.

Findings

The 24-dimensional field modification is more beautiful than the 45-dimensional one.

A continuous parameter y around 0.8 yields the closest match to the original SU(5) model.

The approach provides a quantitative measure of model aesthetic in grand unified theories.

Abstract

We revisit the fermion mass problem of the $SU(5)$ grand unified theory using machine learning techniques. The original $SU(5)$ model proposed by Georgi and Glashow is incompatible with the observed fermion mass spectrum. Two remedies are known to resolve this discrepancy, one is through introducing a new interaction via a 45-dimensional field, and the other via a 24-dimensional field. We investigate which modification is more beautiful, defining the beauty as proximity to the original Georgi-Glashow $SU(5)$ model. Our analysis shows that, in both supersymmetric and non-supersymmetric scenarios, the model incorporating the interaction with the 24-dimensional field is more beautiful under this criterion. We then generalise these models by introducing a continuous parameter $y$, which takes the value 3 for the 45-dimensional field and 1.5 for the 24-dimensional field. Numerical optimisation reveals that $y \approx 0.8$ yields the closest match to the original $SU(5)$ model, indicating that this value corresponds to the most beautiful model according to our definition.