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

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 natural, defining naturalness 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 natural 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 natural model according to our definition.