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 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 ≈ 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.