Revisiting $SU(5)$ Yukawa Sectors Through Quantum Corrections

TL;DR

This paper demonstrates that including one-loop quantum corrections in minimal $SU(5)$ models allows for accurate reproduction of fermion masses and mixing angles, overcoming previous tree-level limitations.

Contribution

It shows that quantum corrections enable minimal $SU(5)$ models with only the $45_H$ irrep to match observed fermion data, with significant threshold effects and scalar mass splittings.

Findings

One-loop corrections reconcile $SU(5)$ models with observed fermion spectra.

Scalar mass splittings up to 13 orders of magnitude are necessary.

Augmenting with $15_H$ or combining $5_H$ and $15_H$ irreps also reproduces data.

Abstract

This article revisits the validity of tree-level statements regarding the Yukawa sector of various minimal-renormalisable $SU(5)$ frameworks at the loop level. It is well-known that an $SU(5)$ model with only the $45_{\rm{H}}$ dimensional irreducible representation~(irrep) contributing to the Yukawa sector is highly incompatible in yielding the low-energy observables. However, this study shows that when one-loop corrections from heavy degrees of freedom are included in the various Yukawa vertices, the model can accurately reproduce the charged fermion mass spectrum and mixing angles. Furthermore, the fitted couplings remain within the perturbative range. The fitted parameters also necessitate mass splitting among various scalars of $45_{\rm{H}}$ dimensional irrep, with at least one scalar's mass differing by as much as 13 orders of magnitude from the matching scale $(M_{\rm{GUT}})$, collectively providing substantial threshold corrections. As an extension, the minimal $SU(5)$ model with only the $45_{\rm{H}}$ irrep is augmented with the $15_{\rm{H}}$-dimensional irrep, which also successfully reproduces the observed charged and neutral fermion mass spectra. Finally, the study considers an alternative $SU(5)$ model incorporating both $5_{\rm{H}}$ and $15_{\rm{H}}$ irreps, which also yields the desired fermion mass spectra and mixing angles. This work demonstrates the viability of a minimal $SU(5)$ Yukawa sector in different setups when quantum corrections are considered.