Revisiting $\mathrm{SU}(5)$ Yukawa Sectors Through Quantum Corrections

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 \(45_{\mathrm{H}}\) 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 reproduce the charged fermion mass spectrum and mixing angles within the assumed experimental uncertainty. The fitted Yukawa couplings remain within the perturbative range. The scenario also necessitates mass splitting among various scalars of $45_{\mathrm{H}}$ dimensional irrep, with some of the scalars' mass deviating significantly from the matching scale \((M_{GUT})\), collectively providing substantial threshold corrections. The effect of the lightest scalar on the RGE evolution of the SM parameters has also been considered. It is shown that this scenario reproduces the SM spectrum at low energy. As an extension, the minimal \(SU(5)\) model with only the \(45_{\mathrm{H}}\) irrep is augmented with the \(15_{\mathrm{H}}\)-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 \(5_{\mathrm{H}}\) and \(15_{\mathrm{H}}\) 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.

Version published in Physical Review D. 34 pages with references, 5 tables, and 6 captioned figures. The revised version includes new plots illustrating the RGE effects of the lightest scalar, updated numerical fits, and expanded proton-decay constraints. Conclusions unchanged, textually and presentationally revised