Quantum corrections and the minimal Yukawa sector of $SU(5)$

Abstract

It is well-known that the $SU(5)$ grand unified theory, with the standard model quarks and leptons unified in $\overline{5}$ and $10$ and the electroweak Higgs doublet residing in $5$ dimensional representations, leads to relation, $Y_d=Y_e^T$, between the Yukawa couplings of the down-type quarks and the charged leptons. We show that this degeneracy can be lifted in a phenomenologically viable way when quantum corrections to the tree-level matching conditions are taken into account in the presence of one or more copies of gauge singlet fermions. The 1-loop threshold corrections arising from heavy leptoquark scalar and vector bosons, already present in the minimal model, and heavy singlet fermions can lead to realistic Yukawa couplings provided their masses differ by at least two orders of magnitude. The latter can also lead to a realistic light neutrino mass spectrum through the type I seesaw mechanism if the colour partner of the Higgs stays close to the Planck scale. Most importantly, our findings demonstrate the viability of the simplest Yukawa sector when quantum corrections are considered and sizeable threshold effects are present.