Flavor physics in SU(5) GUT with a 45 scalar representation

We study a realistic SU(5) grand unified model, where a 45 representation of scalar fields is added to the Georgi-Glashow model in order to realize the gauge coupling unification and the masses and mixing of quarks and leptons. The gauge coupling unification together with constraints from proton decay implies mass splittings in scalar representations. We assume that an SU(2) triplet component of the 45 scalar, which is called $S_3$ leptoquark, has a TeV-scale mass, and color-sextet and color-octet ones have masses of the order of $10^6$ GeV. We calculate one-loop beta functions for Yukawa couplings in the model, and derive the low-energy values of the $S_3$ Yukawa couplings which are consistent with the grand unification. We provide predictions for lepton-flavor violation and lepton-flavor-universality violation induced by the $S_3$ leptoquark, and find that current and future experiments have a chance to find a footprint of our SU(5) model.