SUSY threshold corrections to quark and lepton mixing inspired by $SO(10)$ GUT models

TL;DR

This paper investigates how supersymmetric threshold corrections influence the unknown diagonalizing matrices in $SO(10)$ GUT models, potentially affecting flavor violations and mixing angles, with implications for fermion mass relations and SUSY scale effects.

Contribution

It demonstrates the impact of SUSY threshold corrections on the diagonalizing matrices in $SO(10)$ GUT models, linking these effects to flavor violations and mixing angles.

Findings

Diagonalizing matrix elements can reach CKM mixing angles.

Higher SUSY scales tend to increase mixing angles.

Strong cancellation is required for electroweak symmetry breaking.

Abstract

In the standard model (SM), the Cabibbo-Kobayashi-Maskawa (CKM) matrix is the only origin of flavor violations (FVs). On the other hand, in general, there are a lot of sources of the FVs in a physics beyond the SM, through the diagonalizing matrices which make Yukawa matrices diagonal. Although most of the diagonalizing matrices are unknown ones, grand unified theories (GUTs) can fix these matrices. In particular, if we consider a GUT model based on the $SO(10)$ group, these diagonalizing matrices are strongly related to each other because of the matter unification. However, this unification causes the problem on the realization of measured SM fermion masses and mixing angles. Up to now, many people showed that supersymmetric (SUSY) threshold corrections can solve this problem, especially unfavorable fermion mass relations. In this paper, we show that how these SUSY threshold corrections affect unknown diagonalizing matrices. Since these contributions are also related to the FVs induced by SUSY particles, we can estimate the maximal effect to the diagonalizing matrices. We found that the $(1, 3)$ and $(3, 1)$ elements of diagonalizing matrices for quarks can be as large as the corresponding mixing angle of the CKM matrix. Moreover, we found that the higher SUSY scale can predict the larger mixing angles, although strong cancellation between the Higgs mass parameters is needed to realize the electroweak symmetry breaking.