Revisiting fermion mass and mixing fits in the minimal SUSY $SO(10)$ GUT

TL;DR

This paper revisits fermion mass and mixing fits in minimal SUSY $SO(10)$ GUT models, analyzing the impact of large $v_R$ scales on flavor structure, low-energy phenomena, and CP phase predictions.

Contribution

It provides a new sum rule inputting lepton mass matrices, clarifies features of solutions at large $v_R$, and explores implications for low-energy observables and CP phases.

Findings

Sum rule analysis at large $v_R$ scales enhances understanding of flavor structure.

Calculated $ ext{BR}( ext{mu} o e ext{gamma})$ and electron EDM dependence on $v_R$.

Predicted CP phase in neutrino oscillations testable soon.

Abstract

Supersymmetric $SO(10)$ grand unified models with renormalizable Yukawa couplings involving only ${\bf 10}$ and $\overline{\bf 126}$ Higgs fields have been shown to realize the fermion masses and mixings economically. In previous works, the sum rule of the fermion mass matrices are given by inputting the quark matrices, and the neutrino mixings are predicted in this framework. Now the three neutrino mixings have been measured, and in this paper, we give the sum rule by inputting the lepton mass matrices, which makes clear certain features of the solution, especially if the vacuum expectation values of ${\bf 126}+ \overline{\bf126}$ ($v_R$) are large and the right-handed neutrinos are heavy. We perform the $\chi^2$ analyses to fit the fermion masses and mixings using the sum rule. In previous works, the best fit appears at $v_R \sim 10^{13}$ GeV, and the fit at the large $v_R$ scale ($\sim 10^{16}$ GeV) has been less investigated. Our expression of the sum rule has a benefit to understand the flavor structure in the large $v_R$ solution. Using the fit results, we perform the calculation of the $\mu \to e\gamma$ process and the electric dipole moment of electron, and the importance of $v_R$ dependence emerges in low energy phenomena. We also show the prediction of the CP phase in the neutrino oscillations, which can be tested in the near future.