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

Abstract

Supersymmetric $SO(10)$ grand unified models with renormalizable Yukawa couplings involving only $10$ and $\overline{126}$ 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 $126+\overline{126}$ ($v_R$) 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.

This is the version to be published in Phys.Rev.D. The old subsection of proton decay is discussed in a separate form, arXiv:1609.08640

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• New Weak-Scale Physics from SO(10) with High-Scale Supersymmetry
• Sparticle spectroscopy of the minimal SO(10) model
• Probing Minimal Grand Unification through Gravitational Waves, Proton Decay, and Fermion Masses
• Fermion Masses and Mixings, Leptogenesis and Baryon Number Violation in Pati-Salam Model
• Pseudo-Goldstone Dark Matter in $SO(10)$
• Weakly-Interacting Massive Particles in Non-supersymmetric SO(10) Grand Unified Models
• Flavor Hierarchies from Clockwork in SO(10) GUT
• The ATLAS Diboson Resonance in Non-Supersymmetric SO(10)
• Twenty years after the discovery of $\mu -\tau$ symmetry
• Relation between proton decay and PMNS phase in the minimal SUSY $SO(10)$ GUT
• On ${\theta }_{23}$ Octant Measurement in $3+1$ Neutrino Oscillations in T2HKK
• Simple mass matrices of neutrinos and quarks consistent with observed mixings and masses
• Toward Realistic Gauge-Higgs Grand Unification
• Enhanced $\Gamma (p\to K^0{\mu }^{+})/\Gamma (p\to K^{+}{\bar{\nu }}_{\mu })$ as a Signature of Minimal Renormalizable SUSY $SO(10)$ GUT
• Alternative Renormalizable Minimal SO(10) GUTs and Data Fitting
• Neutrinoless Double Beta Decay and $<\eta >$ Mechanism in the Left-Right Symmetric Model
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• Renormalizable $SO(10)$ GUT with Suppressed Dimension-5 Proton Decays
• Examining A Renormalizable Supersymmetric SO(10) Model