Discrete symmetries and mixing of Dirac neutrinos

Abstract

We study mixing of the Dirac neutrinos in the residual symmetries approach. The key difference from the Majorana case is that the Dirac mass matrix may have larger symmetries: $G_{\nu }={\mathbf{Z}}_n$ with $n\ge 3$. The symmetry group relations have been generalized to the case of Dirac neutrinos. Using them we have found all new relations between mixing parameters and corresponding symmetry assignments which are in agreement with the present data. The viable relations exist only for the charged lepton residual symmetry $G_{\ell }={\mathbf{Z}}_2$. The relations involve elements of the rows of the PMNS matrix and lead to precise predictions of the 2-3 mixing angle and certain ranges of the CP violation phase. For larger symmetries $G_{\ell }$, an agreement with data can be achieved if $\sim 10\%$ corrections related to breaking of $G_{\ell }$ and $G_{\nu }$ are included.

17 pages, 1 figure; v2: references added, one section added and discussion improved

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Cited by in corpus (10)

• Flavor structures of charged fermions and massive neutrinos
• The $\mu$-$\tau$ reflection symmetry of Majorana neutrinos
• Peccei-Quinn symmetry for Dirac seesaw and leptogenesis
• Leptogenesis with testable Dirac neutrino mass generation
• Large Leptonic Dirac CP Phase from Broken Democracy with Random Perturbations
• Hidden flavor symmetries of SO(10) GUT
• Double type-II Dirac seesaw accompanied by Dirac fermionic dark matter
• Breaking flavor democracy with symmetric perturbations
• Rotated $\mu$\,--\,$\tau$ Symmetry for One Generic Neutrino Mixing Angle: An analytical Study
• Broken Democracy with Intermediate ${\mathbb{S}}_2\times {\mathbb{S}}_2$ Residual Symmetry and Random Perturbations