Seesaw mirroring between light and heavy Majorana neutrinos with the help of the $S_3^{}$ reflection symmetry

Abstract

In the canonical seesaw mechanism we require the relevant neutrino mass terms to be invariant under the $S_3^{}$ charge-conjugation transformations of left- and right-handed neutrino fields. Then both the Dirac mass matrix $M_{\mathrm{D}}^{}$ and the right-handed neutrino mass matrix $M_{\mathrm{R}}^{}$ are well constrained, so is the effective light Majorana neutrino mass matrix $M_{\nu }^{}$ via the seesaw formula. We find that these mass matrices can be classified into 22 categories, among which some textures respect the well-known $\mu$-$\tau$ permutation or reflection symmetry and flavor democracy. It is also found that there exist remarkable structural equalities or similarities between $M_{\nu }^{}$ and $M_{\mathrm{R}}^{}$, reflecting a seesaw mirroring relationship between light and heavy Majorana neutrinos. We calculate the corresponding light neutrino masses and flavor mixing parameters as well as the CP-violating asymmetries in decays of the lightest heavy Majorana neutrino, and show that only the flavored leptogenesis mechanism is possible to work for three categories of $M_{\mathrm{D}}^{}$ and $M_{\mathrm{R}}^{}$ in the $S_3^{}$ reflection symmetry limit.

arXiv comment33 pages, 1 table. v2: matches the version accepted for publication in JHEP

References in corpus (38)

• Tri-Bimaximal Mixing and the Neutrino Oscillation Data
• Leptogenesis
• Discrete Flavor Symmetries and Models of Neutrino Mixing
• Non-Abelian Discrete Symmetries in Particle Physics
• Towards a complete theory of thermal leptogenesis in the SM and MSSM
• Global analysis of three-flavour neutrino oscillations: synergies and tensions in the determination of theta_23, delta_CP, and the mass ordering
• Softly Broken A_4 Symmetry for Nearly Degenerate Neutrino Masses
• Tri-Bimaximal Neutrino Mixing, A4 and the Modular Symmetry
• Leptogenesis as the origin of matter
• Nearly Tri-Bimaximal Neutrino Mixing and CP Violation
• Mass and Flavor Mixing Schemes of Quarks and Leptons
• Baryogenesis through leptogenesis
• The importance of flavor in leptogenesis
• Flavour Issues in Leptogenesis
• Mu-Tau Reflection Symmetry in Lepton Mixing and Neutrino Oscillations
• Some Simple Mixing and Mass Matrices for Neutrinos
• Permutation Symmetry, Tri-Bimaximal Neutrino Mixing and the S3 Group Characters
• Neutrino Mass Models
• A 2-3 Symmetry in Neutrino Oscillations
• Lepton Mass Hierarchy and Neutrino Oscillations
• Large Leptonic Flavor Mixing and the Mass Spectrum of Leptons
• Atmospheric Neutrino Oscillation and a Phenomenological Lepton Mass Matrix
• Dirac or Inverse Seesaw Neutrino Masses with $B-L$ Gauge Symmetry and $S_3$ Flavour Symmetry
• A review of mu-tau flavor symmetry in neutrino physics
• Primordial Lepton Family Asymmtries in Seesaw Model
• The solar LMA neutrino oscillation solution in the Zee model
• Broken S_3 Flavor Symmetry of Leptons and Quarks: Mass Spectra and Flavor Mixing Patterns
• Large Mixing Angle MSW Solution in S_3 Flavor Symmetry
• Vacuum Neutrino Oscillations of Solar Neutrinos and Lepton Mass Matrices
• Broken S3 Symmetry in the Neutrino Mass Matrix and Non-Zero theta_{13}
• The Symmetry behind Extended Flavour Democracy and Large Leptonic Mixing
• Flavor Democracy and Type-II Seesaw Realization of Bilarge Neutrino Mixing
• Non-Minimal Flavored ${\mathbf{S}}_3\otimes {\mathbf{Z}}_2$ Left-Right Symmetric Model
• Broken $S_3$ Symmetry in the Neutrino Mass Matrix
• Quantum numbers of heavy neutrinos, tri-bi-maximal mixing through double seesaw with permutation symmetry, and comment on ${\theta }_{\mathrm{sol}}+{\theta }_c\simeq \frac{\pi }{4}$
• Flavored Non-Minimal Left-Right Symmetric Model Fermion Masses and Mixings
• Naturally perturbed S${}_3$ neutrinos
• Broken $S_{3\mathrm{L}}^{}\times S_{3\mathrm{R}}^{}$ Flavor Symmetry and Leptonic CP Violation

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• Identifying a minimal flavor symmetry of the seesaw mechanism behind neutrino oscillations
• Diagonal reflection symmetries and universal four-zero texture
• The translational $\mu$-$\tau$ reflection symmetry of Majorana neutrinos
• A comparative study between the modified Fritzsch and nearest neighbor interaction textures
• Scalar and gauge sectors in the 3-Higgs Doublet Model under the S3-symmetry