The translational $\mu$-$\tau$ reflection symmetry of Majorana neutrinos

Abstract

The present neutrino oscillation data allow $m_1^{}=0$ (or $m_3^{}=0$) for the neutrino mass spectrum and support ${\theta }_{23}^{}\simeq \pi /4$ and $\delta \simeq -\pi /2$ as two good approximations for the PMNS lepton flavor mixing matrix $U$. We show that these intriguing possibilities can be a very natural consequence of the {\it translational} $\mu$-$\tau$ reflection symmetry -- the effective Majorana neutrino mass term keeps invariant under the transformations ${\nu }_{e\mathrm{L}}^{}\to ({\nu }_{e\mathrm{L}}^{}{)}^c+U_{ei}^{\ast }{z}_{\nu }^c$, ${\nu }_{\mu \mathrm{L}}^{}\to ({\nu }_{\tau \mathrm{L}}^{}{)}^c+U_{\tau i}^{\ast }{z}_{\nu }^c$ and ${\nu }_{\tau \mathrm{L}}^{}\to ({\nu }_{\mu \mathrm{L}}^{}{)}^c+U_{\mu i}^{\ast }{z}_{\nu }^c$ (for $i=1$ or $3$), where $z_{\nu }^c$ is the charge conjugation of a constant spinor field $z_{\nu }^{}$. Extending such a working flavor symmetry to the canonical seesaw mechanism at a superhigh-energy scale, we calculate its soft breaking effects at the electroweak scale by using the one-loop renormalization-group equations.

LaTeX 24 pages, 2 figures. More discussions and references added, matching the published version

References in corpus (26)

• The Swampland: Introduction and Review
• Flavor structures of charged fermions and massive neutrinos
• Physics Potential of a Long Baseline Neutrino Oscillation Experiment Using J-PARC Neutrino Beam and Hyper-Kamiokande
• Neutrinoless Double-Beta Decay: a Probe of Physics Beyond the Standard Model
• Tri-bimaximal Neutrino Mixing and Flavor-dependent Resonant Leptogenesis
• The minimal seesaw and leptogenesis models
• The smallest neutrino mass
• Neutrino mu-tau reflection symmetry and its breaking in the minimal seesaw
• Hidden Symmetry of the CKM and Neutrino Mapping Matrices
• The $\mu -\tau$ reflection symmetry of Dirac neutrinos and its breaking effect via quantum corrections
• Neutrino Sector with Majorana Mass Terms and Friedberg-Lee Symmetry
• A combination of the neutrino trimaximal mixings and mu-tau reflection symmetry in the type-I seesaw model
• Generalization of Friedberg-Lee Symmetry
• Jarlskog Invariant of the Neutrino Mapping Matrix
• Tri-Bimaximal Mixing from Twisted Friedberg-Lee Symmetry
• On the two-loop radiative origin of the smallest neutrino mass and the associated Majorana CP phase
• Littlest mu-tau seesaw
• Integral solutions to the one-loop renormalization-group equations for lepton flavor mixing parameters and the Jarlskog invariant
• Leptogenesis in a model with Friedberg-Lee symmetry
• Seesaw mirroring between light and heavy Majorana neutrinos with the help of the $S_3^{}$ reflection symmetry
• Generalized Friedberg-Lee model for CP violation in neutrino physics
• Renormalization group evolution induced leptogenesis in the minimal seesaw model with the trimaximal mixing and mu-tau reflection symmetry
• A Timeon Model of Quark and Lepton Mass Matrices
• $\mu$-$\tau$ symmetry breaking and CP violation in the neutrino mass matrix
• The Smallest Neutrino Mass Revisited
• A translational flavor symmetry in the mass terms of Dirac and Majorana fermions

Cited by in corpus (1)

• The $\mu$-$\tau$ reflection symmetry of Majorana neutrinos