A new and trivial CP symmetry for extended $A_4$ flavor

Abstract

The combination of ${\nu }_{\mu }$-${\nu }_{\tau }$ exchange together with CP conjugation in the neutrino sector (known as ${\mathrm{CP}}^{\mu \tau }$ symmetry or $\mu \tau$-reflection) is known to predict the viable pattern: ${\theta }_{23}=45^{\circ }$, maximal Dirac CP phase and trivial Majorana phases. We implement such a CP symmetry as a new CP symmetry in theories with $A_4$ flavor. The implementation in a complete renormalizable model leads to a new form for the neutrino mass matrix that leads to further predictions: normal hierarchical spectrum with lightest mass and $m_{\beta \beta }$ ($0\nu \beta \beta$) of only few meV, and either ${\nu }_1$ or ${\nu }_2$ has opposite CP parity. An approximate $L_{\mu }-L_{\tau }$ symmetry arises naturally and controls the flavor structure of the model. The light neutrino masses are generated by the extended seesaw mechanism with 6 right-handed neutrinos (RHNs). The requirement of negligible one-loop corrections to light neutrino masses, validity of the extended seesaw approximation and not too long-lived BSM states to comply with BBN essentially restricts the parameters of the model to a small region: three relatively light right-handed neutrinos at the GeV scale, heavier neutrinos at the electroweak scale and Yukawa couplings smaller than the electron Yukawa. Such a small Yukawa couplings render these RHNs unobservable in terrestrial experiments.

23pp, 7 figs; v2: published version with small updates in text

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• Alternative Schemes of Predicting Lepton Mixing Parameters from Discrete Flavor and CP Symmetry
• Breakings of the neutrino mu-tau reflection symmetry
• Cobimaximal Neutrino Mixing from $S_3\times Z_2$
• Implications of residual CP symmetry for leptogenesis in a model with two right-handed neutrinos
• Toward a unified interpretation of quark and lepton mixing from flavor and CP symmetries
• Vacuum stability conditions of the economical 3-3-1 model from copositivity
• Cobimaximal Neutrino Mixing from $A_4$ and its Possible Deviation
• Modifications to the neutrino mixing from the mu-tau reflection symmetry
• A study on a minimally broken residual TBM-Klein symmetry with its implications on flavoured leptogenesis and ultra high energy neutrino flux ratios
• Mu-Tau Reflection Symmetry in the Standard Parametrization and Contributions from Charged Lepton Sector
• CP transformed mixed $\mu \tau$ antisymmetry for neutrinos and its consequences
• Consequences of $\mu$-$\tau$ reflection symmetry for $3+1$ neutrino mixing
• On the textures of neutrino mass matrix for maximal atmospheric mixing angle and Dirac CP phase