A modified Friedberg-Lee symmetry for the TM1 neutrino mixing

Abstract

In this letter, we put forward a special neutrino mass matrix which is invariant under a modified Friedberg-Lee (FL) transformation ${\nu }_e^{}\to {\nu }_e^{}-2\theta$ and ${\nu }_{\mu ,\tau }^{}\to {\nu }_{\mu ,\tau }^{}+\theta$ with $\theta$ being a space-time independent element of the Grassmann algebra. Compared to the original FL symmetry (with the transformation ${\nu }_{e,\mu ,\tau }^{}\to {\nu }_{e,\mu ,\tau }^{}+\theta$) which results in the TM2 neutrino mixing, the modified FL symmetry will lead us to the TM1 mixing which has a better agreement with the experimental results. While the original FL symmetry has to be broken in order to produce a realistic neutrino mass spectrum, the modified FL symmetry is allowed to remain intact and give us a vanishing $m_1^{}$. A combination of the FL symmetry with the $\mu$-$\tau$ reflection symmetry is also discussed.

9 pages, 2 figures, references added, to appear in Physical Review D

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Cited by in corpus (8)

• Flavor structures of charged fermions and massive neutrinos
• A review of mu-tau flavor symmetry in neutrino physics
• The $\mu$-$\tau$ reflection symmetry of Majorana neutrinos
• Predictive $S_4$ flavon model with ${\text{TM}}_1$ mixing and baryogenesis through leptogenesis
• Simiplified textures of the seesaw model for the trimaximal neutrino mixings
• A translational flavor symmetry in the mass terms of Dirac and Majorana fermions
• The translational $\mu$-$\tau$ reflection symmetry of Majorana neutrinos
• ${\text{TM}}_1$ neutrino mixing with $\sin {\theta }_{13}=\frac{1}{\sqrt{3}}\sin \frac{\pi }{12}$