Fully Constrained Majorana Neutrino Mass Matrices Using $\Sigma (72\times 3)$

Abstract

In 2002, two neutrino mixing ansatze having trimaximally-mixed middle (${\nu }_2$) columns, namely tri-chi-maximal mixing ($\text{T}\chi \text{M}$) and tri-phi-maximal mixing ($\text{T}\varphi \text{M}$), were proposed. In 2012, it was shown that $\text{T}\chi \text{M}$ with $\chi =\pm \frac{\pi }{16}$ as well as $\text{T}\varphi \text{M}$ with $\varphi =\pm \frac{\pi }{16}$ leads to the solution, ${\sin }^2{\theta }_{13}=\frac{2}{3}{\sin }^2\frac{\pi }{16}$, consistent with the latest measurements of the reactor mixing angle, ${\theta }_{13}$. To obtain $\text{T}\chi {\text{M}}_{(\chi =\pm \frac{\pi }{16})}$ and $\text{T}\varphi {\text{M}}_{(\varphi =\pm \frac{\pi }{16})}$, the type~I see-saw framework with fully constrained Majorana neutrino mass matrices was utilised. These mass matrices also resulted in the neutrino mass ratios, $m_1:m_2:m_3=\frac{\left(2+\sqrt{2}\right)}{1+\sqrt{2(2+\sqrt{2})}}:1:\frac{\left(2+\sqrt{2}\right)}{-1+\sqrt{2(2+\sqrt{2})}}$. In this paper we construct a flavour model based on the discrete group $\Sigma (72\times 3)$ and obtain the aforementioned results. A Majorana neutrino mass matrix (a symmetric $3\times 3$ matrix with 6 complex degrees of freedom) is conveniently mapped into a flavon field transforming as the complex 6 dimensional representation of $\Sigma (72\times 3)$. Specific vacuum alignments of the flavons are used to arrive at the desired mass matrices.

20 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1402.0857

References in corpus (19)

• Observation of electron-antineutrino disappearance at Daya Bay
• Updated fit to three neutrino mixing: exploring the accelerator-reactor complementarity
• The Unique Horizontal Symmetry of Leptons
• Possible Alternatives to Tri-bimaximal Mixing
• The Horizontal Symmetry for Neutrino Mixing
• Symmetry of Lepton Mixing
• Comparing Trimaximal Mixing and Its Variants with Deviations from Tri-bimaximal Mixing
• Lepton Mixing Patterns from a Scan of Finite Discrete Groups
• Degeneracy between ${\theta }_{23}$ octant and neutrino non-standard interactions at DUNE
• A(4) Flavor Symmetry Model for Dirac-Neutrinos and Sizable U(e3)
• Magic Neutrino Mass Matrix and the Bjorken-Harrison-Scott Parameterization
• Group Theory and Dynamics of Neutrino Mixing
• On the finite subgroups of U(3) of order smaller than 512
• Friedberg-Lee Symmetry Breaking and Its Prediction for theta_13
• Probing the leptonic Dirac CP-violating phase in neutrino oscillation experiments
• A Possible Relation between the Neutrino Mass Matrix and the Neutrino Mapping Matrix
• Exact One-Loop Evolution Invariants in the Standard Model
• Trimaximal-Cabibbo neutrino mixing: A parametrization in terms of deviations from tri-bimaximal mixing
• A Combined Limit on the Neutrino Mass from Neutrinoless Double-Beta Decay and Constraints on Sterile Majorana Neutrinos