Fully Constrained Majorana Neutrino Mass Matrices using $��(72\times3)$

• DOI: 10.48550/arxiv.1402.0857
• Publication Date: 2014-01-01
• Authors: Krishnan, R.
• Keywords: High Energy Physics - Phenomenology (hep-ph); FOS: Physical sciences

28 pages, 1 figure<br/>In 2002, two neutrino mixing ansatze having trimaximally mixed middle ($��_2$) columns, namely tri-chi-maximal mixing ($\text{T}��\text{M}$) and tri-phi-maximal mixing ($\text{T}��\text{M}$), were proposed. It was recently shown that $\text{T}��\text{M}$ with $��=\pm \frac��{16}$ as well as $\text{T}��\text{M}$ with $��= \pm \frac��{16}$ leads to the solution, $\sin^2 ��_{13} = \frac{2}{3} \sin^2 \frac��{16}$, consistent with the latest measurements of the reactor mixing angle, $��_{13}$. To obtain $\text{T}��\text{M}_{(��=\pm \frac��{16})}$ and $\text{T}��\text{M}_{(��=\pm \frac��{16})}$, we utilised the type I see-saw framework with fully constrained Majorana neutrino mass matrices. These mass matrices also resulted in a relation among the neutrino masses, $m_1:m_2:m_3=\frac{\left(2+\sqrt{2}\right)}{1+\sqrt{2(2+\sqrt{2})}}:1:\frac{\left(2+\sqrt{2}\right)}{-1+\sqrt{2(2+\sqrt{2})}}$. In this paper we construct a flavour model based on the discrete group $��(72\times3)$ and obtain the aforementioned results. A Majorana neutrino mass matrix (a symmetric $3\times3$ matrix with 6 complex degrees of freedom) is conveniently mapped into a flavon field transforming as the complex 6 dimensional representation of $��(72\times3)$. Specific vacuum alignments of the flavons are used to arrive at the desired mass matrices.<br/>