Neutrino Mass Matrix Subject to $\mu -\tau$ Symmetry and Invariant under a Cyclic Permutation

Abstract

Neutrino masses arise via a seesaw mechanism and its mass hierarchy, with assumption that heavy Majorana neutrino mass matrix subject to $\mu -\tau$ symmetry and invariant under a cyclic permutation, are evaluated. Within this scenario, the neutrino masses: $\left|m_1\right|=\left|m_2\right|<\left|m_3\right|$ are obtained, which are incompatible with the experimental data. By modifying neutrino mass matrix with the zero sum rule condition, the neutrino masses in inverted hierarchy: $\left|m_3\right|<\left|m_1\right|<\left|m_2\right|$ are obtained.

Comments: 6 pages, Talk given at CTP BUE International Conference on Neutrino Physics in the LHC Era, Luxor, Egypt, 15-19 November 2009