The Exact Eigenvalues of the Neutrino Mass Matrix in Global Lepton and   Interchange Symmetry

Agus Purwanto ( Laboratorium Fisika Teori dan Filsafat Alam, Jurusan Fisika, Fakultas Matematika dan Ilmu Pengetahuan Alam, Institut Teknologi Sepuluh Nopember)
Herlik Wibowo ( Grup Fisika Teori, Departemen Fisika, Fakultas Sains dan Teknologi, Universitas Airlangga, Surabaya)

Jurnal Matematika & Sains
Vol 16, No 1 (2011)

The 3x3 Majorana neutrino mass matrix is evaluated. The mass eigenvalues depend on the diagonal entries and three mixing angles. Two spesific cases such as conserving the global lepton number and mu-tau interchange symmetry are considered. In the case of conserving global lepton number, inverted mass hierarchy for bimaximal mixing is obtained. The mixing matrix, namely PMNS matrix, doesnt valid for all cases. The shape of mass matrix satisfying mu-tau interchange symmetry is proposed and the eigenvalues that lead to neutrino mass hierarcy are also obtained after applying a new PMNS matrix.