Neutrino Mixing based on Mass Matrices with a $2\leftrightarrow 3$ Symmetry

Under the assumption that the $2\leftrightarrow 3$ symmetry is broken only through phases, we give a systematical investigation of possible lepton mass matrix forms without referring to the explicit parameter values. The two types of the $2\leftrightarrow 3$ symmetry are investigated: one is that the left- and right-handed fields $(f_L,f_R)$ obey the symmetry, and another one is that only $f_L$ obeys the symmetry. In latter case, in spite of no $2\leftrightarrow 3$symmetryintheMajoranamassmatrix$M_R$for$\nu_R$, the neutrino seesaw mass matrix still obey the $2\leftrightarrow 3$ symmetry. Possible phenomenologies are discussed.