Can the lepton flavor mixing matrix be symmetric?

Abstract

Current neutrino oscillation data indicate that the $3\ifmmode\times\else\texttimes\fi{}3$ lepton flavor mixing matrix V is likely to be symmetric about its ${V}_{e3}\ensuremath{-}{V}_{\ensuremath{\mu}2}\ensuremath{-}{V}_{\ensuremath{\tau}1}$ axis. This off-diagonal symmetry corresponds to three pairs of congruent unitarity triangles in the complex plane. Terrestrial matter effects can substantially modify the genuine CP-violating parameter and off-diagonal asymmetries of V in realistic long-baseline experiments of neutrino oscillations.