Bilarge mixing matrix and its invariance under "horizontal conjugation" -- a new discrete transformation for neutrinos

Abstract

In the first part of the note, we consider a neutrino texture, where the Dirac and righthanded Majorana masses are proportional. If the former are approximately proportional also to the charged lepton masses, then taking $Δm^2_{32}\sim3\times 10^{-3}$ eV$^2$ we estimate approximately that $Δm^2_{21}\sim{\cal O}(10^{-5}$ eV$^2)$, what is not very different from the recent KamLAND estimation $Δm^2_{21}\sim7\times 10^{-5}$ eV$^2$, consistent with the LMA solar solution. In the second part, we show generically that the {\it invariance} of neutrino mixing matrix under the simultaneous discrete transformations $ν_e\to-ν_e$, $ν_μ\toν_τ$, $ν_τ\toν_μ$ and $ν_1\to-ν_1$, $ν_2\to-ν_2$, $ν_3\toν_3$ (neutrino "horizontal conjugation") {\it characterizes} the familiar bilarge form of mixing matrix, favored phenomenologically at present. Then, in the case of this form, the mass neutrinos $ν_1$, $ν_2$, $ν_3$ get a new quantum number, {\it covariant} in their mixings (neutrino "horizontal parity", equal to $-1,-1, 1$, respectively). Conversely, such a covariance may be the {\it origin} of the bilarge mixing matrix. In Section 5, the "horizontal parity" is embedded in a group structure.