Is there a dynamical group structure behind the bilarge form of neutrino mixing matrix?

Abstract

We observe that the {\it invariance} of neutrino mixing matrix under the simultaneous discrete transformations ${\nu }_1,{\nu }_2,{\nu }_3\to -{\nu }_1,-{\nu }_2,{\nu }_3$ and ${\nu }_e,{\nu }_{\mu },{\nu }_{\tau }\to -{\nu }_e,{\nu }_{\tau },{\nu }_{\mu }$ (neutrino "horizontal conjugation") {\it characterizes} (as a sufficient condition for it) the familiar bilarge form of neutrino mixing matrix, favored experimentally at present. Thus, the mass neutrinos ${\nu }_1,{\nu }_2,{\nu }_3$ get a new quantum number, {\it covariant} with respect to their mixings into the flavor neutrinos ${\nu }_e,{\nu }_{\mu },{\nu }_{\tau }$ (neutrino "horizontal parity" equal to -1, -1,1, respectively). The "horizontal parity" turns out to be embedded in a group structure consisting of some Hermitian and real $3\times 3$ matrices ${\mu }_1,{\mu }_2,{\mu }_3$ and ${\varphi }_1,{\varphi }_2,{\varphi }_3$, forming pairs interconnected through neutrino mixings. They generate some discrete transformations of mass and flavor neutrinos, respectively, in such a way that the group relations ${\mu }_1{\mu }_2={\mu }_3$ (cyclic) and ${\varphi }_1{\varphi }_2={\varphi }_3$ (cyclic) hold, while ${\mu }_a{\mu }_b={\mu }_b{\mu }_a$ and ${\varphi }_a{\varphi }_b={\varphi }_b{\varphi }_a$. Then, for instance, the ${\mu }_3$ matrix may be chosen equal to the "horizontal parity".

Comments: 1+9 pages, latex, no figures