Full parametrization of the6×6flavor mixing matrix in the presence of three light or heavy sterile neutrinos

Abstract

In addition to three active neutrinos ${\ensuremath{\nu}}_{e}$, ${\ensuremath{\nu}}_{\ensuremath{\mu}}$, and ${\ensuremath{\nu}}_{\ensuremath{\tau}}$, one or more light sterile neutrinos have been conjectured to account for the LSND, MiniBooNE, and reactor antineutrino anomalies (at the sub-eV mass scale) or for warm dark matter in the Universe (at the keV mass scale). Heavy Majorana neutrinos at or above the TeV scale have also been assumed in some seesaw models. Such hypothetical particles can weakly mix with active neutrinos, and thus their existence can be detected at low energies. In the $(3+3)$ scenario with three sterile neutrinos we present a full parametrization of the $6\ifmmode\times\else\texttimes\fi{}6$ flavor mixing matrix in terms of 15 rotation angles and 15 phase angles. We show that this standard parametrization allows us to clearly describe the salient features of some problems in neutrino phenomenology, such as (a) possible contributions of light sterile neutrinos to the tritium beta decay and neutrinoless double-beta decay, (b) leptonic $CP$ violation and deformed unitarity triangles of the $3\ifmmode\times\else\texttimes\fi{}3$ flavor mixing matrix of three active neutrinos, (c) a reconstruction of the $6\ifmmode\times\else\texttimes\fi{}6$ neutrino mass matrix in the type-(I+II) seesaw mechanism, and (d) flavored and unflavored leptogenesis scenarios in the type-I seesaw mechanism with three heavy Majorana neutrinos.