A full parametrization of the $9\times 9$ active-sterile flavor mixing matrix in the inverse or linear seesaw scenario of massive neutrinos

Abstract

The inverse and linear seesaw scenarios are two typical extensions of the canonical seesaw mechanism, which contain much more sterile degrees of freedom but can naturally explain the smallness of three active neutrino masses at a sufficiently low energy scale (e.g., the TeV scale). To fully describe the mixing among three active neutrinos, three sterile neutrinos and three extra gauge-singlet neutral fermions in either of these two seesaw paradigms, we present the {\it first} full parametrization of the $9\times 9$ flavor mixing matrix in terms of 36 rotation angles and 36 CP-violating phases. The exact inverse and linear seesaw formulas are derived, respectively; and possible deviations of the $3\times 3$ active neutrino mixing matrix from its unitary limit are discussed by calculating the effective Jarlskog invariants and unitarity nonagons.

23 pages, 1 figure. Minor changes, references added. Accepted for publication in Nucl. Phys. B

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• Linear seesaw leptogenesis before/after electroweak symmetry breaking
• Exploring the feasibility of the charged lepton flavor violating decay $\mu \to e+\gamma$ in inverse and linear seesaw mechanisms with $A_4$ flavour symmetry
• General Approach to Neutrino Mass Mechanisms with Sterile Neutrinos
• Impact of unitarity violation on sensitivity of the leptonic CP phase at Hyper-Kamiokande and DUNE