On the orthogonal matrix in the Casas-Ibarra parametrization for the Yukawa interactions of Majorana neutrinos

TL;DR

This paper generalizes the Casas-Ibarra parametrization for Majorana neutrinos by incorporating exact seesaw relations and non-unitarity, providing a new expression for the orthogonal matrix in terms of neutrino masses and mixing parameters.

Contribution

It derives a new form of the orthogonal matrix in the Casas-Ibarra parametrization considering full seesaw relations and non-unitarity effects.

Findings

Expressed the orthogonal matrix as a function of neutrino masses and mixing parameters.

Showed that specific patterns of the orthogonal matrix impose conditions on the seesaw parameter space.

Connected the orthogonal matrix structure to flavor mixing and mass hierarchies.

Abstract

The Casas-Ibarra (CI) parametrization of the Yukawa coupling matrix of Majorana neutrinos is generalized by considering the exact seesaw relation and including non-unitarity of the $3 \times 3$ Pontecorvo-Maki-Nakagawa-Sakata (PMNS) flavor mixing matrix. With the help of a full $6 \times 6$ Euler-like block description of the flavor structure for the seesaw mechanism, we find that the orthogonal matrix $\mathbb{O}$ in the CI parametrization can be expressed as $\mathbb{O}^{}_{ij} = \sqrt{M^{}_j/m^{}_i} \hspace{0.05cm} F^{}_{ij}$ with $m^{}_i$ and $M^{}_j$ being the masses of light and heavy Majorana neutrinos and $F^{}_{ij}$ consisting of the PMNS and active-sterile flavor mixing parameters (for $i, j = 1, 2, 3$). Assuming a specific pattern of $\mathbb{O}$ is therefore equivalent to imposing some special conditions on the seesaw parameter space.