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

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 3×3 Pontecorvo-Maki-Nakagawa-Sakata (PMNS) flavor mixing matrix. With the help of a full 6×6 Euler-like block description of the flavor structure for the seesaw mechanism, we find that the orthogonal matrix O in the CI parametrization can be expressed as Oij=Mj/miFij with mi and Mj being the masses of light and heavy Majorana neutrinos and Fij consisting of the PMNS and active-sterile flavor mixing parameters (for i,j=1,2,3). Assuming a specific pattern of O is therefore equivalent to imposing some special conditions on the seesaw parameter space.