Non-Minimal Approximation for the Type-I Seesaw Mechanism

A non-minimal approximation for effective masses of light and heavy neutrinos in the framework of a type-I seesaw mechanism with three generations of sterile Majorana neutrinos which recover the symmetry between quarks and leptons is considered. The main results are: (a) the next-order corrections to the effective mass matrix of heavy neutrinos due to terms O({\theta}MD) are obtained, which modify the commonly used representation for the effective mass (MD is a Dirac neutrino mass when the electroweak symmetry is spontaneously broken); and (b) the general form of the mixing matrix is found in non-minimal approximation parametrized by a complex 3x3 matrix satisfying a nontrivial constraint. Numerical analysis within the {\nu}MSM framework demonstrates the very small effect of new contributions of direct collider observables as opposed to their possible significance for cosmological models.