A general formula by LDLT decomposition for the type-I seesaw mechanism

Abstract

Abstract By performing an approximate spectral decomposition on the inverse mass matrix of the right-handed neutrinos M−1, we obtain a basis-independent formula for the type-I seesaw mechanism. Mathematically, it is based on the generalized Cholesky (or LDLT) decomposition of the symmetric matrix M−1 = LDLT, with a diagonal matrix D and a lower unitriangular matrix L. Since the diagonalization of L can be inverted without solving cubic equations, the formula will be useful in investigating the general properties of the mechanism, such as flavor symmetries, generalized CP symmetries, and fine-tunings.