In this letter, we perform chiral perturbative diagonalization of the type-I seesaw mechanism by hierarchical singular values $\lambda_{ i}$ of the Dirac mass matrix $m_{ D}$ up to the next-to-leading order (NLO). Since the mass matrix of right-handed neutrinos $M_{ R}$ has parity symmetries under $\lambda_{ i} \leftrightarrow - \lambda_{ i}$, the singular values $M_{ i}$ and mixing angles of diagonalization of $M_{ R}$ are written by only even and odd orders of $\lambda_{ i}$ respectively. We confirm this fact by specific perturbative expansions of the third- and the fourth-order by $\lambda_{ i}$. As a result, as long as the chiral perturbation theory is valid, the NLO contributions are generally suppressed by $O(\lambda_{ i}^{ 2} / \labmda_{ j}^{ 2}) \lesssim 1\%$ compared to the leading-order expressions that have sufficient accuracies.
Categories: hep-ph