Chiral perturbative solution for the type-I seesaw mechanism in next-to-leading order

Abstract

In this letter, we perform chiral perturbative diagonalization of the type-I seesaw mechanism by hierarchical singular values $λ_{i}$ 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 $λ_{i} \leftrightarrow - λ_{i}$, the singular values $M_{i}$ and mixing angles of diagonalization of $M_{R}$ are written by only even and odd orders of $λ_{i}$ respectively. We confirm this fact by specific perturbative expansions of the third- and the fourth-order by $λ_{i}$. As a result, as long as the chiral perturbation theory is valid, the NLO contributions are generally suppressed by $O(λ_{i}^{2} / \labmda_{j}^{2}) \lesssim 1\%$ compared to the leading-order expressions that have sufficient accuracies.