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 ${\lambda }_i$ 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 $O(λ_{i}^{2} / \labmda_{j}^{2}) \lesssim 1\%$ compared to the leading-order expressions that have sufficient accuracies.

9 pages