Chiral perturbative analysis for an almost massless neutrino in the type-I seesaw mechanism

TL;DR

This paper uses chiral perturbation theory to analyze how an almost massless neutrino arises in the type-I seesaw mechanism, deriving explicit expressions and constraints on model parameters based on symmetry considerations.

Contribution

It provides a novel perturbative framework to analyze the light neutrino mass and eigenvector deviations in the type-I seesaw, highlighting symmetry-based parameter constraints.

Findings

Explicit formulas for eigenvector deviation and light neutrino mass.

Constraints on Dirac mass parameters from symmetry considerations.

Parameters are stable under renormalization.

Abstract

In this paper, we perform chiral perturbative analysis of an approximate lepton number symmetry associated with a sufficiently light neutrino in the type-I seesaw mechanism. For the Dirac mass matrix $m_{D} = (\bm A \, , \bm B \, , \bm C)$, linearly independent components of $\bm C$ from $\bm A$ and $\bm B$ are treated as symmetry-breaking parameters. A deviation in the eigenvector of the massless mode $\delta \bm u$ occurs in the first-order perturbation and the lightest mass $m_{1 \, \rm or \, 3} \propto \det m_{D}^{2} / M_{3}$ emerges in the second-order. By solving the perturbation theory, we obtained specific expressions of $\delta \bm u$ and $m_{1 \, \rm or \, 3}$. As a result, two complex parameters in $m_{D}$ are bounded to some extent from the eigenvector. These constraints are associated with the chiral symmetry and are not susceptible to renormalization.