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

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 $m_D=(\mathbf{A},\mathbf{B},\mathbf{C})$, linearly independent components of $\mathbf{C}$ from $\mathbf{A}$ and $\mathbf{B}$ are treated as symmetry-breaking parameters. A deviation in the eigenvector of the massless mode $\delta \mathbf{u}$ occurs in the first-order perturbation and the lightest mass $m_{1\mathrm{or}3}\propto \det m_D^2/M_3$ emerges in the second-order. By solving the perturbation theory, we obtained specific expressions of $\delta \mathbf{u}$ and $m_{1\mathrm{or}3}$. 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.

Comments: 12 pages, final version will be published in Nuclear Physics B