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.

arXiv comment12 pages, final version will be published in Nuclear Physics B

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