Neutrino mixing in Seesaw model

TL;DR

This paper analyzes neutrino mixing in the seesaw model, showing how the mixing matrix can naturally be large without fine-tuning, aligning with experimental observations.

Contribution

It introduces a method to determine the neutrino mixing matrix using a unitary transformation that triangularizes the Yukawa matrix, explaining large mixing angles naturally.

Findings

Large mixing can occur without fine tuning of Yukawa matrices.

The mixing matrix is determined by a unitary transformation S.

Results are consistent with atmospheric neutrino oscillation data.

Abstract

We study the neutrino mixing matrix (the MNS matrix) in the seesaw model. By assuming a large mass hierarchy for the heavy right-handed Majorana mass, we show that, in the diagonal Majorana base, the MNS matrix is determined by a unitary matrix, $S$, which transforms the neutrino Yukawa matrix, $y_{\nu}$, into a triangular form, $y_{\triangle}$. The mixing matrix of light leptons is $V_{KM} S^{\prime *}$, where $V_{KM} \equiv {V_{Le}}^{\dagger} V_{L \nu}$ %$V_{Le}$ and $V_{L\nu}$ diagonalize %the Yukawa matrices of charged leptons, %$y_e y_e^{\dagger}$, and neutrinos, $y_{\nu} y_{\nu}^{\dagger}$, %respectively, and $S^{\prime *} \equiv {V_{L\nu}}^{\dagger} S^*$. Large mixing may occur without fine tuning of the matrix elements of $y_{\triangle}$ even if the usual KM-like matrix $V_{KM}$ is given by $V_{KM} =1$. This large mixing naturally may satisfy the experimental lower bound of the mixing implied by the atmospheric neutrino oscillation.