Neutrino mixing in Seesaw model

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, $y_{△}$. The mixing matrix of light leptons is $V_{KM}{S}^{\prime \ast }$, where $V_{KM}\equiv {V_{Le}}^{†}{V}_{L\nu }$ %$V_{Le}$ and $V_{L\nu }$ diagonalize %the Yukawa matrices of charged leptons, %$y_e{y}_e^{†}$, and neutrinos, $y_{\nu }{y}_{\nu }^{†}$, %respectively, and $S^{\prime \ast }\equiv {V_{L\nu }}^{†}{S}^{\ast }$. Large mixing may occur without fine tuning of the matrix elements of $y_{△}$ 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.

14 pages, 4 figures, PTPTeX