Neutrino Mass Matrix with No Adjustable Parameters

Abstract

On the basis of the so-called "yukawaon" model, we found out a special form of the neutrino mass matrix $M_\nu$ which gives reasonable predictions. The $M_\nu$ is given by a multiplication form made of charged lepton mass matrix $M_e$ and up-quark mass matrix $M_u$. This $M_\nu$ has no adjustable parameters except for those in $M_e$ and $M_u$. Here, $M_e$ and $M_u$ are described by one parameter $a_e$ (real) and two parameters $a_u$ (complex), respectively, and those parameters are constrained by their observed mass ratios. With this form of $M_\nu$, in spite of having only three parameters, the $M_\nu$ can give reasonable predictions $\sin^2 2\theta_{atm} \simeq 0.99$, $\sin^2 2\theta_{13} \simeq 0.015$, $\Delta m^2_{21}/\Delta m^2_{32} \simeq 0.030$, $< m_{ee}> \simeq 0.0039$ eV, and so on, by using observed values of $m_e/m_\mu$, $m_\mu/m_\tau$, $m_c/m_t$, and $\sin^2 \theta_{solar}$ as input values.