Neutrino Mass Matrix with No Adjustable Parameters

On the basis of the so-called "yukawaon" model, we found out a special form of the neutrino mass matrix $M_ν$ which gives reasonable predictions. The $M_ν$ is given by a multiplication form made of charged lepton mass matrix $M_e$ and up-quark mass matrix $M_u$. This $M_ν$ 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 $M_ν$, in spite of having only three parameters, the $M_ν$ can give reasonable predictions $\sin^2 2θ_{atm} \simeq 0.99$, $\sin^2 2θ_{13} \simeq 0.015$, $Δm^2_{21}/Δm^2_{32} \simeq 0.030$, $< m_{ee}> \simeq 0.0039$ eV, and so on, by using observed values of $m_e/m_μ$, $m_μ/m_τ$, $m_c/m_t$, and $\sin^2 θ_{solar}$ as input values.

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