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 ${\sin }^{2}2{\theta }_{atm}\simeq 0.99$, ${\sin }^{2}2{\theta }_{13}\simeq 0.015$, $\Delta m_{21}^2/\Delta m_{32}^2\simeq 0.030$, $<m_{ee}>\simeq 0.0039$ 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.

Comments: 18 pages, 4 figures, title changed, version accepted by EPJC