Neutrino mass matrix with no adjustable parameters

Abstract

On the basis of the so-called “yukawaon” model, we found 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: sin²2θ _atm ≃0.99, sin²2θ ₁₃≃0.015, $\Delta m^{2}_{21}/\Delta m^{2}_{32} \simeq0.030$, 〈m _ee 〉≃0.0039 eV, and so on, by using observed values of m _e /m _μ , m _μ /m _τ , m _c /m _t , and sin² θ _solar as input values.