Parameter-independent quark mass relation in the U(3) × U(3)‧ model

Recently, we have proposed a quark mass matrix model based on U(3) × U(3)‧ family symmetry, in which up- and down-quark mass matrices Mu and Md are described only by complex parameters au and ad, respectively. When we use charged lepton masses as additional input values, we can successfully obtain predictions for quark masses and Cabibbo-Kobayashi-Maskawa mixing. Since we have only one complex parameter aq for each mass matrix Mq, we can obtain a parameter-independent mass relation by using three equations for Tr[Hq], Tr[HqHq] and detHq, where Hq ≡ MqMq† (q = u,d). In this paper, we investigate the parameter-independent feature of the quark mass relation in the model.