CP violation of quarks in A 4 modular invariance

摘要

We discuss the quark mass matrices in theA4modular symmetry, where theA4triplet of Higgs is introduced for each up-quark and down-quark sectors, respectively. The model has six real parameters and two complex parameters in addition to the modulusτ. By inputting six quark masses and three CKM mixing angles, we can predict the CP violation phaseδand the Jarlskog invariantJCP. The predicted ranges ofδandJCPare consistent with the observed values. The absolute value ofVubis smaller than 0.0043, whileVcbis larger than 0.0436. In conclusion, our quark mass matrices with theA4modular symmetry can reproduce the CKM mixing matrix completely with observed quark masses.