CP violation of quarks in $A_4$ modular invariance

Understand

We discuss the quark mass matrices in the $A_4$ modular symmetry, where the $A_4$ triplet 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 modulus $\tau$.
• By inputting six quark masses and three CKM mixing angles, we can predict the CP violation phase $\delta$ and the Jarlskog invariant $J_{CP}$.
• The predicted ranges of $\delta$ and $J_{CP}$ are consistent with the observed values.