Mass matrices with CP phase in modular flavor symmetry

Abstract

Abstract We study the CP violation and the CP phase of quark mass matrices in modular flavor symmetric models. The CP symmetry remains at τ = e2πi/3 by a combination of the T-symmetry of the modular symmetry. However, T-symmetry breaking may lead to CP violation at the fixed point τ = e2πi/3. We study such a possibility in magnetized orbifold models as examples of modular flavor symmetric models. These models, in general, have more than one candidate for Higgs modes, while generic string compactifications also lead to several Higgs modes. These Higgs modes have different behaviors under the T-transformation. The light Higgs mode can be a linear combination of those modes so as to lead to realistic quark mass matrices. The CP phase of the mass matrix does not appear in a certain case, which is determined by the T-transformation behavior. Deviation from this is important to realize the physical CP phase. We discuss an example leading to a non-vanishing CP phase at the fixed point τ = e2πi/3.