New A4 lepton flavor model from S4 modular symmetry

We study a flavor model with A(4) symmetry which originates from S-4 modular group. In S-4 symmetry, Z(2) subgroup can be anomalous, and then S-4 can be violated to A(4). Starting with a S-4 symmetric Lagrangian at the tree level, the Lagrangian at the quantum level has only A(4) symmetry when Z(2) in S-4 is anomalous. We obtain modular forms of two singlets and a triplet representations of A(4) by decomposing S-4 modular forms into A(4) representations. We propose a new A(4) flavor model of leptons by using those A(4) modular forms. We succeed in constructing a viable neutrino mass matrix through the Weinberg operator for both normal hierarchy (NH) and inverted hierarchy (IH) of neutrino masses. Our predictions of the CP violating Dirac phase delta(CP) and the mixing sin(2)theta(23) depend on the sum of neutrino masses for NH.