New A4 lepton flavor model from S4 modular symmetry

We study a flavor model with A4 symmetry which originates from S4 modular group. In S4 symmetry, Z2 subgroup can be anomalous, and then S4 can be violated to A4. Starting with a S4 symmetric Lagrangian at the tree level, the Lagrangian at the quantum level has only A4 symmetry when Z2 in S4 is anomalous. We obtain modular forms of two singlets and a triplet representations of A4 by decomposing S4 modular forms into A4 representations. We propose a new A4 flavor model of leptons by using those A4 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 δCP and the mixing sin2θ23 depend on the sum of neutrino masses for NH.