New A 4 lepton flavor model from S 4 modular symmetry

• Published in: The journal of high energy physics Vol. 2020; no. 2; pp. 1 - 17
• Main Authors: Tatsuo Kobayashi, Yusuke Shimizu, Kenta Takagi, Morimitsu Tanimoto, Takuya H. Tatsuishi
• Format: Journal Article
• Language: English
• Published: SpringerOpen 01.02.2020
• Subjects: Compactification and String Models; CP violation; Discrete Symmetries; Neutrino Physics
• ISSN: 1029-8479
• DOI: 10.1007/JHEP02(2020)097

Abstract 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 δ CP and the mixing sin2 θ 23 depend on the sum of neutrino masses for NH.