Modulus τ linking leptonic CP violation to baryon asymmetry in A4 modular invariant flavor model
Hiroshi Okada, Yusuke Shimizu, Morimitsu Tanimoto, Takahiro Yoshida
Abstract
A bstract We propose an A 4 modular invariant flavor model of leptons, in which both CP and modular symmetries are broken spontaneously by the vacuum expectation value of the modulus τ . The value of the modulus τ is restricted by the observed lepton mixing angles and lepton masses for the normal hierarchy of neutrino masses. The predictive Dirac CP phase δ CP is in the ranges [0° , 50°], [170° , 175°] and [280° , 360°] for Re [ τ ] < 0, and [0° , 80°], [185° , 190°] and [310° , 360°] for Re [ τ ] > 0. The sum of three neutrino masses is predicted in [60 , 84] meV, and the effective mass for the 0 νββ decay is in [0.003, 3] meV. The modulus τ links the Dirac CP phase to the cosmological baryon asymmetry (BAU) via the leptogenesis. Due to the strong wash-out effect, the predictive baryon asymmetry Y B can be at most the same order of the observed value. Then, the lightest right-handed neutrino mass is restricted in the range of M 1 = [1 . 5 , 6 . 5] × 10 13 GeV. We find the correlation between the predictive Y B and the Dirac CP phase δ CP . Only two predictive δ CP ranges, [5° , 40°] (Re [ τ ] > 0) and [320° , 355°] (Re [ τ ] < 0) are consistent with the BAU.