Neutrino mass and mixing from a novel scenario with \(A_4\) symmetry

Abstract

We propose a standard model (SM) extension with \(A_4\) symmetry giving rise to the desired neutrino mass matrix structure with the suitable correlation \((M_\nu )_{22}= -2 (M_\nu )_{13}\) by the contributions of the Weinberg-type operators and the type-I seesaw mechanism. We find the parameters of the model that can predict the sum of neutrino masses, the effective neutrino mass, the Dirac and Majorana CP phases for both the normal ordering (NO) and the inverted ordering (IO). Our analysis reveals a narrow range for the sum of neutrino masses, approximately 131 meV for NO and 157 for IO, two mass squared differences \(\Delta m_{21}^2\in (52.390, 99.390)\, \mathrm{meV}^2\) and \(\Delta m_{31}^2\in (2.528, 2.570)10^3\,\mathrm{meV}^2\) for NO, while \(\Delta m_{21}^2\in (52.500, 99.350)\, \mathrm{meV}^2\) and \(\Delta m_{31}^2\in (-2.475, -2.426)10^3\,\mathrm{meV}^2\) for IO, and the Dirac phase \(s_\delta \in (-0.289, -0.146)\) for IO and \(s_\delta \in (-0.970, -0.968)\) for IO. Utilizing these constraints, we determine the effective Majorana mass, two Majorana phases and the lightest neutrino mass for both NO and IO. Finally, we estimate the magnitude of the Yukawa-like couplings which can naturally account for the charged-lepton and neutrino mass hierarchies.