Texture-zeros in minimal seesaw from non-invertible symmetry fusion rules

Abstract

The $Z_2$ gauging of $Z_N$ symmetry can enforce certain elements of the fermion Yukawa couplings to vanish. We have performed a systematical study of texture zero patterns of lepton mass matrices in the minimal seesaw model, and we present all the possible patterns of the charged lepton Yukawa coupling $Y_E$, neutrino Yukawa coupling $Y_{\nu}$, right-handed neutrino mass matrix $M_R$ and the light neutrino mass matrix $M_{\nu}$ which can be derived from the $Z_2$ gauging of $Z_N$ symmetry. The realization of the textures with the maximum number of zeros and the second maximum number of zeros from non-invertible symmetry is studied, and the phenomenological implications in neutrino oscillation are discussed.