Effects of RG running in breaking $\mu -\tau$ reflection symmetry, conventional versus minimal seesaw

Abstract

The $\mu$--$\tau$ reflection symmetry has attracted considerable attention owing to its prediction of a maximal atmospheric mixing angle and a Dirac CP-violating phase $\delta =3\pi /2$, consistent with indications from the T2K and NO$\nu$A experiments. Since current neutrino oscillation data exhibit small but significant deviations from the exact symmetry predictions, understanding the origin of its breaking has become an important problem. In this work, we investigate the radiative breaking of $\mu$--$\tau$ reflection symmetry within the framework of the minimal seesaw model through the renormalization group (RG) evolution of neutrino parameters. Assuming the symmetry to be exact at the flavor symmetry (seesaw) scale, we examine whether the observed low-energy neutrino oscillation data can be reproduced after RG evolution. Owing to the rank-two structure of the minimal seesaw model, one light neutrino mass eigenvalue vanishes, reducing the number of independent high-energy neutrino parameters from five to four. We perform a systematic numerical analysis to determine the allowed high-energy parameter space capable of reproducing the current experimental constraints at low energies. Furthermore, a comparative study between the conventional Type-I seesaw and the minimal seesaw frameworks is carried out by analyzing the RG evolution of the solar and atmospheric mass-squared differences.