One texture zero for Dirac neutrinos in a diagonal charged lepton basis

TL;DR

This work examines one-texture-zero patterns in the Hermitian Dirac neutrino mass matrix $M_ u$ within a diagonal charged-lepton basis, analyzing both normal and inverted ordering using current oscillation data. It combines analytic relations with full numerical fits to identify which of the six patterns are viable, finding four NH-compatible textures (including $T_1$, $T_3$, $T_4$, and $T_5$) and a single IH-viable pattern ($T_2$). A key result is that CP violation is nonzero only when the texture zero sits on a diagonal entry, while off-diagonal zeros force $J=0$. The findings constrain neutrino masses, mixing angles, and the Dirac CP phase, with implications for cosmological bounds and flavor symmetries that could underlie texture zeros.

Abstract

An analytic and numerical systematic study of the neutrino mass matrix with one texture zero is presented in a basis where the charged leptons are diagonal. Under the assumption that neutrinos are Dirac particles, the analysis is carried out in detail for the normal and inverted hierarchy mass spectrum. Our study is performed without any approximations, first analytically and then numerically, using current neutrino oscillation data. The analysis constrains the parameter space in such a way that, among the six possible one-texture-zero patterns, only four are favored in the normal hierarchy and, one in the inverted hierarchy, by current oscillation data at the $3 σ$ level. Phenomenological implications for the lepton CP-violating phase and neutrino masses are also explored.