2026/07/19 by N. Razzaghi
#hep-ph #hep-th
We investigate a generalized Friedberg--Lee (FL) framework for neutrino masses, focusing on the singular parameter space at Point D (α= β= -1/3). At this limit, the neutrino mass matrix exhibits a democratic texture governed by the S3 permutation symmetry. Although theoretically profound, the exact democratic limit is phenomenologically excluded as it predicts a degenerate mass spectrum and a vanishing reactor angle (θ13=0). To reconcile this high-symmetry limit with experimental observations, we introduce a minimal and systematic perturbation that preserves the Twisted Friedberg--Lee (TFL) symmetry. This mechanism effectively lifts the mass degeneracy and breaks the magic and μ--τ symmetries in a controlled manner. Our derivation avoids ad hoc parameters, establishing a robust framework that yields a realistic inverted mass hierarchy (m3=0), a non-zero θ13, and intrinsic CP violation. We demonstrate that the model predicts maximal atmospheric mixing and a significant Dirac CP phase. The obtained numerical ranges for the neutrino masses and the Jarlskog invariant show excellent agreement with global fit data, providing a theoretically motivated foundation for neutrino flavor physics within the TFL scheme.