μ-τ symmetry in Zee-Babu model

We study the Zee-Babu two-loop neutrino mass generation model and look for a possible flavor symmetry behind the tri-bimaximal neutrino mixing. We find that there probably exists the μ-τ symmetry in the case of the normal neutrino mass hierarchy, whereas there may not be in the inverted hierarchy case. We also propose a specific model based on a Froggatt-Nielsen-like Z5 symmetry to naturally accomplish the μ-τ symmetry on the neutrino mass matrix for the normal hierarchy case.