Deviation of atmospheric mixing from maximal and structure in the leptonic flavor sector

I attempt to quantify how far from maximal one should expect the atmospheric mixing angle to be given a neutrino mass matrix that leads, at zeroth order, to a ν₃ mass eigenstate that is 0% νₑ, 50% ν_μ, and 50% ν_τ. This is done by assuming that the solar mass-squared difference is induced by an ``anarchical'' first order perturbation, an approach then can naturally lead to experimentally allowed values for all oscillation parameters. In particular, both |cos2θₐₜₘ| (the measure for the deviation of atmospheric mixing from maximal) and |Uₑ₃| are of order √Δmₛₒₗ²/Δmₐₜₘ² in the case of a normal neutrino mass hierarchy or of order Δmₛₒₗ²/Δmₐₜₘ² in the case of an inverted one. Hence, if any of the textures analyzed here has anything to do with reality, next-generation neutrino experiments can see a nonzero cos2θₐₜₘ in the case of a normal mass hierarchy, while in the case of an inverted mass hierarchy only neutrino factories should be able to see a deviation of sin²2θₐₜₘ from 1.