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 [Formula Presented] mass eigenstate that is 0% [Formula Presented] 50% [Formula Presented] and 50% [Formula Presented] 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 [Formula Presented] (the measure for the deviation of atmospheric mixing from maximal) and [Formula Presented] are of order [Formula Presented] in the case of a normal neutrino mass hierarchy or of order [Formula Presented] 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 [Formula Presented] 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 [Formula Presented] from 1.