Phenomenology of maximal and near-maximal lepton mixing

The possible existence of maximal or near-maximal lepton mixing constitutes an intriguing challenge for fundamental theories of flavor. We study the phenomenological consequences of maximal and near-maximal mixing of the electron neutrino with other $(x=\mathrm{tau}$ and/or muon) neutrinos. We describe the deviations from maximal mixing in terms of a parameter $\epsilon \equiv 1-2{\sin }^2{\theta }_{\mathrm{ex}}$ and quantify the present experimental status for $|\epsilon |<\mathrm{0.3.}\mathrm{}$ We show that both probabilities and observables depend on $\epsilon$ quadratically when effects are due to vacuum oscillations and they depend on $\epsilon$ linearly if matter effects dominate. The most important information on ${\nu }_e$ mixing comes from solar neutrino experiments. We find that the global analysis of solar neutrino data allows maximal mixing with confidence level better than 99% for ${10}^{-8}$ ${\mathrm{eV}}^2\lesssim \Delta m^2\lesssim 2\times {10}^{-7}$ ${\mathrm{eV}}^2.$ In the mass ranges $\Delta m^2\gtrsim 1.5\times {10}^{-5}$ ${\mathrm{eV}}^2$ and $4\times {10}^{-10}$ ${\mathrm{eV}}^2\lesssim \Delta m^2\lesssim 2\times {10}^{-7}$ ${\mathrm{eV}}^2$ the full interval $|\epsilon |<0.3\mathrm{}$ is allowed within $\sim 4\sigma$ (99.995% CL) We suggest ways to measure $\epsilon$ in future experiments. The observable that is most sensitive to $\epsilon$ is the rate [NC]/[CC] in combination with the day-night asymmetry in the SNO detector. With theoretical and statistical uncertainties, the expected accuracy after 5 years is $\Delta \epsilon \sim \mathrm{0.07.}$ We also discuss the effects of maximal and near-maximal ${\nu }_e$ mixing in atmospheric neutrinos, supernova neutrinos, and neutrinoless double beta decay.