Neutrino mixing,CPandTviolation, and textures in four-neutrino models

We examine the prospects for determining the neutrino mixing matrix and for observing $\mathrm{CP}$ and $T$ violation in neutrino oscillations in four-neutrino models. We focus on a general class of four-neutrino models with two pairs of nearly degenerate mass eigenstates separated by approximately 1 eV, which can describe the solar, atmospheric and LSND neutrino data. We present a general parametrization of these models and discuss in detail the determination of the mixing parameters and the mass matrix texture from current and future neutrino data in the case where ${\nu }_e$ and ${\nu }_{\mu }$ each mix primarily with one other neutrino. We find that measurable $\mathrm{CP}$ or $T$ violation in long-baseline experiments, with amplitude at the level of the LSND signal, is possible given current experimental constraints. Also, additional oscillation effects in short- and long-baseline experiments may be measurable in many cases. We point out that, given separate scales for the mass-squared differences of the solar and atmospheric oscillations, observable $\mathrm{CP}$ or $T$ violation effects in neutrino oscillations signal the existence of a sterile neutrino. We examine several textures of the neutrino mass matrix and determine which textures can have measurable $\mathrm{CP}$ or $T$ violation in neutrino oscillations in long-baseline experiments. We also briefly discuss some possible origins of the neutrino mass terms in straightforward extensions of the standard model.