Neutrino masses and leptonicCPviolation

Neutrino oscillations as solutions of the solar neutrino problems and the atmospheric neutrino deficits may restrict neutrino mass squared differences and mixing angles in the three-neutrino mixing scheme. Currently we have several solutions depending on the interpretation of the solar neutrino problem. Combining the neutrino oscillation solutions and a mass matrix ansatz, we investigate the neutrino mass bounds and find a possible leptonic $\mathrm{CP}$-violating rephasing-invariant quantity $J_{\mathrm{CP}}^l<~0.012$ for the large mixing angle MSW and just-so vacuum oscillation solutions, and $J_{\mathrm{CP}}^l<~0.0013$ for the small mixing angle MSW solution.