Cosmological Constant Problem and violation of the Weak Equivalence Principle

To discover the rest mass of neutrinos is one of the most challenging tasks bearing fundamental implications to particle physics, astrophysics and cosmology. In the present paper we have estimated the rest mass of neutrinos by combining the experimental data for the solar and atmospheric neutrinos with a new theoretical assumption, having a simple physical interpretation in the framework of the neutrino-antineutrino pair production from the vacuum by a strong external field.