  We examine the constraints from the recent HEIDELBERG-MOSCOW double beta
decay experiment. It leads us to the almost degenerate or inverse hierarchy
neutrino mass scenario. In this scenario, we obtain possible upper bounds for
the Majorana CP violating phase in the lepton sector by incorporating the data
from the neutrino oscillation, the single beta decay experiments, and from the
astrophysical observation. We also predict the neutrino mass that may be
measurable in the future beta decay experiments.
