Neutrino mass patterns, WMAP, and Neutrinoless double beta decay

Based on the observed neutrino mass-square differences and mixings, we derive a few general patterns for the neutrino mass matrix in the flavor basis, which can correctly describe the atmospheric and solar neutrino data. Upon the most recent result on the absolute neutrino mass bound from WMAP, we can rule out a large portion of the parameter space that claimed by the positive signal in the Heidelberg-Moscow $0\nu\beta\beta$ experiment. In the case when one of the majorana phases is $\pi$, the effective neutrino mass obtained is inconsistent with the claim.