Dark Matter Neutrinos Must Come with Degenerate Masses

Abstract

It has been known that there are two schemes in the framework of three flavor neutrinos to accommodate the global features of the hot dark matter neutrinos, the solar neutrino deficit and the atmospheric neutrino anomaly in a manner consistent with terrestrial neutrino experiments, i.e., hierarchical mass neutrinos and almost degenerate neutrinos. We demonstrate that the recent result by the CHOOZ experiment excludes the scheme of hierarchical neutrinos. We also point out in the scheme of almost degenerate neutrinos that if neutrinos are Majorana particles then the double $\beta$ decay experiments must see positive signals on their way to reach a limit more stringent than the present one by a factor of 5.