Neutrinoless double beta decay can constrain neutrino dark matter

We examine how constraints can be placed on the neutrino component of dark matter by an accurate measurement of neutrinoless double beta (0νββ) decay and the solar oscillation amplitude. We comment on the alleged evidence for 0νββ decay. The detection of neutrinoless double beta decay would imply the violation of lepton number conservation. The process could be induced by Majorana neutrino mass terms, or by less trivial modifications of the standard model. Here we consider the former possibility wherein there are exactly three left-handed neutrino states with Majorana masses. The measurement of 0νββ decay, together with what has been learned from studies of solar and atmospheric neutrinos, has direct consequences on the spectrum of neutrino masses and therefore on the effects of neutrinos on structure formation. We define what will be necessary to determine the neutrino component of dark matter from terrestrial experiments. The charged-current eigenstates are related to the mass eigenstates by a unitary transformation