Abstract
We discuss the relation between the absolute neutrino mass scale, the effective mass measured in neutrinoless double beta decay, and the Majorana $CP$ phases. Emphasis is placed on estimating the upper bound on the nuclear matrix element entering calculations of the double beta decay half-life. Combining the claimed evidence for neutrinoless double beta decay with the neutrino mass bound from cosmology, one of the Majorana $CP$ phases can be constrained.
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