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It is pointed out that in theories with CP invariance and two (or more) massive Majorana neutrinos the relative sign of their CP eigenvalues is significant. For opposite values of the CP eigenvalue the contributions of the two neutrinos to neutrinoless double beta decay tend to cancel, so that published bounds on the mass of a Majorana electron neutrino do not apply. In the case of the Zee model of the Majorana neutrino mass matrix, the cancellation is complete and the double beta decay rate vanishes identically.
L. Wolfenstein (Tue,) studied this question.