Extracting Majorana properties from strong bounds on neutrinoless double beta decay

Assuming that neutrinos are Majorana particles, we explore what information can be inferred from future strong limits (i.e. nonobservation) for neutrinoless double beta decay. Specifically we consider the case where the mass hierarchy is normal and the different contributions to the effective mass $⟨m{⟩}_{ee}$ partly cancel. We discuss how this fixes the two Majorana $CP$ phases simultaneously from the Majorana triangle and how it limits the lightest neutrino mass ${m}_{1}$ within a narrow window. The two Majorana $CP$ phases are in this case even better determined than in the usual case for larger $⟨m{⟩}_{ee}$. We show that the uncertainty in these predictions can be significantly reduced by the complementary measurement of reactor neutrino experiments, especially the medium baseline version JUNO/RENO-50. We also estimate the necessary precision on $⟨m{⟩}_{ee}$ to infer nontrivial Majorana $CP$ phases and the upper limit $⟨m{⟩}_{ee}\ensuremath{\lesssim}1\text{ }\text{ }\mathrm{meV}$ sets a target for the design of future neutrinoless double beta decay experiments.