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Multi-isotope degeneracy of neutrinoless double beta decay mechanisms in the quasi-particle random phase approximation

We calculate nuclear matrix elements (NME) of neutrinoless double beta decay in four different candidate nuclei (Ge-76, Se-82, Mo-100, Te-130) within the quasiparticle random phase approximation (QRPA) and its uncertainties. We assume (up to) four coexisting mechanisms for neutrinoless double beta decay, mediated by light Majorana neutrino exchange, heavy Majorana neutrino exchange, R-parity breaking supersymmetry, and squark-neutrino, interfering either constructively or destructively with each other. We find that, unfortunately, current NME uncertainties appear to prevent a robust determination of the relative contribution of each mechanism to the decay amplitude, even assuming accurate measurements of decay lifetimes. The near-degeneracy of the decay mechanisms is analyzed with simple algebraic techniques, which do not involve assumptions about the statistical distribution of errors. We discuss implications of such degeneracy on prospective searches for absolute neutrino masses.