Theoretical estimates for the half-life of neutrinoless double beta decay ($0\nu \beta \beta$) in candidate nuclei are affected by both particle and nuclear physics uncertainties, which may complicate the interpretation of decay signals or limits. We study such uncertainties and their degeneracies in the following context: three $0\nu \beta \beta$ nuclei of great interest for large-scale experiments (${}^{76}\mathrm{Ge}$, ${}^{130}\mathrm{Te}$, ${}^{136}\mathrm{Xe}$), two representative particle physics mechanisms (light and heavy Majorana neutrino exchange), and a large set of nuclear matrix elements (NME), computed within the quasiparticle random phase approximation (QRPA). It turns out that the main theoretical uncertainties, associated with the effective axial coupling $g_A$ and with the nucleon-nucleon potential, can be parametrized in terms of NME rescaling factors, up to small residuals. From this parametrization, the following QRPA features emerge: (1) the NME dependence on $g_A$ is milder than quadratic, (2) in each of the two mechanisms, the relevant lepton number violating parameter is largely degenerate with the NME rescaling factors, and (3) the light and heavy neutrino exchange mechanisms are basically degenerate in the above three nuclei. We comment on the challenging theoretical and experimental improvements required to reduce such particle and nuclear physics uncertainties and their degeneracies.

• Received 19 June 2015

DOI:https://doi.org/10.1103/PhysRevD.92.093004