  Theoretical estimates for the half life of neutrinoless double beta decay 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 nuclei of great interest for large-scale experiments (76-Ge,
130-Te, 136-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.

High Energy Physics - Phenomenology;High Energy Physics - Experiment;Nuclear Experiment;Nuclear Theory