Assessment of uncertainties in QRPA $0\nu\beta\beta$-decay nuclear matrix elements

The nuclear matrix elements $M^{0\nu}$ of the neutrinoless double beta decay ($0\nu\beta\beta$) of most nuclei with known $2\nu\beta\beta$-decay rates are systematically evaluated using the Quasiparticle Random Phase Approximation (QRPA) and Renormalized QRPA (RQRPA). The experimental $2\nu\beta\beta$-decay rate is used to adjust the most relevant parameter, the strength of the particle-particle interaction. New results confirm that with such procedure the $M^{0\nu}$ values become essentially independent on the size of the single-particle basis. Furthermore, the matrix elements are shown to be also rather stable with respect to the possible quenching of the axial vector strength parametrized by reducing the coupling constant $g_A$, as well as to the uncertainties of parameters describing the short range nucleon correlations. Theoretical arguments in favor of the adopted way of determining the interaction parameters are presented. Furthermore, a discussion of other implicit and explicit parameters, inherent to the QRPA method, is presented. Comparison is made of the ways these factors are chosen by different authors. It is suggested that most of the spread among the published $0\nu\beta\beta$ decay nuclear matrix elements can be ascribed to these choices.