Impact of nuclear matrix element calculations for current and future neutrinoless double beta decay searches

Nuclear matrix elements (NME) are a crucial input for the interpretation of neutrinoless double beta decay data. We consider a representative set of recent NME calculations from different methods and investigate the impact on the present bound on the effective Majorana mass $m_{\beta\beta}$ by performing a combined analysis of the available data as well as on the sensitivity reach of future projects. A crucial role is played by the recently discovered short-range contribution to the NME, induced by light Majorana neutrino masses. Depending on the NME model and the relative sign of the long- and short-range contributions, the current $3\sigma$ bound can change between $m_{\beta\beta} < 40$ meV and 600 meV. The sign-uncertainty may either boost the sensitivity of next-generation experiments beyond the region for $m_{\beta\beta}$ predicted for inverted mass ordering or prevent even advanced setups to reach this region. Furthermore, we study the possibility to distinguish between different NME calculations by assuming a positive signal and by combining measurements from different isotopes. Such a discrimination will be impossible if the relative sign of the long- and short-range contribution remains unknown, but can become feasible if $m_{\beta\beta} \gtrsim 40$ meV and if the relative sign is known to be positive. Sensitivities will be dominated by the advanced $^{76}$Ge and $^{136}$Xe setups assumed here, but NME model-discrimination improves if data from a third isotope is added, e.g., from $^{130}$Te or $^{100}$Mo.