Neutrinoless double- β decay in the neutrino-extended standard model

We investigate neutrinoless double-beta decay ($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) in the minimal extension of the standard model of particle physics, the $\ensuremath{\nu}\mathrm{SM}$, where gauge-singlet right-handed neutrinos give rise to Dirac and Majorana neutrino mass terms. We focus on the associated sterile neutrinos and argue that the usual evaluation of their contributions to $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$, based on mass-dependent nuclear matrix elements, is missing important contributions from neutrinos with ultrasoft and hard momenta. We identify the hadronic and nuclear matrix elements that enter the new contributions, and calculate all relevant nuclear matrix elements for $^{136}\mathrm{Xe}$ using the nuclear shell model. Finally, we illustrate the impact on $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ rates in specific neutrino mass models and show that the new contributions significantly alter the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ rate in most parts of the $\ensuremath{\nu}\mathrm{SM}$ parameter space.