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

We investigate neutrinoless double-beta decay (0νββ) in the minimal extension of the standard model of particle physics, the νSM, 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 0νββ, 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 ¹³⁶Xe using the nuclear shell model. Finally, we illustrate the impact on 0νββ rates in specific neutrino mass models and show that the new contributions significantly alter the 0νββ rate in most parts of the νSM parameter space.