Neutrinoless double beta decay in the minimal type-I seesaw model: mass-dependent nuclear matrix element, current limits and future sensitivities

In this work we discuss the neutrino mass dependent nuclear matrix element (NME) of the neutrinoless double beta decay process and derive the limit on the parameter space of the minimal Type-I seesaw model from the current available experimental data as well as the future sensitivities from the next-generation experiments. Both the explicit many-body calculations and naive extrapolations of the mass dependent NME are employed in the current work. The uncertainties of the theoretical nuclear structure models are taken into account. By combining the latest experimental data from $^{76}$Ge-based experiments, GERDA and MAJORANA, the $^{130}$Te-based experiment, CUORE and the $^{136}$Xe-based experiments, KamLAND-Zen and EXO-200, the bounds on the parameter space of the minimal Type-I seesaw model are obtained and compared with the limits from other experimental probes. Sensitivities for future experiments utilizing $^{76}$Ge-based (LEGEND-1000), $^{82}$Se-based (SuperNEMO), $^{130}$Te based (SNO+II) and $^{136}$Xe-based (nEXO), with a ten-year exposure, are also derived.