The $ν$ generation: present and future constraints on neutrino masses from cosmology and laboratory experiments

Abstract: We perform a joint analysis of current data from cosmology and laboratory experiments to constrain the neutrino mass parameters in the framework of bayesian statistics, also accounting for uncertainties in nuclear modeling, relevant for neutrinoless double $\beta$ decay ($0\nu2\beta$) searches. We find that a combination of current oscillation, cosmological and $0\nu2\beta$ data constrains $m_{\beta\beta}~<~0.045\,\mathrm{eV}$ ($0.014 \, \mathrm{eV} < m_{\beta\beta} < 0.066 \,\mathrm{eV}$) at 95\% C.L. for normal (inverted) hierarchy. This result is in practice dominated by the cosmological and oscillation data, so it is not affected by uncertainties related to the interpretation of $0\nu2\beta$ data, like nuclear modeling, or the exact particle physics mechanism underlying the process. We then perform forecasts for forthcoming and next-generation experiments, and find that in the case of normal hierarchy, given a total mass of $0.1\,$ eV, and assuming a factor-of-two uncertainty in the modeling of the relevant nuclear matrix elements, it will be possible to measure the total mass itself, the effective Majorana mass and the effective electron mass with an accuracy (at 95\% C.L.) of $0.05$, $0.015$, $0.02\,\mathrm{eV}$ respectively, as well as to be sensitive to one of the Majorana phases. This assumes that neutrinos are Majorana particles and that the mass mechanism gives the dominant contribution to $0\nu2\beta$ decay. We argue that more precise nuclear modeling will be crucial to improve these sensitivities.