The Power of Neutrino Mass Sum Rules for Neutrinoless Double Beta Decay Experiments

Neutrino mass sum rules relate the three neutrino masses within generic classes of flavour models, leading to restrictions on the effective mass parameter measured in experiments on neutrinoless double beta decay as a function of the lightest neutrino mass. We perform a comprehensive study of the implications of such neutrino mass sum rules, which provide a link between model building, phenomenology, and experiments. After a careful explanation of how to derive predictions from sum rules, we discuss a large number of examples both numerically, using all three global fits available for the neutrino oscillation data, and analytically wherever possible. In some cases, our results disagree with some of those in the literature for reasons that we explain. Finally we discuss the experimental prospects for many current and near-future experiments, with a particular focus on the uncertainties induced by the unknown nuclear physics involved. We find that, in many cases, the power of the neutrino mass sum rules is so strong as to allow certain classes of models to be tested by the next generation of neutrinoless double beta decay experiments. Our study can serve as both a guideline and a theoretical motivation for future experimental studies.