Minimally Allowed Neutrinoless Double Beta Decay Rates From Approximate Flavor Symmetries

Neutrinoless double beta decay ($\beta\beta0\nu$) is among the only realistic probes of Majorana neutrinos. In the standard scenario, dominated by light neutrino exchange, the process amplitude is proportional to $m_{ee}$, the $e-e$ element of the Majorana mass matrix. Naively, current data allows for vanishing $m_{ee}$, but this should be protected by an appropriate flavor symmetry. All such symmetries lead to mass matrices inconsistent with oscillation phenomenology. I perform a spurion analysis to break all possible Abelian symmetries that guarantee vanishing $\beta\beta0\nu$ rates and search for minimally allowed values. I survey 230 broken structures to yield $m_{ee}$ values and current phenomenological constraints under a variety of scenarios. This analysis also extracts predictions for both neutrino oscillation parameters and kinematic quantities. Assuming reasonable tuning levels, I find that $m_{ee}>4\times 10^{-6}$ eV at 99% confidence. Bounds below this value might indicate the Dirac neutrino nature or the existence of new light (eV-MeV scale) degrees of freedom that can potentially be probed elsewhere.