Neutrinoless Double Beta Decay without Vacuum Majorana Neutrino Mass

We present a proof-of-concept extension to the Standard Model that can generate a non-vanishing neutrinoless double beta decay ($0\nu\beta\beta$) signal without the existence of Majorana neutrinos or lepton number violation in the zero-density vacuum-ground-state Lagrangian. We propose that the $0\nu\beta\beta$ can be induced by the capture of an ultralight scalar field, a potential dark matter candidate, that carries two units of lepton number. This makes the observable $0\nu\beta\beta$ spectrum indistinguishable from the usual $0\nu\beta\beta$ mechanisms by any practical means. We find that a non-zero $0\nu\beta\beta$ rate does not require neutrinos to be fundamentally Majorana particles. However, for sizeable decay rates within the range of next-generation experiments, the neutrino will, generally, acquire an (effective) Majorana mass as the scalar field undergoes a transition to the Bose-Einstein condensate phase. We also discuss the distinction between the aforementioned scenario and the case in which the emission of a lepton-number-two scalar leads to $0\nu\beta\beta$, exhibiting discernible qualitative features that make it experimentally distinguishable from the conventional scenario.