Neutrinoless double-beta decay with massive scalar emission

Searches for neutrino-less double-beta decay (0 nu 2 beta) place an important constraint on models where light fields beyond the Standard Model participate in the neutrino mass mechanism. While 0 nu 2 beta-experimental collaborations often consider various massless majoron models, including various forms of majoron couplings and multi-majoron final-state processes, none of these searches considered the scenario where the "majoron" phi is not massless, m(phi) similar to MeV, of the same order as the Q-value of the 0 nu 2 beta reaction. We consider this parameter region and estimate 0 nu 2 beta phi constraints for m(phi) of order MeV. The constraints are affected not only by kinematical phase space suppression but also by a change in the signal to background ratio charachterizing the search. As a result, 0 nu 2 beta phi constraints for m(phi) > 0 diminish significantly below the reaction threshold. This has phenomenological implications, which we illustrate focusing on high-energy neutrino telescopes. The spectral shape of high-energy astrophysical neutrinos could exhibit features due to resonant nu nu -> phi -> nu nu scattering. Such features fall within the sensitivity range of IceCube-like experiments, if m(phi) is of order MeV, making 0 nu 2 beta phi key complimentary laboratory constraint on the scenario. Our results motivate a dedicated analysis by 0 nu 2 beta collaborations, analogous to the dedicated analyses targeting massless majoron models.