scale suggested by atmospheric neutrino oscillations, $\sqrt{\Delta m^2_{\rm
atm}} \simeq 0.05$ eV [@Tortola:2012te]. If the next generation of [$0\nu\beta\beta$ ]{}decay experiments detects a signal, one might expect that future cosmological data [@Lesgourgues:2006nd; @Hannestad:2010kz; @Wong:2011ip] also provide indications for non-zero neutrino masses. Contradicting results from [$0\nu\beta\beta$ ]{}(observation) and cosmology (limit) then might point to a non-standard explanation for [$0\nu\beta\beta$ ]{}decay, see [@Bergstrom:2011dt] for a detailed discussion of the interplay of different data.

Contributions to the [$0\nu\beta\beta$ ]{}decay rate can be divided into a short-range [@Pas:2000vn] and a long-range [@Pas:1999fc] part. The long-range contributions, which the neutrino mass mechanism belongs to, can lead in some cases to very stringent limits on the new physics scale $\Lambda \gsim$ $\lambda^{\mathrm{eff}}_{\rm
LNV}\times$($10^2 - 10^3$) TeV, where $\lambda^{\mathrm{eff}}_{\rm
LNV}$ is some effective Lepton Number Violating (LNV) coupling that depends on the model under consideration. Therefore, for some of the “exotic” mechanisms discussed in the literature, falling into this category, the half-life limits from [$0\nu\beta\beta$ ]{}decay themselves yield the most stringent bounds. On the other hand, in the case of the short-range contribution, i.e., the [$0\nu\beta\beta$ ]{}amplitude is mediated only by heavy mediators with masses at a high energy scale $\Lambda$, the effective Lagrangian describing [$0\nu\beta\beta$ ]{}decay 