Effect of steriles states on lepton magnetic moments and neutrinoless double beta decay

We address the impact of sterile fermion states on the anomalous magnetic moment of charged leptons, as well as their contribution to neutrinoless double beta decays. We illustrate our results in a minimal, effective extension of the Standard Model by one sterile fermion state, and in a well-motivated framework of neutrino mass generation, embedding the Inverse Seesaw into the Standard Model. The simple "3+1" effective case succeeds in alleviating the tension related to the muon anomalous magnetic moment, albeit only at the 3$\sigma$ level, and for light sterile states (corresponding to a }cosmologically disfavoured regime). Interestingly, our analysis shows that a future $0 \nu 2 \beta$ observation does not necessarily imply an inverted hierarchy for the active neutrinos in this simple extension. Although the Inverse Seesaw realisation here addressed could indeed ease the tension in $(g-2)_\mu$, bounds from lepton universality in kaon decays mostly preclude this from happening. However, these scenarios can also have a strong impact on the interpretation of a future $0 \nu 2 \beta$ signal regarding the hierarchy of the active neutrino mass spectrum.