Unraveling the $0\nu\beta\beta$ Decay Mechanisms

We discuss the possibilities of distinguishing among different mechanisms of neutrinoless double beta decay arising in the effective field theory framework. Following the review and detailed investigation of the particular ways of discrimination, we conclude that the 32 different low-energy effective operators can be split into multiple groups that are in principle distinguishable from each other by measurements of the phase-space observables and by comparison of the decay rates obtained using different isotopes. This would require not only a substantial experimental precision but necessarily also a considerable improvement of the current theoretical knowledge of the underlying nuclear physics. Specifically, the limiting aspect in our approach turns out to be the currently unknown or uncertain values of low-energy constants. Besides the study adopting the effective field theory language we also look into several typical UV models.