Unraveling New Physics with Double Beta Decays and Beyond

The quest for neutrinoless double beta decay (0νββ) represents a prominent probe of physics beyond the Standard Model. The new particle physics underlying any potential lepton-number-violating signal can be parametrized within the framework of effective field theory in terms of a set of higher-dimensional operators triggering a variety of distinct 0νββ mechanisms. While it seems to be challenging to unravel the dominant contribution from the observation of this rare nuclear process itself, the (non-)conservation of lepton number can be also tested in a variety of other experiments. We will discuss the phenomenological consequences of double beta decay searches, the limitations and the complementary probes of lepton number violation.