Lepton Number Violation and Neutrinoless Double Beta Decay

In this talk I will discuss the significance of neutrinoless double beta decay as a probe of lepton number violation (LNV). After an introduction on lepton number in particle physics and cosmology, I will describe an end-to-end effective field theory (EFT) framework connecting the possibly very high scale at which LNV originates to the nuclear scale. Such a framework is essential to assess the discovery potential and model diagnosing power of neutrinoless double beta decay searches. On the high-energy end, the EFT allows one to classify the sources of LNV according to the mass scale at which they arise. On the low-energy end, the EFT allows one to organize contributions to hadronic and nuclear matrix elements in a systematic expansion, which together with nuclear many body methods is the basis to reach controlled uncertainties in the near future. After discussing recent developments in the EFT approach, I will illustrate the framework through explicit examples, such as the high scale seesaw model and the TeV scale left-right-symmetric model.