On Baryon and Lepton Number Violation

In this report we discuss the main theories to understand the origin of baryon and lepton number violation in physics beyond the Standard Model. We present the theoretical predictions for rare processes such as neutrinoless double beta decay, proton decay, and neutron-antineutron oscillation, and overview the prospects to discover these rare processes in the near future. The possibility to observe baryon and lepton violating signatures at current and future colliders and through precision studies of other rare processes, and the testability of different baryogenesis mechanisms is discussed in detail. A healthy and broad experimental program looking for proton decay, neutrinoless double beta decay and neutron-antineutron oscillations is essential to make new discoveries in this field. These searches are carried out at various experimental facilities in the US and abroad, and use instrumentation arching across traditional HEP/NP boundaries. In addition, experiments such as those at the Large Hadron Collider could discover exotic baryon and/or lepton number violating signatures connected to low energy scale theories for neutrino masses, supersymmetric models with R-parity violation, new gauge theories or other mechanisms for physics beyond the Standard Model. The landscape presented in this report could be crucial to discover the underlying mechanism for neutrino masses and the matter-antimatter asymmetry in the universe.