The search for neutrinoless double beta decay (NLDBD) provides the most powerful and comprehensive means for testing the conservation of total lepton number at the classical (Lagrangian) level. I discuss the theoretical implications of NLDBD searches for our understanding of the origin of neutrino mass and the cosmic matter-antimatter asymmetry. I also illustrate the interplay of NLDBD searches with terrestrial and astrophysical probes of neutrino properties and tests of lepton number conservation.

Argonne Physics Division Colloquium Schedule