Search for Lepton Number Violation and Neutrino Nature with Neutrinoless Double Beta Decay

Despite nine decades of research on neutrinos, their fundamental nature remains a mystery. Two possibilities exist: (1) Dirac neutrinos, in which neutrinos and anti-neutrinos are different particles and (2) Majorana neutrinos, in which neutrinos and anti-neutrinos are the same particle. In the latter case, lepton number would have no meaning for neutrinos, and lepton-number nonconserving interactions could occur. One such process is neutrinoless double beta decay (0nbb), in which two electrons and no antineutrinos($\Delta$ L=2) are emitted. If 0nbb decay is discovered, then neutrinos must be Majorana. I will give an overview the leading experiments giving half-life limits for 0nbb decay of up to $10^26$ years and proposals for next-generation experiments with half-life sensitivity of $10^28$ years. Of personal interest is the possibility of observing the $Ba^136$ daughter of one $Xe^136$ 0nbb decay using single atom or single molecule imaging, which may allow even higher sensitivity to be achieved.