Upper bounds on lepton-number violating processes

We consider four lepton-number violating (L) processes: (a) neutrinoless double-beta decay (0 nu beta beta), (b) Delta L=2 tau decays, (c) Delta L=2 rare meson decays and (d) nuclear muon-positron conversion. In the absence of exotic L interactions, the rates for these processes are determined by effective neutrino masses < m >(l1l2), which can be related to the sum of light neutrino masses, the neutrino mass-squared differences, the neutrino mixing angles, a Dirac phase and two Majorana phases. We sample the experimentally allowed ranges of < m >(l1l2) based on neutrino oscillation experiments as well as cosmological observations, and obtain a stringent upper bound < m >(l1l2)less than or similar to 0.14 eV. We then calculate the allowed ranges for < m >(l1l2) from the experimental rates of direct searches for the above Delta L=2 processes. Comparing our calculated rates with the currently or soon available data, we find that only the 0 nu beta beta experiment may be able to probe < m >(ee) with a sensitivity comparable to the current bound. Muon-positron conversion is next in sensitivity, while the limits of direct searches for the other Delta L=2 processes are several orders of magnitude weaker than the current bounds on < m >(l1l2). Any positive signal in those direct searches would indicate new contributions to the L interactions beyond those from three light Majorana neutrinos.