Upper Bounds on Lepton-number Violating Processes

We consider four lepton-number violating (\lv) processes: (a) neutrinoless double-beta decay (0\nu\beta\beta), (b) Delta L = 2 tau decays, © Delta L = 2 rare meson decays and (d) nuclear muon-positron conversion. In the absence of exotic \lv interactions, the rates for these processes are determined by effective neutrino masses <m>{\ell_1\ell_2}, 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>{\ell_1\ell_2} based on neutrino oscillation experiments as well as cosmological observations, and obtain a stringent upper bound <m>{\ell_1\ell_2} \lsim 0.14 eV. We then calculate the allowed ranges for <m>{\ell_1\ell_2} 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>{\ell_1\ell_2}. Any positive signal in those direct searches would indicate new contributions to the \lv interactions beyond those from three light Majorana neutrinos.