Upper bounds on lepton-number violating processes

We consider four lepton-number violating (L\;) processes: (a) neutrinoless double-beta decay (0), (b) =2 tau decays, (c) =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⟩₁{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⟩₁{₂} based on neutrino oscillation experiments as well as cosmological observations, and obtain a stringent upper bound ⟨m⟩₁{₂}0. 14 eV. We then calculate the allowed ranges for ⟨m⟩₁{₂} from the experimental rates of direct searches for the above =2 processes. Comparing our calculated rates with the currently or soon available data, we find that only the 0 experiment may be able to probe ⟨m⟩₄₄ with a sensitivity comparable to the current bound. Muon-positron conversion is next in sensitivity, while the limits of direct searches for the other =2 processes are several orders of magnitude weaker than the current bounds on ⟨m⟩₁{₂}. Any positive signal in those direct searches would indicate new contributions to the L\; interactions beyond those from three light Majorana neutrinos.