Upper bounds on lepton-number violating processes

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We consider four lepton-number violating ($\mathrm{L\ensuremath{\llap{\not\;}}}$) processes: (a) neutrinoless double-beta decay $(0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta})$, (b) $\ensuremath{\Delta}L=2$ tau decays, (c) $\ensuremath{\Delta}L=2$ rare meson decays and (d) nuclear muon-positron conversion. In the absence of exotic $\mathrm{L\ensuremath{\llap{\not\;}}}$ interactions, the rates for these processes are determined by effective neutrino masses $⟨m{⟩}_{{\ensuremath{\ell}}_{1}{\ensuremath{\ell}}_{2}}$, 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 $⟨m{⟩}_{{\ensuremath{\ell}}_{1}{\ensuremath{\ell}}_{2}}$ based on neutrino oscillation experiments as well as cosmological observations, and obtain a stringent upper bound $⟨m{⟩}_{{\ensuremath{\ell}}_{1}{\ensuremath{\ell}}_{2}}\ensuremath{\lesssim}0.14\text{ }\text{ }\mathrm{eV}$. We then calculate the allowed ranges for $⟨m{⟩}_{{\ensuremath{\ell}}_{1}{\ensuremath{\ell}}_{2}}$ from the experimental rates of direct searches for the above $\ensuremath{\Delta}L=2$ processes. Comparing our calculated rates with the currently or soon available data, we find that only the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ 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 $\ensuremath{\Delta}L=2$ processes are several orders of magnitude weaker than the current bounds on $⟨m{⟩}_{{\ensuremath{\ell}}_{1}{\ensuremath{\ell}}_{2}}$. Any positive signal in those direct searches would indicate new contributions to the $\mathrm{L\ensuremath{\llap{\not\;}}}$ interactions beyond those from three light Majorana neutrinos.