Lepton-number violation (LNV), in general, implies nonzero Majorana masses for the Standard Model neutrinos. Since neutrino masses are very small, for generic candidate models of the physics responsible for LNV, the rates for almost all experimentally accessible LNV observables -except for neutrinoless double-beta decay -are expected to be exceedingly small. Guided by effective-operator considerations of LNV phenomena, we identify a complete family of models where lepton number is violated but the generated Majorana neutrino masses are tiny, even if the new-physics scale is below 1 TeV. We explore the phenomenology of these models, including charged-lepton flavor-violating phenomena and baryon-number-violating phenomena, identifying scenarios where the allowed rates for µ − → e + -conversion in nuclei are potentially accessible to next-generation experiments.
I. INTRODUCTIONLepton number and baryon number are, at the classical level, accidental global symmetries of the renormalizable Standard Model (SM) Lagrangian. * If one allows for generic non-renormalizable operators consistent with the SM gauge symmetries and particle content, lepton number and baryon number will no longer be conserved. Indeed, lepton-number conservation is violated by effective operators of dimension five or higher while baryon-number conservation (sometimes together with lepton number) is violated by effective operators of dimension six or higher. In other words, generically, the addition of new degrees-of-freedom to the SM particle content violates baryon-number and lepton-number conservation.Experimentally, in spite of ambitious ongoing experimental efforts, there is no evidence for the violation of leptonnumber or baryon-number conservation [5]. There are a few different potential explanations for these (negative) experimental results, assuming degrees-of-freedom beyond those of the SM exist. Perhaps the new particles are either very heavy or very weakly coupled in such a way that phenomena that violate lepton-number or baryon-number conservation are highly suppressed. Another possibility is that the new interactions are not generic and that lepton-number or baryon-number conservation are global symmetries of the Beyond-the-Standard-Model Lagrangian. Finally, it is possible that even though baryon number or lepton number are not conserved and the new degrees-of-freedom are neither weakly coupled nor very heavy, only a subset of baryon-number-violating or lepton-number-violating phenomena are within reach of particle physics experiments. This manuscript concentrates on this third option, which we hope to elucidate below.The discovery of nonzero yet tiny neutrino masses is often interpreted as enticing -but certainly not definitive! -indirect evidence for lepton-number-violating new physics. In this case, neutrinos are massive Majorana fermions and one can naturally "explain" why the masses of neutrinos are much smaller than those of all other known massive particles (see, for example, [6-8] for discussions of this point). Searches for th...