We begin by working out an effective field theory valid below some new physics scale for Dirac neutrinos and Majorana neutrinos, respectively. For Dirac neutrinos, we obtain a complete basis of effective dimension four and dimension six operators that are invariant under the gauge symmetry of the Standard Model. As for Majorana neutrinos, we come up with a complete basis of effective dimension five and dimension seven operators that are invariant under the gauge symmetry of the Standard Model. Using the effective theory, we derive model-independent, "naturalness" upper bounds on the magnetic moments of Dirac neutrinos and Majorana neutrinos generated by physics above the scale of electroweak symmetry breaking. In the absence of fine-tuning of effective operator coefficients, for Dirac neutrinos, we find that current information on neutrino mass implies that the bound on neutrino magnetic moments is several orders of magnitude stronger than those obtained from analyses of solar and reactor neutrino data and astrophysical observations. As for Majorana neutrinos, the magnetic moment contribution to the mass is Yukawa suppressed. The bounds we derive for magnetic moments of Majorana neutrinos are weaker than present experimental limits if neutrino magnetic moments are generated by new physics at around 1 TeV, and surpass current experimental sensitivity only for new physics scales >10-100 TeV. The discovery of a neutrino magnetic moment near present limits would thus signify that neutrinos are Majorana particles. Then, we use the scale of neutrino mass to derive model-independent naturalness constraints on possible contributions to muon decay Michel parameters. We show that -- in the absence of fine-tuning -- the most stringent bounds on chirality-changing operators relevant to muon decay arise from one-loop contributions to neutrino mass. The bounds we obtain on their contributions to the Michel parameters are four or more orders of magnitude stronger than bounds previously obtained in the literature. We also show that, if neutrinos are Dirac fermions, there exist chirality-changing operators that contribute to muon decay but whose flavor structure allows them to evade neutrino mass naturalness bounds. We discuss the implications of our analysis for the interpretation of muon decay experiments. Finally, we use the upper limit on the neutrino mass to derive model-independent naturalness constraints on some non-Standard-Model interactions of beta decays. In the absence of fine-tuning of effective operator coefficients, our results yield constraints on scalar and tensor weak interactions one or more orders of magnitude stronger than a recent global fit after combined with the current experimental limits. We also show that, if neutrinos are Majorana fermions, there exist four-fermion operators that contribute to beta decay but whose flavor structure allows them to evade neutrino mass naturalness bounds. Constraints on the beta decay parameters by CKM Unitarity, ratio of positive pion decays, and pion beta decays are discussed as well.
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