Analysis of muon decay with lepton-number-nonconserving interactions

We analyze muon decay using the most general local, derivative-free, Lorentz-invariant, lepton-number-nonconserving interactions. We show that, neglecting neutrino masses, there is a one-to-one correspondence between the coupling constants in the lepton-number-conserving case and combinations of coupling constants in the lepton-number-violating case; i.e., it is not possible, even in principle, to test lepton-number conservation in muon decay if the final neutrinos are massless and are not observed. Using these relations, we are able to use previous analyses of (lepton-number-conserving) muon and inverse muon decay to put stringent limits on certain combinations of parameters. If fine-tuned cancellations are not allowed, these limits constrain the individual coupling constants. We discuss to what extent it is directly tested that the (left-handed) neutrino emitted in muon decay is the same as that which is produced in ${\pi }_{\mu 2}$ decay.