muon and tau decay

Why don't the heavier leptons stick around? Because nature lets heavy particles shed their extra mass-energy by turning into lighter ones, and the muon and tau both have lighter relatives to fall toward. The electron, being the lightest charged lepton, has nowhere lighter to go and so is stable forever; the muon and tau do not have that luxury, so they decay.

Both decays are driven by the weak force, working through the same machinery. The heavy lepton emits a W boson and converts into its own neutrino; the W boson, being unstable, immediately turns into the decay products. For a muon the W almost always becomes an electron and an electron antineutrino, so the full story is: muon to electron plus muon neutrino plus electron antineutrino. The tau works identically when it goes the 'leptonic' route, becoming an electron or a muon plus neutrinos. But because the tau is so much heavier, its W can also turn into a quark-antiquark pair, which emerges as hadrons — the tau's 'hadronic' decays.

These decays are textbook weak processes and superb tests of the theory. The muon's lifetime, measured to many decimal places, is one of the cleanest ways to pin down the strength of the weak force (the Fermi constant). And comparing the rates and patterns of muon and tau decays checks whether the weak force really couples to all lepton generations with the same strength — the principle of lepton universality, which the Standard Model insists upon and experiments keep scrutinising.