Muon DecayEdit
Muon decay is the process by which the muon, a heavier cousin of the electron, transforms into lighter particles through the weak interaction. In free space, the dominant decay modes are mu- → e- + ν̄e + νμ and μ+ → e+ + νe + ν̄μ. The mean lifetime of a free muon is about 2.196 microseconds, and the decay products include an electron (or positron) whose energy distribution—known as the Michel spectrum—serves as a clean probe of the structure of the weak interaction. Because muon decay involves only leptons and neutrinos, it provides a relatively pristine laboratory for testing the Standard Model and the universality of the weak force across lepton families Muon Lepton Weak interaction Standard Model.
Fundamental Theory
The muon is a second-generation lepton with properties that make it ideal for precision tests of particle physics. The decay of the muon is mediated by the charged-current weak interaction, typically described at low energies by an effective four-fermion interaction with the Fermi coupling constant Fermi coupling constant and, in the full theory, by the exchange of a W boson W boson within the electroweak sector of the Standard Model.
A key feature of muon decay is its V−A (vector minus axial-vector) structure, which implies a specific helicity pattern for the final-state leptons. The energy and angular distributions of the decay electron in the muon rest frame are parameterized by Michel parameters, a set of quantities that encode the Lorentz structure of the interaction. The classic spectrum is often described in terms of the parameter ρ and related quantities such as η, ξ, and δ, which experimental measurements are designed to constrain. The existence and values of these parameters test the extent to which the weak interaction adheres to the Standard Model\'s predictions for lepton couplings Michel parameters Lepton universality.
The decay also respects conservation laws that shape the process: lepton number is conserved, and the decay products include neutrinos that carry away missing energy and angular momentum. Neutrinos themselves are fundamental to the weak interaction and are associated with the lepton family numbers: νe, νμ, and ντ, which participate in charged- and neutral-current processes mediated by the weak force Neutrino Weak interaction.
In addition to the dominant two-body lepton final-state channels, rarer processes such as radiative muon decay (μ → e ν ν̄ γ) occur, providing further tests of quantum electrodynamics in concert with the weak interaction. Searches for nonstandard couplings or forbidden decay modes (for example, lepton-flavor-violating channels) place stringent limits on physics beyond the Standard Model, illustrating how muon decay serves as a precision frontier for new theories Radiative muon decay Lepton flavor violation.
Experimental Observables
Decay channels and electron energy spectrum: The main decay modes produce an electron (or positron) with a characteristic energy spectrum whose shape is predicted by the underlying V−A structure. The endpoint of the spectrum corresponds to the maximum electron energy allowed by kinematics in the muon rest frame, and precise measurements of the spectrum test the details of the weak interaction and the presence of possible scalar or tensor contributions beyond the Standard Model. Experimental studies of the Michel spectrum measure parameters such as ρ and η, among others, to compare with theoretical expectations Michel parameters.
Lifetime measurements: The free muon lifetime is a fundamental observable. For a negative muon bound in matter, an additional process—muon capture on nuclei—shortens the effective lifetime relative to the free muon case. Negative muons can be captured by protons in nuclei, producing neutrons and neutrinos, which alters the observed decay rate in materials but not the intrinsic free-muon lifetime. This distinction must be accounted for in precision tests and when extracting the Fermi constant G_F from muon decay data Muon capture.
Tests of lepton universality: Because the same weak interaction is responsible for muon and tau decays, muon decay provides a crucial benchmark for lepton universality—the idea that all leptons couple to the weak force with the same strength, modulo mass effects. Comparing muon decay results with those from tau decays and other processes helps confirm or constrain any departure from universality, a topic of ongoing experimental verification within the Standard Model framework Lepton universality.
Radiative muon decay and nonstandard decays: Radiative muon decay, where a photon accompanies the standard decay products, is a sensitive test of higher-order processes and radiative corrections in the electroweak theory. Beyond-Standard-Model scenarios may permit rare or forbidden decays, such as lepton-flavor-violating channels (e.g., μ → e γ in certain models), which are stringently limited by experiments. The absence of observed nonstandard decays reinforces the Standard Model but continues to guide searches for new physics Radiative muon decay Lepton flavor violation.
Historical notes and measurements have continually refined the precision with which muon decay parameters are known. Early discoveries established that muons decay via the weak interaction, and subsequent experiments have tested the Michel parameters and the V−A structure to increasingly tight limits, reinforcing the role of muon decay as a clean probe of fundamental symmetries and couplings in particle physics Muon Weak interaction.