Michel parameter

Michel parameter. In particle physics, the Michel parameters are a set of dimensionless quantities that describe the energy and angular distributions of the charged leptons produced in the weak decay of muons and tau leptons. They were introduced by the French physicist Louis Michel in 1950 to provide a model-independent framework for analyzing the structure of the weak interaction in leptonic decays. The precise measurement of these parameters serves as a powerful test of the Standard Model of particle physics, particularly the V−A theory, and can reveal signatures of new physics beyond the established framework.

Definition and significance

The parameters are defined from the most general, local, derivative-free, lepton-number-conserving four-fermion point interaction for the decay process. In the decay of a polarized muon, the differential decay rate for the emitted electron depends on its energy and the angles relative to the muon's spin direction. This rate is parameterized by four main parameters: ρ (rho), η (eta), ξ (xi), and δ (delta). The parameter ρ governs the shape of the electron energy spectrum, η is a parameter for CP-violating effects, ξ determines the asymmetry in the angular distribution relative to the muon spin, and δ describes the angular dependence of the decay electrons. Their significance lies in their direct sensitivity to the chiral structure and possible scalar, tensor, or other non-Standard Model couplings in the weak interaction, providing a window into physics that might not be described by the pure V−A structure of the Standard Model.

Experimental determination

The most precise determinations come from high-statistics experiments studying muon decay, particularly those using highly polarized muon beams. Key experiments have been performed at facilities like the Paul Scherrer Institute (PSI), TRIUMF, and the Brookhaven National Laboratory. Experiments measure the energy spectrum of decay positrons, their angular distribution relative to the muon spin, and the positron's polarization to extract the parameters. The TWIST experiment at TRIUMF provided one of the most precise sets of measurements. For tau lepton decays, experiments at electron–positron colliders like LEP at CERN, the SLAC National Accelerator Laboratory, and Belle at KEK have also constrained the equivalent parameters, though with less precision due to the shorter lifetime and more complex decay modes of the tau lepton.

Theoretical predictions

In the Standard Model, which incorporates the V−A theory of the weak interaction and assumes lepton universality, the Michel parameters have specific predicted values. For pure V−A coupling, the predictions are ρ = 0.75, η = 0, ξ = 1, and δ = 0.75. These values arise directly from the maximally parity-violating, left-handed structure of the charged-current interaction mediated by the W boson. Any significant deviation from these values would be a clear indication of physics beyond the Standard Model, such as the presence of right-handed currents, scalar or tensor interactions, or a breakdown of lepton universality. Theoretical frameworks like supersymmetry or models with additional Higgs boson doublets can predict small deviations in these parameters.

Values and constraints

World averages from experiments, primarily on muon decay, are in excellent agreement with the Standard Model predictions, strongly confirming the V−A structure. The current Particle Data Group averages give ρ = 0.7499 ± 0.0004, η = 0.000 ± 0.034, ξ = 1.0009 ± 0.0022, and δ = 0.7506 ± 0.0010. The parameter η, sensitive to CP-violating or time-reversal-violating interactions, is consistent with zero. The extreme precision of these measurements, particularly for ρ and δ, places stringent constraints on possible non-Standard Model contributions. For example, they limit the mass scale of possible right-handed W bosons or the coupling constants for hypothetical scalar and tensor interactions to very high levels, often in the multi-TeV range.

Applications in particle physics

The Michel parameters are fundamental tools in precision tests of the electroweak interaction. Their confirmed agreement with the Standard Model reinforces the framework of V−A theory and lepton universality. They are used to set bounds on parameters in extensions of the Standard Model, such as those involving leptoquarks, extra Z' bosons, or in the context of muon g−2 anomalies. Furthermore, the methodology developed for their measurement is applied to analyze the decay dynamics of the tau lepton and heavy mesons like B mesons at facilities like the LHCb experiment and Belle II experiment, searching for similar deviations that could indicate new physics. Their study remains a critical component of the research programs at major laboratories including CERN, Fermilab, and KEK. Category:Particle physics Category:Physical constants Category:Weak interaction