Michel parameters
Encyclopedia
The Michel parameters, usually denoted by and , are four parameters used in describing the phase space distribution of leptonic decays of charged lepton
Lepton
A lepton is an elementary particle and a fundamental constituent of matter. The best known of all leptons is the electron which governs nearly all of chemistry as it is found in atoms and is directly tied to all chemical properties. Two main classes of leptons exist: charged leptons , and neutral...

s, . They are named after the physicist Louis Michel
Louis Michel (physicist)
Louis Michel was a French mathematical physicist at IHES. He was born in Roanne, near Loire, on 4 May 1923 and died in Bures-sur-Yvette on 30 December 1999.-Biography:...

. Sometimes instead of , the product is quoted. Within the Standard Model
Standard Model
The Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...

 of electroweak interaction
Electroweak interaction
In particle physics, the electroweak interaction is the unified description of two of the four known fundamental interactions of nature: electromagnetism and the weak interaction. Although these two forces appear very different at everyday low energies, the theory models them as two different...

s, these parameters are expected to be
Precise measurements of energy and angular distributions of the daughter leptons in decays of polarized muon
Muon
The muon |mu]] used to represent it) is an elementary particle similar to the electron, with a unitary negative electric charge and a spin of ½. Together with the electron, the tau, and the three neutrinos, it is classified as a lepton...

s and tau lepton
Tau lepton
The tau , also called the tau lepton, tau particle or tauon, is an elementary particle similar to the electron, with negative electric charge and a spin of . Together with the electron, the muon, and the three neutrinos, it is classified as a lepton...

s are so far in good agreement with these predictions of the Standard Model.

Muon decay

Let us consider the decay of the positive muon:
In the muon rest frame
Rest frame
In special relativity the rest frame of a particle is the coordinate system in which the particle is at rest.The rest frame of compound objects is taken to be the frame of reference in which the average momentum of the particles which make up the substance is zero In special relativity the rest...

, energy and angular distributions of the positron
Positron
The positron or antielectron is the antiparticle or the antimatter counterpart of the electron. The positron has an electric charge of +1e, a spin of ½, and has the same mass as an electron...

s emitted in the decay of a polarised muon expressed in terms of Michel parameters are the following, neglecting electron and neutrino
Neutrino
A neutrino is an electrically neutral, weakly interacting elementary subatomic particle with a half-integer spin, chirality and a disputed but small non-zero mass. It is able to pass through ordinary matter almost unaffected...

 masses and the radiative corrections:
where is muon polarisation, , and is the angle between muon spin
Spin (physics)
In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...

 direction and positron momentum direction. For the decay of the negative muon, the sign of the term containing should be inverted.

For the decay of the positive muon, the expected decay distribution for the Standard Model
Standard Model
The Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...

values of Michel parameters is
Integration of this expression over electron energy gives the angular distribution of the daughter positrons:
The positron energy distribution integrated over the polar angle is
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