Michel Parameters - Muon Decay

Muon Decay

See also: Muon#Muon decay

Let us consider the decay of the positive muon:

In the muon rest frame, energy and angular distributions of the positrons emitted in the decay of a polarised muon expressed in terms of Michel parameters are the following, neglecting electron and neutrino masses and the radiative corrections:

\frac{d^2\Gamma}{x^2dxd\cos\theta} \sim (3-3x) + \frac{2}{3}\rho (4x-3) + P_{\mu}\xi\cos\theta ,

where is muon polarisation, and is the angle between muon spin 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 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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