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An example of the weak interaction - the muon decay rate
The mean lifetime of a muon in the rest frame is 2.2 μs. We’ll calculate that from the Fermi weak coupling. The decay is _ μ- → νμ + e
- + νe
p1μ = q1
μ + p2μ + q2
μ
The Feynman diagram
The W-boson propagator is
But MW = 80 GeV is much larger than the muon mass, so we can approximate
Also, we define the Fermi weak coupling G by
For example,
Calculate the square of M.
Symmetric part
Antisymmetric part
Result
|M|2 = 64 G2 p1.q2 p2.q1
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