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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 - → ν μ + e - + ν e p 1 μ = q 1 μ + p 2 μ + q 2 μ The Feynman diagram The W-boson propagator is But M W = 80 GeV is much larger than the muon mass, so we can approximate Also, we define the Fermi weak coupling G by

The mean lifetime of a muon in the rest · The Feynman diagram The W-boson propagator is But M W = 80 GeV is much larger than the muon mass, so we can approximate Also, we define

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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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