1. Decay width of in the Weinberg-Salam model
Giordano Cerizza
P611 – Fall 08
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2. Standard Model of Particle Physics
Electroweak interaction
Late 60s Weinberg and Salam described how it would be possible to treat electromagnetic and weak interactions as different aspect of a single electroweak interaction (single coupling “e”)
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3. Electroweak Interactions: Timeline
From an analysis of all the experiment on weak interactions Sudarshan and Marshak showed that the electroweak interaction is a V-A interaction
The existence of the electroweak interactions was experimentally established in two stages:
Discovery of the neutral currents in neutrino scattering (Gargamelle, 1973)
Discovery of the W and Z bosons at SPS, CERN (U1,U2, 1983)
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4. Decay of the W Boson
The coupling of the leptons to W boson are flavor-independent (i.e. it is the same for all leptons). This property is called lepton universality
where
with p 4-momentum, e polarization 4-vector, s spin 4-vector
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5. Decay Width: Calculations
The differential decay rate is defined as
V-A
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6. Decay Width: Calculations
Assuming the approximations:
W decays at rest 
the differential decay rate simplifies to
Now we need to evaluate the integral…
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7. Decay Width: Calculations
For simplicity let’s assume the W boson polarization
The matrix element squared is:
Summing over all the possible final spin state and averaging over the initial polarization state
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8. Decay Width: Calculations
Energy projection operators
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9. Decay Width: Calculations
The decay rate is so approximated by
Assuming
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10. Decay Width: Results GeV GeV GeV Plug in the values of the constants:
The experimental full decay width (from PDG’08):
GeV
With a branching fraction for the decay mode
Results in
GeV
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