Decay width of in the Weinberg-Salam model

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Decay width of in the Weinberg-Salam model Giordano Cerizza P611 – Fall 08 2/28/2019

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”) 2/28/2019

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) 2/28/2019

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 2/28/2019

Decay Width: Calculations The differential decay rate is defined as V-A 2/28/2019

Decay Width: Calculations Assuming the approximations: W decays at rest  the differential decay rate simplifies to Now we need to evaluate the integral… 2/28/2019

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 2/28/2019

Decay Width: Calculations Energy projection operators 2/28/2019

Decay Width: Calculations The decay rate is so approximated by Assuming 2/28/2019

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 2/28/2019