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Unformatted text preview: Homework Set No. 5, Physics 880.02 Deadline – Friday, March 13, 2009 1. (15 pts) In the SU (2) L ⊗ U (1) Y Electroweak theory the Lagrangian for the gauge fields is L gauge =- 1 4 f μν f μν- 1 4 ~ F μν · ~ F μν . It involves an Abelian gauge field B μ with the field strength tensor f μν = ∂ μ B ν- ∂ ν B μ and a non-Abelian field ~ W μ = ( W 1 μ , W 2 μ , W 3 μ ) with the field strength tensor F a μν = ∂ μ W a ν- ∂ ν W a μ + g abc W b μ W c ν . Rewrite the Lagrangian L gauge in terms of the W ± , Z , and photon fields W μ = 1 √ 2 ( W 1 μ- i W 2 μ ) W † μ = 1 √ 2 ( W 1 μ + i W 2 μ ) Z μ =- B μ sin θ W + W 3 μ cos θ W A μ = B μ cos θ W + W 3 μ sin θ W . Simplify L gauge and separate the kinetic terms of the fields W μ , Z μ , A μ from the interaction terms. List all the possible interaction vertices for W ± , Z , and the photon. (You do not have to spell out the Feynman rules for the vertices.) 2. A dedicated effort is underway by experimentalists at the B factories (BABAR collab-...
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