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HW 10 problems/solutions

# HW 10 problems/solutions - Homework 10 1 Homework X...

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Unformatted text preview: Homework 10 1 11/29/2005 Homework X Problems: X.1 Consider the weak decay of the muon µ − → ν µ + e − + ⎯ν e : a. Draw the Feynman diagrams for both the Fermi four-point interaction, and the first-order dia- gram which has the intermediate weak vector boson. b. Calculate the differential decay rate d Γ /d E e for the weak process; assume the muon current has the form: j µ = g / √ 2 ⎯ψ ( ν ) γ µ ( 1 / 2 )(1 − λγ 5 ) ψ ( µ ) , where E e is the electron energy, and λ an a priori unknown parameter. As before, ⎯ψ repre- sents the adjoint spinor. c. Calculate the total decay rate for the muon; as above you will obtain an expression contain- ing the parameter λ . d. Plot and graph d Γ /d E e versus E e , for values of λ =0 (Fermi model), and λ =1 (V − A theory), and λ = − 1 (V+A theory). Hints: see class notes handed out. Solution: a. Feynman Diagram: b. Amplitude for this process: ( ) ( ) 2 5 1 5 2 3 4 ( ) (1 ) (1 ) 2 fi p iG i u u u u m µ µ γ λ γ γ λ γ − − = − − (I.1) The matrix element squared, averaged and summed over the initial and final spins respectively, becomes: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 2 3 4 1 2 3 4 2 † 2 5 1 5 2 5 1...
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HW 10 problems/solutions - Homework 10 1 Homework X...

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