HW 10 problems/solutions

HW 10 problems/solutions - Homework 10 1 11/29/2005...

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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 + e + 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 /d E e for the weak process; assume the muon current has the form: j = g / 2 ( ) ( 1 / 2 )(1 5 ) ( ) , where E e is the electron energy, and an a priori unknown parameter. As before, 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 . d. Plot and graph d /d E e versus E e , for values of =0 (Fermi model), and =1 (V A theory), and = 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 = (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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This note was uploaded on 02/22/2009 for the course PHYSICS 557 taught by Professor Michaelrijssenbeek during the Fall '05 term at SUNY Stony Brook.

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HW 10 problems/solutions - Homework 10 1 11/29/2005...

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