PS8 - 253a/Schwartz Due November 2 2010 Problem Set 8 1 Mo...

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Unformatted text preview: 253a/Schwartz Due November 2, 2010 Problem Set 8 1. Mo ller scattering is the process e − e − → e − e − . Of the tree-level processes in QED in is especially interesting because it involves identical particles. a) Calculate the spin-averaged differential cross section for Moller scattering e − e − → e − e − . Express your answer in terms of s, t, u and m e . b) Show that in the non-relativistic limit you get what we guessed by spin-conversa- tion arguments in Problem Set 4: dσ d Ω = m e 4 α 2 E cm 2 p 4 parenleftbigg 1 +3 cos 2 θ sin 4 θ parenrightbigg , p 2 = ( E cm 2 ) 2- m e 2 (1) c) Simplify the Mo ller scattering formula in the ultra-relativistic limit ( m e → ). [Hint: you should get something proportional to (3+ cos 2 θ ) 2 ]. 2. Spin vs helicity. a) Use the left and right helicity projection operators 1 2 (1 ± γ 5 ) so show that the QED vertex ψ ¯ h γ μ ψ h ′ vanishes unless h = h ′ ....
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PS8 - 253a/Schwartz Due November 2 2010 Problem Set 8 1 Mo...

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