hw22 - s = ( p + p 2 ) 2 , t = ( k 2-p 2 ) 2 , u = ( k 1-p...

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Homework Set No. 2, Physics 880.08 Deadline – Wednesday, February 2, 2011 1. (35 pts) Problem 4.1 in Peskin and Schroeder. (Hints: Reading pp. 32-33 in Peskin and Schroeder frst may help understand the problem. Assume that j ( x ) is real. Each item is worth the Following amounts oF points: (a) - 3, (b) - 5, (c) - 10, (d) - 8, (e) - 7, (F) - 2.) 2. (20 pts) Consider 2 2 scattering oF identical particles oF mass m . Suppose the production cross section oF a particle with 4-momentum p is given by E p d 3 p = f ( s, t, u ) δ ( s + t + u - 4 m 2 ) where f is some Function oF s = ( k 1 + k 2 ) 2 , t = ( k 1 - p ) 2 , and u = ( k 1 - p 2 ) 2 , with
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Unformatted text preview: s = ( p + p 2 ) 2 , t = ( k 2-p 2 ) 2 , u = ( k 1-p 2 ) 2 = u (see fgure below). Just like in class k 1 = ( E k 1 , v k 1 ), k 2 = ( E k 2 , v k 2 ), p = ( E p , v p ), and p 2 = ( E p 2 , v k 1 + v k 2-v p ). k 1 k 2 p p 2 Show that d dt = r s ( s-4 m 2 ) f ( s, t, u ) where u is now defned by u = 4 m 2-s-t and s = ( k 1 + k 2 ) 2 still. (Hint: it is easier to prove this result by picking either the CMS Frame or the rest Frame oF one oF the initial state particles.) 1...
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This note was uploaded on 07/28/2011 for the course PHYSICS 880.08 taught by Professor Staff during the Fall '10 term at Ohio State.

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