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Unformatted text preview: Homework Set No. 4, Physics 880.02 Deadline – Thursday, June 4, 2009 1. (20 pts) Similar to what we did in class, solve the DGLAP equation for gluon distri- bution Q 2 ∂ ∂Q 2 G ( x, Q 2 ) = α s 2 π Z 1 x dx x γ GG ( x/x ) G ( x , Q 2 ) with γ GG ( z ) = 2 N c z in the small- x asymptotics, but now with fixed coupling constant α s (independent of Q 2 ). In particular show that, in the saddle point approximation, the small- x asymptotics for gluon distribution is given by xG ( x, Q 2 ) ∼ exp 2 s α s N c π ln 1 x ln Q 2 Q 2 ! . This is called double logarithmic approximation (DLA) of DGLAP, since we resum both ln 1 x and ln Q 2 Q 2 in the new parameter α s ln 1 x ln Q 2 Q 2 . 2. (30 pts) Calculate the cross section for gluon + gluon → quark + antiquark at the Born level shown in the figure below. The figure is for the amplitude , which needs to be squared and multiplied by appropriate factors to get the cross section....
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