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HW 7 problems/solutions

# HW 7 problems/solutions - Homework 6 1 Homework VII...

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Homework 6 1 11/1/2005 Homework VII Problems: VII.1 Scattering of spinless particles: a. Calculate d σ / d * and the total cross section σ tot for electromagnetic lowest-order electromag- netic scattering of spin-0 bosons A and B, both with charge + e . b. How does the result change for bosons that have opposite charges? Solution: For the process a + b a’ + b’ , with m a = m a’ and m b = m b’ we have found (assuming a b ): ( ) ( ) ( ) 2 ' ' ' ' 2 2 4 2 2 ' ' ' ' ' ' 2 4 2 4 4 2 2 2 2 2 2 4 ' ' ' ' 4 4 1 =, with 64 ( ) ( ) ( ) ( ) ( ) ( ) In CMS variable a b a b a b a b a b a b a a b b a a b b a b a b a b b a a b a b d d s ig e ie p p ie p p p p p p q q e e s u p p p p p p p p s m m u m m e q q t m m µν ν µ µ µ σ π + + + + + + = = + + = + + = + + + = + − + + = ' ' ' ' 2 2 1 1 ' 2 2 2 2 ' s: cos( ) 2 1 cos ( ) cos 1 cos a b a a a a b b b b p a b a b a b a b a b E E m m a a a a a E E m m s u p p p p E E p E E p t m p p m E p CMS π θ β β θ θ θ = − = = = = + + + + + = = = − + p p where β i 1 stands for E i / p for particle i . In case where all masses can be neglected, β i 1 =1, the dif- ferential cross section becomes: 2 4 ' ' 2 CMS, ignoring all masses 3 cos 64 1 cos a b a b d e d s σ θ π θ + + + = which can be integrated. Note that the cross section goes to infinity for θ 0, which is related to the infinite range of the electromagnetic interaction! In practice, we define a minimum scattering angle, which depend on our interest and on the smallest angle that can be detected by our detec- tor. Physics sets a practical limit as well: small scattering angles correspond to large impact pa-

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HW 7 problems/solutions - Homework 6 1 Homework VII...

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