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Cross-section for elastic scattering?

  1. Aug 28, 2013 #1
    Hi All,

    Following on from the last dumb question I asked...

    Suppose you calculate the tree-level approximation to the elastic scattering of two charged fermions
    to find that the result varies as ##\sim 1/t##, where t is the Mandelstam variable describing the squared momentum transfer in the centre of mass frame.

    To work out the corresponding cross-section, you integrate the square modulus of this over t with t=0 as one of your limits of integration, so that the result diverges. Why is this not regarded as a problem?
  2. jcsd
  3. Aug 28, 2013 #2


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    This is regarded as a problem, a socalled collinear singularity. It always occurs for theories with massless particles exchanged in the t and u channels. The cure is a resummation in this channel. Look at Weinberg, Quantum Theory of Fields, Vol. I. There's a whole chapter is devoted to infrared problems.
  4. Aug 28, 2013 #3
    Thanks for your reply. I've heard of collinear singularities, but I'd always had the impression that such singularities cancelled other divergences from the same order in perturbation theory- e.g. infrared divergences in loop integrals being cancelled by those from bremstrahlung, so I couldn't see how such higher-order terms would cancel a tree-level effect. Guess I need to look into Weinberg, thanks.
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