Cross-section for elastic scattering?

[muppet]

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?

 

[vanhees71]

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.

 

[muppet]

Thanks for your reply. I've heard of collinear singularities, but I'd always had the impression that such singularities canceled other divergences from the same order in perturbation theory- e.g. infrared divergences in loop integrals being canceled 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.