In QFT when one works out the cross section between two colliding electrons one gets a formula which is proportional to $\theta^{-4}$ where $\theta$ is the scattering angle which is due to a nearly on-shell photon with momentum $\approx 0$. See for example Peskin and Schroeder pg 155. This is also seen in ordinary Rutherford scattering and apparently is not a problem experimentally as one can't detect particles along the collision beam. Also, in Rutherford scattering the singularity gets removed if one takes into account the screening of the nucleus by the electron cloud (see QM by Messiah (1961), pg 422) which modifies the Coulomb nature of the potential.
I was wondering if this singularity is indicating some problem with the calculation? Is there some effect in the calculation which has been neglected which when included would remove the singularity? Could renormalization effects maybe have a similar effect to the electron cloud in the Rutherford case?
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