Calculation without IR divergence of the soft photon high energy limit of final state radiation for the process $e^{+}e^{-}\rightarrow\mu^{+}\mu^{-}\gamma$

Abstract

In this paper it is shown that the final state radiation process $e^{+}e^{-}\rightarrow\mu^{+}\mu^{-}\gamma$ at tree level is not associated with any IR divergence in the soft photon high energy limit if the calculation is done using a careful treatment of a certain distributional object (in fact, a measure) arising from the Feynman amplitude for the process. Thus there need be no "infrared catastrophe" associated with the process. It is shown that, in fact, the cross section for the final state photons for the the process vanishes in the soft photon high energy limit.