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

TL;DR

This paper demonstrates that the process $e^{+}e^{-} ightarrow ext{muon pair}+ ext{photon}$ at tree level does not exhibit IR divergence in the soft photon high energy limit when using a careful distributional approach, eliminating the infrared catastrophe.

Contribution

It introduces a method to compute the process without IR divergence by carefully handling a distributional object, showing the cross section vanishes in the limit.

Findings

No IR divergence in the soft photon high energy limit.

Cross section for final state photons vanishes in this limit.

Infrared catastrophe is avoided with the new approach.

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.