Speaker
Description
Infrared divergences have long been heralded to cancel in sufficiently inclusive cross sections, according to the famous Kinoshita-Lee-Nauenberg (KLN) theorem. The theorem states that summing over all initial and final states with energies in some compact energy window around a reference energy $E_0$ guarantees finiteness. While well-motivated, this theorem is much weaker than necessary: for finiteness, one need only sum over initial or final states. Moreover, the cancellation generically requires the inclusion of the forward scattering process. We provide some examples showing the importance of this revised understanding. The process $e^+ e^- \to Z$ can be made IR finite at next-to-leading order in three ways: One can sum over either initial or final states with a finite number of photons if forward scattering is included, as dictated by the KLN theorem, or use a third way of summing over certain initial and final states with an arbitrary number of extra photons. We furthermore discuss why the rate for γγ to scatter into photons alone is infrared divergent but the rate for γγ to scatter into photons or charged particles is finite. This new understanding sheds light on the importance of including degenerate initial states in physical predictions, the relevance of disconnected Feynman diagrams, the importance of dressing initial or final-state charged particles, and the quest to properly define the S matrix.
