# Infrared divergences in scattering amplitude The S-matrix for scattering massless particles can have so-called infrared divergences associated to singularities when external legs become [[0009 Soft theorems|soft]] or [[0078 Collinear limit|collinear]]. More precisely, in theories like Yang-Mills and gravity, an infrared cutoff, $\Lambda_{I R}$, must be introduced in order to define the S-matrices. As $\Lambda_{I R} \rightarrow 0$, the amplitudes simply vanish because the emission of infinitely many soft particles dominates the scattering process. ## Refs - historical - [[BlochNordsieck1937]]: the first to consider IR divergences (in QED) - KLN theorem - [[Kinoshita1962]] - [[LeeNauenberg1964]] - [[2021#Magnea]] - review - [[2021#Agarwal, Magnea, Signorile-Signorile, Tripathi]] ## Infrared effective action - [[NguyenSalzer2020]] - [[2021#Nguyen, Salzer]] ## 2D models for the IR sector - [[2020#Kalyanapuram]]: QED - [[2021#Magnea]]: non-Abelian ## Soft factorisation - [[0009 Soft theorems]] - [[0609 Soft factorisation]] ## Collinear singularity - [[0078 Collinear limit]] - [[0077 Multi-collinear limit]] ## By theory - soft magnetic charges of Maxwell and soft charges of YM - [[2021#Cohen]] ## Hilbert space with memory and superscattering matrix - [[2022#Prabhu, Satishchandran, Wald]] - [[2024#Prabhu, Satishchandran]]