Exact Infrared Triangle in Massless sQED with Long-range Interactions

TL;DR

This paper investigates the asymptotic symmetries and soft photon theorems in massless scalar QED, revealing that certain divergent charges vanish and that long-range interactions do not produce velocity memory effects.

Contribution

It extends the understanding of soft photon theorems and asymptotic symmetries to massless matter, showing the vanishing of divergent superphase rotation charges and analyzing infrared corrections.

Findings

Divergent superphase rotation charge vanishes to all orders.

Infrared corrections to subleading soft photon charge computed.

Velocity kick memory due to long-range interactions vanishes.

Abstract

The logarithmic soft photon theorem in four spacetime dimensions encodes an infinite-dimensional asymptotic symmetry which acts on massive matter as a divergent superphaserotation. Here we extend this result to massless matter which is both more subtle and surprising. We derive the charge associated to divergent superphaserotations and show that it exactly vanishes to all orders in the electromagnetic coupling. This is in agreement with the vanishing of the classical logarithmic soft photon theorem which is one-loop exact. Special care is required for massless matter due to potential collinear divergences which, as we show, do however not affect the superphaserotation charge. We furthermore compute the infrared corrections to the charge associated to the subleading tree-level soft photon theorem. As a corollary of our result, we find that the tail to the velocity kick memory due to the long-range interactions between soft electromagnetic radiation and massless matter vanishes.