# Soft Photon Theorem for High Energy Amplitudes in Yukawa and Scalar Theories

## TL;DR

This paper extends the soft photon theorem to high energy scattering in Yukawa and scalar theories, revealing how subleading corrections depend on jet structures and employing advanced techniques like jet Ward identities and Grammer-Yennie decomposition.

## Contribution

It adapts methods from QED to scalar and Yukawa theories, analyzing subleading soft photon corrections and their relation to jet structures at all loop orders.

## Key findings

- Subleading corrections depend on non-leading jet structures.
- Jet Ward identities help analyze soft photon emissions.
- Gauge invariant contributions are isolated via Grammer-Yennie decomposition.

## Abstract

We study the emission of soft photons coupling to high energy fixed angle scattering processes at first order in the electromagnetic coupling but to all loop orders in a class of theories without soft divergences, including massive and massless Yukawa and scalar theories. We adapt a method introduced by del Duca for quantum electrodynamics to show that subleading corrections to the soft photon theorem are sensitive to the structure of non leading external jets of collinear lines. Our techniques are based on a power counting analysis of loop integrals and an application of jet Ward identities. We also apply Grammer and Yennie's decomposition to isolate separately gauge invariant contributions to the soft photon expansion. These are interpreted as infrared sensitive matrix elements coupling to a field strength tensor.