Universality of Loop Corrected Soft Theorems in 4d

TL;DR

This paper demonstrates the universality of loop-corrected soft theorems in four dimensions across various spins and couplings, extending previous scalar-based results and discussing quantum corrections.

Contribution

It generalizes the derivation of loop-corrected soft theorems to include spinning particles with non-minimal couplings, confirming their universal nature.

Findings

Soft factors are universal across different spins and couplings.

Loop corrections up to two loops are summarized for QED and gravity.

Conjectures on quantum soft factors are proposed.

Abstract

In \cite{1808.03288}, logarithmic correction to subleading soft photon and soft graviton theorems have been derived in four spacetime dimensions from the ratio of IR-finite S-matrices. This has been achieved after factoring out IR-divergent components from the traditional electromagnetic and gravitational S-matrices using Grammer-Yennie prescription. Although the loop corrected subleading soft theorems are derived from one-loop scattering amplitudes involving scalar particles in a minimally coupled theory with scalar contact interaction, it has been conjectured that the soft factors are universal (theory independent) and one-loop exact (don't receive corrections from higher loops). This paper extends the analysis conducted in \cite{1808.03288} to encompass general spinning particle scattering with non-minimal couplings permitted by gauge invariance and general coordinate invariance. By re-deriving the $\ln\omega$ soft factors in this generic setup, we establish their universal nature. Furthermore, we summarize the results of loop corrected soft photon and graviton theorems up to sub-subleading order, which follows from the analysis of one and two loop QED and quantum gravity S-matrices. While the classical versions of these soft factors have already been derived in the literature, we put forth conjectures regarding the quantum soft factors and outline potential strategies for their derivation.