From Scattering Amplitudes to Classical Physics: Universality, Double Copy and Soft Theorems

TL;DR

This paper develops a covariant multipole expansion for scattering amplitudes involving massive particles emitting photons or gravitons, revealing universal features and a new double copy relation, with applications to classical radiation and memory effects.

Contribution

It introduces a covariant multipole expansion and a novel double copy procedure for massive spinning states, linking quantum amplitudes to classical observables in gravity.

Findings

Amplitudes exhibit universality, soft exponentiation, and multipole structures.

A new double copy relates photon and graviton amplitudes for spinning states.

Derived an exponential soft theorem connecting conservative effects and gravitational radiation.

Abstract

We introduce a covariant Multipole Expansion for the scattering of a massive particle emitting photons or gravitons in $D$ dimensions. We find that these amplitudes exhibit very powerful features such as universality, soft exponentiation, orbit and spin multipoles, etc. Using ${\rm{SO}}(D)$ representation theory we show that the photon and graviton amplitudes are related via a new double copy procedure for massive spinning states. All these features are then promoted to properties of the observables arising in the classical version of such theories. Focusing on radiation, we provide two main applications: 1) An exponential Soft Theorem relating conservative effects and gravitational radiation to all orders in $\omega$; whose leading order directly leads to the $D=4$ Memory Effect. 2) A classical double copy to evaluate gravitational radiation from QED Bremsstrahlung, matching previous classical computations and extending them to spin-quadrupole order.