On-shell recursion relations for higher-spin Compton amplitudes

TL;DR

This paper develops on-shell recursion relations for constructing higher-spin electromagnetic and gravitational amplitudes, extending the method's applicability up to certain high spins and clarifying their physical properties.

Contribution

It introduces a recursive construction method for higher-spin Compton amplitudes using all-line transverse momentum shifts, valid up to specific spins, and derives unique four-point amplitudes free of unphysical poles.

Findings

Successfully construct higher-spin Compton amplitudes up to s=3/2 and 5/2.

Derive unique four-point amplitudes free from spurious poles.

Explore non-minimal interactions and features of higher-spin particles.

Abstract

We recursively construct tree-level electromagnetic and gravitational Compton amplitudes of higher-spin massive particles by the all-line transverse momentum shift. With three-point amplitude as input, we demonstrate that higher-point electromagnetic and gravitational Compton amplitudes are on-shell constructible up to spin $s = 3/2$ and $s = 5/2$, respectively, under the all-line transverse shift after imposing the current constraint condition. We unambiguously derive the four-point electromagnetic and gravitational Compton amplitudes for $s \leq 3/2$ and $s \leq 5/2$, which are uniquely determined by the on-shell recursion relation and are free from unphysical spurious poles. In addition, we explore amplitudes of spin-$3/2$ particles with non-minimal three-point interactions with photon, as well as $s > 3/2$ particles, and comment on their notable features. Our work furthers the understanding of on-shell methods for massive amplitudes, with hopes to shed light on physical observables in particle physics and higher-spin amplitudes relevant for Kerr black-hole scattering.