On-shell recursion relations for higher-spin Compton amplitudes

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 ≤ 3/2 and s ≤ 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.