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arXiv · 2506.02106

On-shell recursion relations for higher-spin Compton amplitudes

Yohei Ema·Ting Gao·Wenqi Ke·Zhen Liu·Ishmam Mahbub
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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.

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Yohei Ema, Ting Gao, Wenqi Ke, Zhen Liu, Ishmam Mahbub. 2025-06-02. On-shell recursion relations for higher-spin Compton amplitudes. https://arxiv.org/abs/2506.02106

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