Computing Massive Five-Point Amplitudes from On-Shell Methods.

Over the past two decades, complex momentum shifts have enabled the computation of previously intractable scattering amplitudes. One such shift scheme—the all-line transverse shift for massive particles—has recently been applied to compute four-point electromagnetic and gravitational Compton amplitudes involving massive higher-spin particles. This method has also been shown to extend constructibility to five-point amplitudes with four massive external legs up to spin-5/2 in the gravitational case. In this work, we compute the electromagnetic and gravitational five-point amplitudes for four equal-mass scalars coupled to a photon or graviton. These results are particularly relevant to modeling Kerr black hole scattering. Our amplitudes are manifestly free of spurious poles. To support our computation, we also employed an inverse-soft approach, reconstructing the five-point amplitude from its soft limit. We are currently extending this analysis to the gravitational amplitude for spin-5/2 particles and electromagnetic amplitude for spin-3/2.