Recursion in the classical limit and the neutron-star Compton amplitude

We study the compatibility of recursive techniques with the classical limit of scattering amplitudes through the construction of the classical Compton amplitude for general spinning compact objects. This is done using BCFW recursion on three-point amplitudes expressed in terms of the classical spin vector and tensor, and expanded to next-to-leading-order in h by using the heavy on-shell spinors. Matching to the result of classical computations, we find that lower-point quantum contributions are, in general, required for the recursive construction of classical, spinning, higher-point amplitudes with massive propagators. We are thus led to conclude that BCFW recursion and the classical limit do not commute. In possession of the classical Compton amplitude, we remove non-localities to all orders in spin for opposite graviton helicities, and to fifth order in the same-helicity case. Finally, all possible on-shell contact terms potentially relevant to black-hole scattering at the second post-Minkowskian order are enumerated and written explicitly.

Automated summary

In this study, we investigate the compatibility of recursive techniques and the classical limit of scattering amplitudes by constructing the classical Compton amplitude for spinning compact objects. By using BCFW recursion on three-point amplitudes expressed in terms of classical spin vector and tensor, and expanding it to next-to-leading-order using heavy on-shell spinors, we match the result with classical computations and find that lower-point quantum contributions are generally required for building classical spinning higher-point amplitudes with massive propagators. Therefore, we conclude that BCFW recursion and the classical limit do not commute. We also remove non-localities in all orders of spin for opposite graviton helicities and up to fifth order for the same-helicity case. Finally, we list and explicitly write all possible on-shell contact terms that are potentially relevant to black-hole scattering at the second post-Minkowskian order.