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

TL;DR

This paper investigates how recursive amplitude techniques relate to the classical limit, revealing that they do not commute, and constructs classical Compton amplitudes for spinning objects, with implications for black-hole scattering.

Contribution

It demonstrates the non-commutativity of BCFW recursion and the classical limit and constructs explicit classical Compton amplitudes for spinning objects up to high orders.

Findings

Lower-point quantum contributions are needed for classical amplitude recursion.

Classical Compton amplitudes are obtained with reduced non-localities.

Explicit contact terms for black-hole scattering at second post-Minkowskian order are provided.

Abstract

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 $\hbar$ 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.