Spinning the Probe in Kerr with WQFT

Abstract

We investigate the gravitational scattering of a spinning probe mass in a Kerr background using the worldline quantum field theory (WQFT) approach. This corresponds to the leading term (0SF) in the gravitational self-force expansion for the spinning two-body problem with large mass hierarchy. By reformulating the geodesic and Mathisson-Papapetrou-Dixon equations as a recursive Berends-Giele type equation known from multi-gluon scattering, we develop a novel integration-by-parts formalism on the worldline that enables systematic computation of scattering observables - specifically the impulse and spin kick - to arbitrary orders in Newton's constant and spin. Here, the transition to a position space formalism is key. We present explicit results up to and including the physical 7PM order, thereby incorporating all relevant higher-spin and higher-curvature terms on the worldline, advancing beyond previous calculations. This work represents an initial step to reconceptualise the gravitational self-force expansion through worldline quantum field theory.