Bootstrapping spinning two body problem in dynamical Chern-Simons gravity using worldline QFT

TL;DR

This paper calculates the eikonal phase for spinning black hole scattering in dynamical Chern-Simons gravity using worldline QFT, providing new insights into spin effects at high orders.

Contribution

It introduces a novel computation of the spinning black hole scattering phase in dynamical Chern-Simons gravity using worldline quantum field theory techniques.

Findings

Computed the linear-in-spin eikonal phase up to 3PM order.

Developed two-loop integral calculations using IBP and differential equations.

Analyzed the dependence of the phase on black hole spin orientations.

Abstract

In this paper, we compute the WQFT partition function, specifically the eikonal phase in a black hole scattering event in the dynamical Chern-Simons theory, using the techniques of spinning worldline quantum field theory. We consider the scattering of spinning black holes and highlight the necessary details for the calculation of the partition function. We present the $\epsilon$-expansion of the essential two-loop integrals using Integration-by-Parts (IBP) reduction and differential equation techniques, which we then utilize to compute the linear-in-order spin eikonal phase up to 3PM. Additionally, we discuss the dependence of the phase on the spin orientations of the black holes.