Tidal effects in quantum field theory

TL;DR

This paper extends the gravitational action with higher-dimensional operators to include tidal effects, computes leading-order tidal effects for spinless particles, and derives corrections to the Hamiltonian and scattering angle.

Contribution

It introduces a complete basis of higher-dimensional operators for tidal effects using the Hilbert series and applies it to compute leading post-Minkowskian tidal effects.

Findings

Derived all spinless tidal effects at leading post-Minkowskian order.

Simplified calculations using the heavy limit and classical contributions.

Obtained $ ext{O}(G^2)$ tidal corrections to Hamiltonian and scattering angle.

Abstract

We apply the Hilbert series to extend the gravitational action for a scalar field to a complete, non-redundant basis of higher-dimensional operators that is quadratic in the scalars and the Weyl tensor. Such an extension of the action fully describes tidal effects arising from operators involving two powers of the curvature. As an application of this new action, we compute all spinless tidal effects at the leading post-Minkowskian order. This computation is greatly simplified by appealing to the heavy limit, where only a severely constrained set of operators can contribute classically at the one-loop level. Finally, we use this amplitude to derive the $\mathcal{O}(G^{2})$ tidal corrections to the Hamiltonian and the scattering angle.