Graviton particle statistics and coherent states from classical scattering amplitudes

TL;DR

This paper analyzes graviton particle distributions from classical scattering amplitudes, showing that the final radiation state can be described as a coherent state up to a certain order, with implications for quantum-classical correspondence.

Contribution

It introduces a method to compute graviton distributions using scattering amplitudes and demonstrates the coherent state nature of classical radiation at a specific perturbative order.

Findings

Final graviton distribution deviates from Poissonian due to quantum effects.

The classical radiation state can be modeled as a coherent state up to order G^4.

The amplitude calculations agree using different methods, confirming the results.

Abstract

In the two-body scattering problem in general relativity, we study the final graviton particle distribution using a perturbative approach. We compute the mean, the variance and the factorial moments of the distribution from the expectation value of the graviton number operator in the KMOC formalism. For minimally coupled scalar particles, the leading deviation from the Poissonian distribution is given by the unitarity cut involving the six-point tree amplitude with the emission of two gravitons. We compute this amplitude in two independent ways. First, we use an extension of the Cheung-Remmen parametrization that includes minimally coupled scalars. We then repeat the calculation using on-shell BCFW-like techniques, finding complete agreement. In the classical limit, this amplitude gives a purely quantum contribution, proving that we can describe the final semiclassical radiation state as a coherent state at least up to order $\mathcal{O}(G^4)$ for classical radiative observables. Finally, we give general arguments about why we expect this to hold also at higher orders in perturbation theory.