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

Graviton particle statistics and coherent states from classical scattering amplitudes