Graviton particle statistics and coherent states from classical scattering amplitudes

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 $$ \mathcal{O} $$ O (G4) for classical radiative observables. Finally, we give general arguments about why we expect this to hold also at higher orders in perturbation theory.

The Uncertainty Principle and Classical Amplitudes

“…One of our central observations was that six-point tree amplitudes are suppressed in the classical region. We showed explicitly that this suppression hold in scalar QED, but our more general arguments indicate that the suppression should hold in general relativity [39] and in perturbative/classical applications of Yang-Mills theory. This suppression of the six-point tree amplitude is consistent with classical intuition.…”

“…The question, then, of the fate of the six-point tree amplitude in the expectation value of two field strengths becomes a question of the overall scaling of six-point tree amplitudes in QED and gravity. We will shortly demonstrate explicitly that the QED amplitude in fact scale as −4 ; the gravitational case will be discussed in reference [39]. Two powers of cancel; consequently the contribution of the six-point tree to the variance is entirely at the quantum level.…”

“…We now compute the leading contribution in of the six-point tree amplitude. We will discuss the computation explicitly in electromagnetism, and explain only the mechanism for cancellation of apparent excess powers of in gravity (see also [39]).…”

Massive On-shell Recursion Relations for n-point Amplitudes

“…For example, we can give up condition (2.4) for massive particles and construct a shift, where masses are no longer invariants. The validity of this kind of shifts was examined numerically for the amplitudes with graviton and scalar bosons [23]. Here we try to satisfy all conditions.…”

Scattering Amplitudes and The Cotton Double Copy

“…Recent developments in scattering amplitudes have led to some intriguing formulations of purely classical physics directly in terms of the on-shell scattering amplitudes [1][2][3][4][5][6], including in theories in lower dimensions [7][8][9][10][11]. The double copy, which relates gauge and gravitational scattering amplitudes [8,9, also has several interesting classical formulations that relate solutions [39][40][41][42][43][44][45][46][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63] including the Weyl double copy [64][65][66][67][68][69][70], which we will explore here.…”