Abstract
We initiate a study into the eikonal exponentiation of the amplitude in impact-parameter space when spinning particles are involved in the scattering. Considering the gravitational scattering of two spin-1/2 particles, we demonstrate that the leading eikonal exhibits exponentiation up to $\mathcal{O}(G^{2})$ in the limit where the spacetime dimension $D\rightarrow4$. We find this to hold for general spin orientations. The exponentiation of the leading eikonal including spin is understood through the unitarity properties at leading order in $\hbar$ of momentum-space amplitudes, allowing the extension of our results to arbitrary-spin scattering.
Highlights
The application of scattering amplitude and quantumfield theoretic techniques to classical systems has expanded rapidly in recent years, largely motivated by describing the inspiral phase of compact binary coalescence
Scattering dynamics are understood for arbitrary spin at 1PM order [17,19,20,22,25], while progress at higher PM orders presently lays at 2PM and quadratic order in spin [23,26,27]
Progress in this direction is restricted by the lack of a unique gravitational Compton amplitude for a massive particle with spin s > 5=2 [16,22,28], with the s 1⁄4 5=2 Compton amplitude being fixed only recently [29]
Summary
The application of scattering amplitude and quantumfield theoretic techniques to classical systems has expanded rapidly in recent years, largely motivated by describing the inspiral phase of compact binary coalescence. Phenomenological predictions have been made accessible to amplitudes-based techniques thanks to various formalisms bridging the gap between quantum field theory and classical physics [1,18,23,25,35,36,37,38,39,40,41,42,43,44,45] One such path to classical observables makes use of the eikonal phase, related to the classical portion of the scattering amplitude in impact-parameter space [7,8,9,46,47,48].
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