Abstract
We study the compatibility of recursive techniques with the classical limit of scattering amplitudes through the construction of the classical Compton amplitude for general spinning compact objects. This is done using BCFW recursion on three-point amplitudes expressed in terms of the classical spin vector and tensor, and expanded to next-to-leading-order in ћ by using the heavy on-shell spinors. Matching to the result of classical computations, we find that lower-point quantum contributions are, in general, required for the recursive construction of classical, spinning, higher-point amplitudes with massive propagators. We are thus led to conclude that BCFW recursion and the classical limit do not commute. In possession of the classical Compton amplitude, we remove non-localities to all orders in spin for opposite graviton helicities, and to fifth order in the same-helicity case. Finally, all possible on-shell contact terms potentially relevant to black-hole scattering at the second post-Minkowskian order are enumerated and written explicitly.
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Acknowledgments
Four-vector manipulations were performed using FeynCalc [86,87,88]. I am grateful in particular to Lucile Cangemi, Henrik Johansson, and Andres Luna for very helpful discussions about this work. I would also like to thank Francesco Alessio, Rafael Aoude, Fabian Bautista, Alessandro Georgoudis, Andreas Helset, Paolo Pichini, and Justin Vines for stimulating discussions about this and related topics. Furthermore, I thank Andres Luna and Fei Teng, and Muddu Saketh and Justin Vines for sharing unpublished versions of their Compton amplitudes for comparison. For comments on the manuscripts, I thank Rafael Aoude, Andreas Helset, Henrik Johansson, Jung-Wook Kim, and Andres Luna. I am grateful to Nordita for their ongoing hospitality. This work is supported by the Knut and Alice Wallenberg Foundation under grants KAW 2018.0116 (From Scattering Amplitudes to Gravitational Waves) and KAW 2018.0162.
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Haddad, K. Recursion in the classical limit and the neutron-star Compton amplitude. J. High Energ. Phys. 2023, 177 (2023). https://doi.org/10.1007/JHEP05(2023)177
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DOI: https://doi.org/10.1007/JHEP05(2023)177