Abstract
We compute the next-to-leading order term in the scattering waveform of uncharged black holes in classical general relativity and of half-BPS black holes in \( \mathcal{N} \) = 8 supergravity. We propose criteria, generalizing explicit calculations at next-to-leading order, for determining the terms in amplitudes that contribute to local observables. For general relativity, we construct the relevant classical integrand through generalized unitarity in two distinct ways, (1) in a heavy-particle effective theory and (2) in general relativity minimally-coupled to scalar fields. With a suitable prescription for the matter propagator in the former, we find agreement between the two methods, thus demonstrating the absence of interference of quantum and classically-singular contributions. The classical \( \mathcal{N} \) = 8 integrand for massive scalar fields is constructed through dimensional reduction of the known five-point one-loop integrand. Our calculation exhibits novel features compared to conservative calculations and inclusive observables, such as the appearance of master integrals with intersecting matter lines and the appearance of a classical infrared divergence whose absence from classical observables requires a suitable definition of the retarded time.
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Acknowledgments
We thank A. Elkhidir, D. O’Connell, M. Sergola, I. Vazquez-Holm, and A. Brandhuber, G. Brown, G. Chen, S. De Angelis, J. Gowdy, G. Travaglini for coordination on ongoing work. We also thank N. Arkani-Hamed, R. Akhoury, J. Berman, R. Britto, L. Dixon, H. Elvang, S. Mizera and C.-H. Shen for stimulating discussions. RR and FT also thank Z. Bern, E. Herrmann, J. Parra-Martinez, M. Ruf, C.-H. Shen, and M. Zeng for collaboration on related topics, and especially M. Ruf for providing valuable comments on our draft. RR and FT would like to thank the Kavli Institute for Theoretical Physics at the University of California, Santa Barbara, for hospitality during the program “High-Precision Gravitational Waves”. Their research there was supported in part by the National Science Foundation under Grant No. NSF PHY-1748958. AH is supported by a Rackham Predoctoral Fellowship from the University of Michigan. RR and FT are supported by the U.S. Department of Energy (DOE) under award number DE-SC00019066.
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Herderschee, A., Roiban, R. & Teng, F. The sub-leading scattering waveform from amplitudes. J. High Energ. Phys. 2023, 4 (2023). https://doi.org/10.1007/JHEP06(2023)004
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DOI: https://doi.org/10.1007/JHEP06(2023)004