Abstract
We calculate the inelastic 2 → 3 one-loop amplitude for the scattering of two point-like, spinless objects with generic masses involving the additional emission of a single graviton. We focus on the near-forward, or classical, limit. Our results include the leading and subleading orders in the soft-region expansion, which captures all non-analytic contributions in the transferred momentum and in the graviton’s frequency. This allows us to check the first constraint arising from the inelastic exponentiation put forward in refs. [1,2,3], and to calculate the 2 → 3 one-loop matrix element of the N-operator, linked to the S-matrix by S = eiN, showing that it is real, classical and free of infrared divergences. We discuss how our results feature in the calculation of the \( \mathcal{O} \)(G3) corrections to the asymptotic waveform.
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Acknowledgments
We would like to thank Francesco Alessio, Paolo Di Vecchia, Kays Haddad, Martijn Hidding, Henrik Johansson, Gregor Kälin, Stephen Naculich, Ben Page, Rodolfo Russo, Augusto Sagnotti, Fei Teng, and Gabriele Veneziano for very useful discussions. The research of CH is supported by the Knut and Alice Wallenberg Foundation under grant KAW 2018.0116. IVH is supported by the Knut and Alice Wallenberg Foundation under grants KAW 2018.0116 and KAW 2018.0162. Nordita is partially supported by Nordforsk.
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Georgoudis, A., Heissenberg, C. & Vazquez-Holm, I. Inelastic exponentiation and classical gravitational scattering at one loop. J. High Energ. Phys. 2023, 126 (2023). https://doi.org/10.1007/JHEP06(2023)126
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DOI: https://doi.org/10.1007/JHEP06(2023)126