Abstract
The quantum off-shell recursion provides an efficient and universal computational tool for loop-level scattering amplitudes. In this work, we present a new comprehensive computational framework based on the quantum off-shell recursion for binary black hole systems. Using the quantum perturbiner method, we derive the recursions and solve them explicitly up to two-loop order. We introduce an indicator that enables straightforward distinguishing diagrams and deriving integral families in the context of off-shell recursions. By employing the soft expansion technique, we remove irrelevant terms from the loop integrands and express them in terms of master integrals. We classify the one-loop and the two-loop classical diagrams, and their loop integrands are represented by linear combinations of the master integrals. Finally, we explicitly calculate the classical scalar 2 → 2 amplitudes in the potential region up to the 3PM order and reproduce the known results.
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Acknowledgments
We thank Jung-Wook Kim, Seok Kim, Sangmin Lee, and Mao Zeng for their useful comments and discussion. We would like to express our special gratitude to Kimyeong Lee and Jeong-Hyuck Park for suggesting to initiate this work and encouraging us. This work is supported by appointment to the JRG Program at the APCTP through the Science and Technology Promotion Fund and Lottery Fund of the Korean Government. KL is also supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) RS-2023-00249451 and the Korean Local Governments of Gyeongsangbuk-do Province and Pohang City. KC is supported by the NRF grant funded by the Korean government (MSIT) 2022R1F1A1068489.
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Cho, K., Kim, K. & Lee, K. Binary black holes and quantum off-shell recursion. J. High Energ. Phys. 2024, 50 (2024). https://doi.org/10.1007/JHEP05(2024)050
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DOI: https://doi.org/10.1007/JHEP05(2024)050