Abstract
An important element of the S-matrix bootstrap program is the relationship between the modulus of an S-matrix element and its phase. Unitarity relates them by an integral equation. Even in the simplest case of elastic scattering, this integral equation cannot be solved analytically and numerical approaches are required. We apply modern machine learning techniques to studying the unitarity constraint. We find that for a given modulus, when a phase exists it can generally be reconstructed to good accuracy with machine learning. Moreover, the loss of the reconstruction algorithm provides a good proxy for whether a given modulus can be consistent with unitarity at all. In addition, we study the question of whether multiple phases can be consistent with a single modulus, finding novel phase-ambiguous solutions. In particular, we find a new phase-ambiguous solution which pushes the known limit on such solutions significantly beyond the previous bound.
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Acknowledgments
We would like to thank Filip Niewinski for their collaboration in the early stages of this work. We also thank Zohar Komargodski, Piotr Tourkine, and Jiaxin Qiao for useful discussions. AD and MDS are supported in part by the National Science Foundation under Cooperative Agreement PHY-2019786 (The NSF AI Institute for Artificial Intelligence and Fundamental Interactions). This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement number 949077).
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Dersy, A., Schwartz, M.D. & Zhiboedov, A. Reconstructing S-matrix Phases with Machine Learning. J. High Energ. Phys. 2024, 200 (2024). https://doi.org/10.1007/JHEP05(2024)200
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DOI: https://doi.org/10.1007/JHEP05(2024)200