Abstract
Under reasonable working assumptions including the polynomial boundedness, one proves the well-known Cerulus-Martin lower bound on how fast an elastic scattering amplitude can decrease in the hard-scattering regime. In this paper we consider two non-trivial extensions of the previous bound. (i) We generalize the assumption of polynomial boundedness by allowing amplitudes to exponentially grow for some complex momenta and prove a more general lower bound in the hard-scattering regime. (ii) We prove a new lower bound on elastic scattering amplitudes in the Regge regime, in both cases of polynomial and exponential boundedness. A bound on the Regge trajectory for negative momentum transfer squared is also derived. We discuss the relevance of our results for understanding gravitational scattering at the non-perturbative level and for constraining ultraviolet completions. In particular, we use the new bounds as probes of non-locality in black-hole formation, perturbative string theory, classicalization, Galileons, and infinite-derivative field theories, where both the polynomial boundedness and the Cerulus-Martin bound are violated.
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Acknowledgments
L. B. is grateful to Anna Tokareva for her hospitality at Imperial College London during the final stages of this work and would like to thank The Royal Society for financial support. Nordita is supported in part by NordForsk. J.T. is supported by IBS under the project code, IBS-R018-D1. M.Y. is supported by IBS under the project code, IBS-R018-D3, and by JSPS Grant-in-Aid for Scientific Research Number JP21H01080.
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Buoninfante, L., Tokuda, J. & Yamaguchi, M. New lower bounds on scattering amplitudes: non-locality constraints. J. High Energ. Phys. 2024, 82 (2024). https://doi.org/10.1007/JHEP01(2024)082
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DOI: https://doi.org/10.1007/JHEP01(2024)082