Abstract
We study positivity bounds in the presence of gravity. We first review the gravitational positivity bound at the tree-level, where it is known that a certain amount of negativity is allowed for the coefficients of higher-derivative operators. The size of these potentially negative contributions is estimated for several tree-level, Reggeized gravitational amplitudes which are unitary at high energies and feature the t-channel pole characteristic of graviton exchange. We also argue for the form of the one-loop Regge amplitude assuming that the branch cut structure associated with the exchange of the graviton and higher-spin particles is reflected. We demonstrate how the one-loop Regge amplitude appears by summing over Feynman diagrams. For our one-loop amplitude proposal, the positivity bounds generically receive a finite contribution from the Regge tower and do not lead to a parametrically small bound on the cut-off scale of the low-energy EFT, consistent with recent studies based on sum rules of the amplitude.
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Acknowledgments
The work of Y.H. and G.L. is supported in part by MEXT Leading Initiative for Excellent Young Researchers Grant Number JPMXS0320210099. The work of S.N. is supported in part by JSPS KAKENHI Grant Number 21J15497.
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Hamada, Y., Kuramochi, R., Loges, G.J. et al. On (scalar QED) gravitational positivity bounds. J. High Energ. Phys. 2023, 76 (2023). https://doi.org/10.1007/JHEP05(2023)076
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DOI: https://doi.org/10.1007/JHEP05(2023)076