Abstract
We obtain the matter-graviton scattering amplitude in the gravitational theory of quadratic curvature, which has \( {R}_{\mu \nu}^2 \) term in the action. Unitarity bound is not satisfied because of the existence of negative norm states, while an analog of unitarity bound for S-matrix unitarity holds due to the cancelation among the positive norm states and negative norm ones in the unitarity summation in the optical theorem. The violation of unitarity bound is a counter example of Llewellyn Smith’s conjecture on the relation between tree-level unitarity and renormalizability. We have recently proposed a new conjecture that an analog of the unitarity bound for S-matrix unitarity gives the equivalent conditions to those for renormalizability. We show that the gravitational theory of quadratic curvature is a nontrivial example consistent with our conjecture.
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Abe, Y., Inami, T. & Izumi, K. High-energy properties of the graviton scattering in quadratic gravity. J. High Energ. Phys. 2023, 213 (2023). https://doi.org/10.1007/JHEP03(2023)213
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DOI: https://doi.org/10.1007/JHEP03(2023)213