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arXiv · 2210.13666

High-energy properties of the graviton scattering in quadratic gravity

Yugo Abe·Takeo Inami·Keisuke Izumi
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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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Yugo Abe, Takeo Inami, Keisuke Izumi. 2022-10-25. High-energy properties of the graviton scattering in quadratic gravity. https://doi.org/10.1007/jhep03(2023)213

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