High-energy properties of the graviton scattering in quadratic gravity

TL;DR

This paper analyzes the high-energy behavior of graviton scattering in quadratic gravity, revealing unitarity violations at the matter level but consistency with a new conjecture relating unitarity and renormalizability.

Contribution

It provides the first detailed calculation of matter-graviton scattering in quadratic gravity and tests a new conjecture linking unitarity bounds to renormalizability.

Findings

Unitarity bound is violated due to negative norm states.

An analog of the unitarity bound for S-matrix unitarity holds.

Quadratic gravity supports the new conjecture relating unitarity and renormalizability.

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.