High-energy properties of the graviton scattering in quadratic gravity

We obtain the matter-graviton scattering amplitude in the gravitational theory of quadratic curvature, which has R-mu upsilon(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.

Automated summary

This paper investigates the matter-graviton scattering amplitude in the gravitational theory of quadratic curvature, which includes an R-mu upsilon(2) term in the action. The existence of negative norm states leads to the violation of unitarity bound, although a version of unitarity bound for S matrix unitarity is still held due to the cancelation among positive and negative norm states in the unitarity summation in the optical theorem. The violation of unitarity bound serves as a counter example for Llewellyn Smith's conjecture, and a new conjecture relating S-matrix unitarity to renormalizability is proposed.