Revisiting unitarity of single scalar field with non-minimal coupling

TL;DR

This paper analyzes the unitarity violation scale of a non-minimally coupled scalar field with quartic self-coupling, demonstrating frame-independence of the results through six-point scattering amplitude calculations.

Contribution

It provides a consistent estimation of the unitarity violation scale in both Jordan and Einstein frames for the first time in this context.

Findings

Frame-independence of unitarity violation scale confirmed

Dominant contribution from scalar potential in single-field case

Results trivial in the zero self-coupling limit

Abstract

We have investigated the unitarity violation scale of a non-minimally coupled scalar field with quartic self-coupling. This model is widely studied in the literature but the estimation of the unitarity violation scale has not been consistently discussed, especially in the Jordan frame. We have calculated the six-point scattering amplitudes of the scalar particles in both the Jordan frame and the Einstein frame, and explicitly shown the frame-independence of the results. Since the extended target space with the conformal mode is trivial in the single-field case, the dominant contribution comes from the potential of the scalar field. The results in both frames become trivial in the vanishing self-coupling limit as expected.