Amplitudes and Renormalization Group Techniques: A Case Study

TL;DR

This paper investigates a simple higher derivative model with renormalization techniques, revealing its scattering behavior and parameter running, offering insights potentially applicable to higher derivative gravity theories.

Contribution

It introduces a toy model with higher derivatives, analyzes its scattering amplitudes and renormalization, and compares results with other methods to gain insights relevant to gravity.

Findings

Amplitude is normal below ghost production threshold

Amplitude becomes unexpectedly soft above threshold

Parameter running matches other methods only in limits

Abstract

We explore the properties of a simple renormalizable shift symmetric model with a higher derivative kinetic energy and quartic derivative coupling, that can serve as a toy model for higher derivative theories of gravity. The scattering amplitude behaves as in a normal effective field theory below the threshold for the production of ghosts, but has an unexpectedly soft behavior above the threshold. The physical running of the parameters is extracted from the 2-point and 4-point amplitudes. The results are compared to those obtained by other methods and are found to agree only in limiting cases. We draw several lessons that may apply also to gravity.