Special Galileon at one loop

TL;DR

This paper provides a comprehensive one-loop renormalization of the Special Galileon S-matrix, including higher derivative operators and symmetry invariance, extending the soft behavior to the quantum level.

Contribution

It offers the first complete one-loop renormalization framework for the Special Galileon, detailing necessary operators and symmetry properties.

Findings

Explicit four-point and five-point one-loop amplitudes computed.

Confirmed invariance of the effective action under Galileon symmetry.

Extended soft behavior validity to one-loop level.

Abstract

We present a complete one-loop renormalization of the Special Galileon $S-$matrix. Especially we give a complete list of the higher derivative operators which are necessary for one-loop on-shell renormalization and prove the invariance of the one-loop on-shell effective action with respect to the Special Galileon symmetry. This enables us to enlarge the validity of the enhanced $O(p^3)$ soft behavior of the scattering amplitudes to the one-loop level. As an illustration we discuss explicitly the four-point and five-point one-loop scattering amplitudes and comment on some conjectures appearing in the existing literature.