Special Galileon at one loop

Understand

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.