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 the one-loop on-shell renormalization and prove the invariance of the oneloop on-shell effective action with respect to the Special Galileon symmetry.
This enables us to enlarge the validity of the enhanced O(p3) 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.