  We investigate the renormalization structure of scalar Galileons in flat
spacetime. We explicitly calculate the ultraviolet divergent one-loop
contributions to the 2-point, 3-point, 4-point, and 5-point functions. We
discuss the structure of the counterterms and their hierarchy within an
effective field theory expansion. We comment on different resummation schemes,
including a geometric resummation for which our results could be generalized to
arbitrary n-point functions.
