Massive Galileon Positivity Bounds
  The EFT coefficients in any gapped, scalar, Lorentz invariant field theory
must satisfy positivity requirements if there is to exist a local, analytic
Wilsonian UV completion. We apply these bounds to the tree level scattering
amplitudes for a massive Galileon. The addition of a mass term, which does not
spoil the non-renormalization theorem of the Galileon and preserves the
Galileon symmetry at loop level, is necessary to satisfy the lowest order
positivity bound. We further show that a careful choice of successively higher
derivative corrections are necessary to satisfy the higher order positivity
bounds. There is then no obstruction to a local UV completion from
considerations of tree level 2-to-2 scattering alone. To demonstrate this we
give an explicit example of such a UV completion.
