Massive Galileon Positivity Bounds

TL;DR

The work examines whether a gapped, Lorentz-invariant scalar EFT with a massive Galileon can admit a local analytic Wilsonian UV completion under positivity bounds. It shows that a mass term $m^2$ is required to satisfy the leading positivity constraint, and that satisfying higher-order bounds necessitates carefully chosen higher-derivative, Galileon-invariant operators. Under a tree-level analysis with $m\ll\Lambda$, there is no obstruction to a local UV completion, and the authors construct an explicit simple UV completion to demonstrate this. The analysis extends beyond the forward limit, illustrating that non-forward positivity bounds can impose nontrivial constraints on the EFT and its UV completion.

Abstract

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.