# Massive Galileon Positivity Bounds

## TL;DR

This paper investigates the positivity bounds on massive Galileon theories, demonstrating that with appropriate higher derivative corrections, these theories can have consistent local UV completions, supported by explicit examples.

## Contribution

It applies positivity bounds to massive Galileon theories and shows how higher derivative corrections enable consistent UV completions.

## Key findings

- Mass term is essential for lowest order positivity bounds.
- Higher derivative corrections are necessary for higher order bounds.
- Explicit UV completion example provided.

## 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.