Beyond Amplitudes' Positivity and the Fate of Massive Gravity
We constrain effective feld theories by going beyond the familiar positivity bounds that follow from unitarity, analyticity, and crossing symmetry of the scattering amplitudes. As interesting examples, we discuss the implications of the bounds for the Galileon and ghost-free massive gravity. The latter is ruled out by our theoretical bounds when combined with the experimental constraints on the graviton mass and from fifth-force experiments, given the impossibility to consistently implement the Vainshtein mechanism. We also show that the Galileon theory must contain symmetry-breaking terms that are at most one-loop suppressed compared to the symmetry-preserving ones.