Positivity constraints for pseudolinear massive spin-2 and vector Galileons

We derive analyticity constraints on a nonlinear ghost-free effective theory of a massive spin-2 particle known as pseudolinear massive gravity, and on a generalized theory of a massive spin-1 particle, both of which provide simple IR completions of Galileon theories. For pseudolinear massive gravity we find that, unlike de Rham, Gabadadze, and Tolley massive gravity, there is no window of parameter space which satisfies the analyticity constraints. For massive vectors which reduce to Galileons in the decoupling limit, we find that no two-derivative actions are compatible with positivity but that higher derivative actions can be made compatible.