Positivity Bounds for Massive Spin-1 and Spin-2 Fields

Abstract: We apply the recently developed positivity bounds for particles with spin, applied away from the forward limit, to the low energy effective theories of massive spin-1 and spin-2 theories. For spin-1 theories, we consider the generic Proca EFT which arises at low energies from a heavy Higgs mechanism, and the special case of a charged Galileon for which the EFT is reorganized by the Galileon symmetry. For spin-2, we consider generic $\Lambda_5$ massive gravity theories and the special `ghost-free' $\Lambda_3$ theories. Remarkably we find that at the level of 2-2 scattering, the positivity bounds applied to $\Lambda_5$ massive gravity theories impose the special tunings which generate the $\Lambda_3$ structure. For $\Lambda_3$ massive gravity theories, the island of positivity derived in the forward limit appears relatively stable against further bounds.