  In this paper, we explore positivity bounds for the effective field
theory~(EFT) of a single weakly coupled massive vector field. The presence of
both mass and spin makes the crossing properties of the amplitudes vastly
complicated -- we address this by parametrizing the amplitudes as products of a
polarization matrix and a vector of appropriately chosen functions with simpler
crossing properties. The resulting framework involves sum rules and null
constraints that allows us to constrain any combination of low-energy
observables, such as EFT amplitudes. By varying the value of the vector mass
over the cutoff scale, some of our bounds asymptote to the bounds obtained in
the context of photons and massless scalars. This work paves the way for future
applications to e.g. non-abelian massive vectors, glueballs and theories with
spin larger than one.
