I've been looking at an example model recently of a massive spin 1 vector field coupled to the conserved current of a massive complex scalar field. My previous question was far too long so I deleted it (it's what I get for posting when I haven't slept in over two days). I'm calling the massive scalar particles phi particles/antiparticles and the massive vector field particles X-Boson's.
Here's my problem; when I compute the tree-level total cross section for the equivalent of Compton Scattering in this theory (one X-boson and one phi particle as the initial state, one X-boson and one phi particle as the final state), I find that the total cross section diverges as we go to arbitrarily high COM three-momenta IF we consider the possibility that the incoming X-boson has a longitudinal polarization. This sort of behavior doesn't happen with a massless spin 1 vector field since such a vector field doesn't have a longitudinal polarization mode. How exactly am I supposed to interpret this? The total cross section is supposed to be bounded between 0 and 1, right? Is perturbation theory just breaking down at high energies? If it is breaking down at high energies, how are you supposed to compute cross sections at those energies?