Scalar scattering via conformal higher spin exchange

Theories containing infinite number of higher spin fields require a particular definition of summation over spins consistent with their underlying symmetries. We consider a model of massless scalars interacting (via bilinear conserved currents) with conformal higher spin fields in flat space. We compute the tree-level four-scalar scattering amplitude using a natural prescription for summation over an infinite set of conformal higher spin exchanges and find that it vanishes (modulo delta-function terms having support on measure-zero domain in phase space). Independently, we show that this vanishing of the scalar scattering amplitude is, in fact, implied by the global conformal higher spin symmetry of this model. We also discuss one-loop corrections to the four-scalar scattering amplitude.