  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.
