Scalar scattering via conformal higher spin exchange

TL;DR

This paper investigates scalar scattering in a model with conformal higher spin fields, showing the amplitude vanishes due to symmetry, with implications for understanding higher spin theories.

Contribution

It introduces a method for summing over infinite conformal higher spin exchanges and demonstrates the amplitude's vanishing from symmetry principles.

Findings

Tree-level four-scalar scattering amplitude vanishes.

Vanishing amplitude is linked to conformal higher spin symmetry.

One-loop corrections are discussed but not explicitly computed.

Abstract

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.