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We have recently shown that continuous-spin particles (CSPs) have covariantsingle-emission amplitudes with the requisite properties to mediate long-rangeforces. CSPs, the most general massless particle type consistent with Lorentzsymmetry, are characterized by a scale \rho. Here, we demonstrate a helicitycorrespondence at CSP energies larger than \rho, in which these amplitudes arewell approximated by the familiar ones for particles of helicity 0, 1, or 2.These properties follow from Lorentz invariance. We also construct tree-levelmulti-emission and CSP-exchange amplitudes that are unitary, appropriatelyanalytic, and consistent with helicity-0 correspondence. We propose sewingrules from which these amplitudes and others can be obtained. We also exhibit acandidate CSP-graviton matrix element, which shows that the Weinberg-Wittentheorem does not apply to CSPs. These results raise the surprising possibilitythat the known long-range forces might be mediated by CSPs with very small\rho, rather than by helicity 1 and 2 particles.

On the Theory of Continuous-Spin Particles: Helicity Correspondence in Radiation and Forces