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

Abstract: We have recently shown that continuous-spin particles (CSPs) have covariant single-emission amplitudes with the requisite properties to mediate long-range forces. CSPs, the most general massless particle type consistent with Lorentz symmetry, are characterized by a scale \rho. Here, we demonstrate a helicity correspondence at CSP energies larger than \rho, in which these amplitudes are well approximated by the familiar ones for particles of helicity 0, 1, or 2. These properties follow from Lorentz invariance. We also construct tree-level multi-emission and CSP-exchange amplitudes that are unitary, appropriately analytic, and consistent with helicity-0 correspondence. We propose sewing rules from which these amplitudes and others can be obtained. We also exhibit a candidate CSP-graviton matrix element, which shows that the Weinberg-Witten theorem does not apply to CSPs. These results raise the surprising possibility that the known long-range forces might be mediated by CSPs with very small \rho, rather than by helicity 1 and 2 particles.