On the theory of continuous-spin particles: helicity correspondence in radiation and forces

A bstractWe 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 ρ. Here, we demonstrate a helicity correspondence at CSP energies larger than ρ, 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 ρ rather than by helicity 1 and 2 particles.

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