The Cygnus X region contains giant molecular cloud complexes and populous associates of massive young stars. The discovery of spatially extended, hard gamma-ray emission in Cygnus X by both Milagro and Fermi indicates that Cygnus X is also a potential source of high-energy Galactic neutrinos. Here, we adapt our single-zone model for cosmic ray interactions in the central molecular zones of starburst galaxies for use in Cygnus X. We calculate the potential neutrino flux corresponding to the hard gamma-ray emission from the Cygnus Cocoon and to the soft, diffuse interstellar gamma-ray emission. We check our results by comparing the corresponding gamma-ray emission against the Fermi interstellar emission model and Milagro, ARGO-YBJ, and HAWC observations. In comparing our results against a recent IceCube analysis and the current sensitivity limits, we find that neutrino emission from the Cocoon has a large enough flux that it could plausibly be detected, provided hadronic interactions are occurring at sufficiently high energies. High-energy neutrinos from Cygnus X would provide direct evidence for the presence of as yet unidentified PeV energy accelerators in the Galactic disk.
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