Mysteries about the origin of high-energy cosmic neutrinos have deepened by the recent IceCube measurement of a large diffuse flux in the 10-100 TeV range. Based on the standard disk-corona picture of active galactic nuclei (AGN), we present a phenomenological model enabling us to systematically calculate the spectral sequence of multimessenger emission from the AGN coronae. We show that protons in the coronal plasma can be stochastically accelerated up to PeV energies by plasma turbulence, and find that the model explains the large diffuse flux of medium-energy neutrinos if the cosmic rays carry only a few percent of the thermal energy. We find that the Bethe-Heitler process plays a crucial role in connecting these neutrinos and cascaded MeV gamma rays, and point out that the gamma-ray flux can even be enhanced by the reacceleration of secondary pairs. Critical tests of the model are given by its prediction that a significant fraction of the MeV gamma-ray background correlates with about 10 TeV neutrinos, and nearby Seyfert galaxies including NGC 1068 are promising targets for IceCube, KM3Net, IceCube-Gen2, and future MeV gamma-ray telescopes.
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