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We study high-energy neutrino and cosmic-ray (CR) emission from the cores of low-luminosity active galactic nuclei (LLAGN). In LLAGN, the thermalization of particles is expected to be incomplete in radiatively inefficient accretion flows (RIAFs), allowing the existence of non-thermal particles. In this work, assuming stochastic particle acceleration due to turbulence in RIAFs, we solve the Fokker-Planck equation and calculate spectra of escaping neutrinos and CRs. The RIAF in LLAGN can emit CR protons with $\gtrsim10$ PeV energies and TeV-PeV neutrinos generated via $pp$ and/or $p\gamma$ reactions. We find that, if $\sim1$\% of the accretion luminosity is carried away by non-thermal ions, the diffuse neutrino intensity from the cores of LLAGN may be as high as $E_\nu^2\Phi_\nu\sim3\times{10}^{-8} {\rm GeV} {\rm cm}^{-2} {\rm s}^{-1}{\rm sr}^{-1}$, which can be compatible with the observed IceCube data. This result does not contradict either of the diffuse gamma-ray background observed by {\it Fermi} or observed diffuse cosmic-ray flux. Our model suggests that, although very-high-energy gamma rays may not escape, radio-quiet AGN with RIAFs can emit GeV gamma-rays, which could be used for testing the model. We also calculate the neutron luminosity from RIAFs of LLAGN, and discuss a strong constraint on the model of jet mass loading mediated by neutrons from the diffuse neutrino observation.

NEUTRINO AND COSMIC-RAY EMISSION AND CUMULATIVE BACKGROUND FROM RADIATIVELY INEFFICIENT ACCRETION FLOWS IN LOW-LUMINOSITY ACTIVE GALACTIC NUCLEI