We investigate the possibility that radio-bright active galactic nuclei (AGN) are responsible for the TeV--PeV neutrinos detected by IceCube. We use an unbinned maximum-likelihood-ratio method, 10 years of IceCube muon-track data, and 3388 radio-bright AGN selected from the Radio Fundamental Catalog. None of the AGN in the catalog have a large global significance. The two most significant sources have global significance of $simeq$ 1.5$sigma$ and 0.8$sigma$, though 4.1$sigma$ and 3.8$sigma$ local significance. Our stacking analyses show no significant correlation between the whole catalog and IceCube neutrinos. We infer from the null search that this catalog can account for at most 30% (95% CL) of the diffuse astrophysical neutrino flux measured by IceCube. Moreover, our results disagree with recent work that claimed a 4.1$sigma$ detection of neutrinos from the sources in this catalog, and we discuss the reasons of the difference.
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