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This paper presents the results of different searches for correlationsbetween very high-energy neutrino candidates detected by IceCube and thehighest-energy cosmic rays measured by the Pierre Auger Observatory and theTelescope Array. We first consider samples of cascade neutrino events and ofhigh-energy neutrino-induced muon tracks, which provided evidence for aneutrino flux of astrophysical origin, and study their cross-correlation withthe ultrahigh-energy cosmic ray (UHECR) samples as a function of angularseparation. We also study their possible directional correlations using alikelihood method stacking the neutrino arrival directions and adoptingdifferent assumptions on the size of the UHECR magnetic deflections. Finally,we perform another likelihood analysis stacking the UHECR directions and usinga sample of through-going muon tracks optimized for neutrino point-sourcesearches with sub-degree angular resolution. No indications of correlations atdiscovery level are obtained for any of the searches performed. The smallest ofthe p-values comes from the search for correlation between UHECRs with IceCubehigh-energy cascades, a result that should continue to be monitored.

journal of cosmology and astroparticle physics

Search for correlations between the arrival directions of IceCube  neutrino events and ultrahigh-energy cosmic rays detected by the Pierre Auger  Observatory and the Telescope Array