Roadmap for searching cosmic rays correlated with the extraterrestrial neutrinos seen at IceCube

We have built sky maps showing the expected arrival directions of 120 EeV ultrahigh-energy cosmic rays (UHECRs) directionally correlated with the latest astrophysical neutrino tracks observed at IceCube, including the four-year high-energy starting events (HESEs) and the two-year northern tracks, taken as point sources. We have considered contributions to UHECR deflections from the Galactic and the extragalactic magnetic field and a UHECR composition compatible with the current expectations. We have used the Jansson-Farrar JF12 model for the Galactic magnetic field and an extragalactic magnetic field strength of 1 nG and coherence length of 1 Mpc. We observe that the regions outside of the Galactic plane are more strongly correlated with the neutrino tracks than those adjacent to or in it, where IceCube HESE events 37 and 47 are good candidates to search for excesses, or anisotropies, in the UHECR flux. On the other hand, clustered northern tracks around (l,b)=(0°,-30°) and (l,b)=(-150°,-30°) are promising candidates for a stacked point source search. For example, we have focused on the region of UHECR arrival directions, at 150 EeV, correlated with IceCube HESE event 37 located at (l,b)=(-137.1°,65.8°) in the northern hemisphere, far away from the Galactic plane, obtaining an angular size ∼5°, being ∼3° for 200 EeV and ∼8° for 120 EeV. We report a p value of 0.20 for a stacked point source search using current Auger and Telescope Array data, consistent with current results from both collaborations. Using Telescope Array data alone, we found a projected live time of 72 years to find correlations, but clearly this must improve with the planned Auger upgrade.