Abstract: | For several decades, the origin of ultra-high-energy cosmic rays (UHECRs) has
been an unsolved question of high-energy astrophysics. One approach for solving
this puzzle is to correlate UHECRs with high-energy neutrinos, since neutrinos
are a direct probe of hadronic interactions of cosmic rays and are not
deflected by magnetic fields. In this paper, we present three different
approaches for correlating the arrival directions of neutrinos with the arrival
directions of UHECRs. The neutrino data is provided by the IceCube Neutrino
Observatory and ANTARES, while the UHECR data with energies above $sim$50 EeV
is provided by the Pierre Auger Observatory and the Telescope Array. All
experiments provide increased statistics and improved reconstructions with
respect to our previous results reported in 2015. The first analysis uses a
high-statistics neutrino sample optimized for point-source searches to search
for excesses of neutrinos clustering in the vicinity of UHECR directions. The
second analysis searches for an excess of UHECRs in the direction of the
highest-energy neutrinos. The third analysis searches for an excess of pairs of
UHECRs and highest-energy neutrinos on different angular scales. None of the
analyses has found a significant excess, and previously reported
over-fluctuations are reduced in significance. Based on these results, we
further constrain the neutrino flux spatially correlated with UHECRs. |