Investigating the correlations between IceCube high-energy neutrinos and Fermi-LAT $\gamma$-ray observations. II

Given that gamma rays with energies larger than TeV are severely absorbed by background radiation fields, for many extragalactic sources, the GeV-TeV gamma-ray observations are the messengers that are closest in energy to the TeV-PeV neutrinos observed by IceCube. Investigating whether there is a correlation between the gamma-ray and neutrino observations can help us identify high-energy neutrino sources and determine which sources are the main contributors to the all-sky diffuse neutrino flux of IceCube. In previous work, we have already studied the possible gamma-neutrino correlations by analyzing 10 years of IceCube muon-track data. In this work, we further investigate such correlations by employing the IceCube p-value sky map of the scan for point sources. We examine the spatial associations of hotspots in the neutrino sky map with various gamma-ray source samples: the third Fermi-LAT catalog of high-energy sources (3FHL), LAT 14-year source catalog (4FGL), the fourth catalog of active galactic nuclei (4LAC) and subsets of these samples. Among all the samples, the 3FHL sample shows a possible correlation with the neutrino hotspots, with a pre-trial p-value of $1.1\times10^{-4}$ ($\sim 3.9\,\sigma$). However, this is found to be caused by three already known neutrino sources/source candidates: NGC 1068, TXS 0506+056, and PKS 1424+240. In order to validate our analysis procedure and to test the robustness of the previously claimed correlation between the 5BZCAT blazars and neutrino hotspots, we also consider 5BZCAT blazars in our correlation study. We find that the way in which mock sources are generated in the simulation used to derive the chance coincidence probability may have a large impact on the claimed correlation.