Investigating the correlations between IceCube high-energy neutrinos and Fermi-LAT <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>γ</mml:mi> </mml:math> -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 public 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 hot spots 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, the fourth catalog of active galactic nuclei, and subsets of these samples. Among all the samples, the 3FHL sample shows a possible correlation with the neutrino hot spots with a pretrial $p$ value of $9.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ ($\ensuremath{\sim}3.9\ensuremath{\sigma}$), corresponding to a posttrial significance of $\ensuremath{\sim}1.7\ensuremath{\sigma}$. However, this is found to be caused by three already known neutrino sources or source candidates: NGC 1068, TXS $0506+056$, and PKS $1424+240$.