We investigate the correlations between IceCube high-energy neutrinos and Fermi-LAT γ-ray sources using an unbinned likelihood analysis. In previous analyses of the same IceCube public dataset, only the spatial information of neutrino events was utilized, while the energy term in the probability density functions (PDFs) was neglected, limiting the achievable sensitivity. In this work, we incorporate both spatial and energy terms into the likelihood, with the energy PDFs constructed from the effective areas and smearing matrices. We focus on the Third Catalog of Hard Fermi-LAT Sources (3FHL) and the Fourth LAT AGN Catalog (4LAC-DR2). To account for the significant difference in IceCube’s sensitivity between the two hemispheres, we perform stacking analyses for the all-sky, Northern hemisphere, and Southern hemisphere source subsets separately, under both equal weighting and flux weighting schemes. No statistically significant neutrino excess is found in any configuration. We therefore derive 95% confidence level upper limits on the total neutrino flux contributed by these source populations. For a spectral index of Γ=−2.5, the all-sky stacking analysis indicates that the 3FHL and 4LAC-DR2 populations contribute at most 3.12% and 2.83% (equal weighting), and 4.45% and 3.49% (flux weighting) of the IceCube diffuse neutrino flux, respectively. Compared to the spatial-only analysis, the inclusion of the energy term improves the constraints on hard-spectrum emission by over one order of magnitude. Our results further demonstrate that the 3FHL and 4LAC-DR2 sources are subdominant contributors to the diffuse astrophysical neutrino flux observed by IceCube.
Wang et al. (Tue,) studied this question.