Probing binary black hole merger populations in AGN disks through future IceCube-Gen2 and Einstein Telescope observations

The detection of astrophysical neutrinos and gravitational waves (GWs) has ushered in a new era of multi-messenger astroparticle physics. While coincident detections of GW and neutrinos alongside electromagnetic signals have already been achieved in separate instances, no common source of GW and neutrinos has yet been identified. To address the implications of non-detection, this work investigates the prospects for identifying binary black hole mergers embedded in AGN disks as common GW-neutrino sources with next-generation facilities, e.g., the Einstein Telescope and IceCube-Gen2. For sources located in the Northern Hemisphere, the detection significance is quantified for both individual mergers and their populations, to be seen by the Einstein Telescope. It is found that, even with improved sensitivity of next-generation detectors, catalogue searches have limited potential. In contrast, stacking offers a viable path to uncover a population of common GW-neutrino sources in the future.