Framework for Gravitational-Wave and Neutrino stacking Analysis

Cosmic rays are charged particles whose trajectories are scrambled by magnetic fields, obscuring direct associations with their astrophysical origins. Identifying the engines capable of accelerating them therefore relies on neutral messengers such as neutrinos and gravitational waves. Compact binary coalescences, with or without neutron stars, are promising source candidates in this regard, as they may produce both gravitational-wave emission and hadronic outflows capable of generating high-energy neutrinos under suitable conditions. The joint interpretation of these signals within a multi-messenger framework enhances our ability to probe the physical conditions of their potential common source environments. However, no individual common source of gravitational waves and neutrinos has been identified with a global significance exceeding 3σ after trial correction. This motivates a population-level analysis to search for correlated neutrino emission from the ensemble of observed compact binary coalescences.