A Multi-messenger Study of the Cygnus bubble

We perform a comprehensive investigation of particle acceleration at the termination shocks of massive star clusters, with a particular focus on the Cygnus region. Building on the particle-acceleration model for cluster-driven winds, we use recently available spectral and spatial measurements of ultra-high-energy $γ$-rays from the Cygnus bubble to place stringent constraints on the physical conditions in the acceleration zone. By jointly modelling the observed $γ$-ray spectrum and spatial morphology, we derive quantitative limits on key parameters such as the maximum particle energy, acceleration efficiency, magnetic-field strength, and shock geometry, and assess their consistency with a hadronic origin of the emission. These data allow us to refine the target gas profiles within and around the bubble, thereby improving estimates of the expected hadronic $γ$-ray and neutrino fluxes. Using this revised gas model, we compute the neutrino emission associated with the Cygnus bubble and evaluate the statistical significance of a potential neutrino signal from this region for current and near-future high-energy neutrino observatories. Taken together, these results provide a more precise characterisation of the particle-acceleration environment at cluster termination shocks and help clarify the role of young massive star clusters as potential Galactic PeVatrons and contributors to the observed diffuse high-energy neutrino and $γ$-ray emissions.