From Nuclear Many-Body Correlations to Energy Detector Correlators

Abstract: Relativistic nuclear collisions have opened an experimental arena for studying many-body correlations in nuclear ground states. However, the connection between initial-state correlations and final-state multi-particle observables measured at colliders is not yet formulated as a systematically improvable matching problem. We show that detector correlators built from asymptotic energy flows provide a natural framework for realizing such a construction. In particular, we express the asymptotic energy flow as a functional of the early-time stress tensor, and expand it in suitable modes to recover the familiar linear hydrodynamic relations at leading order. Then, motivated by small-$x$ QCD, we map angular projections of detector correlators to multipole-operator correlators computed in the colliding nuclei. We thus establish a systematic formalism for matching long-wavelength correlations between incoming and outgoing QCD states in high-energy hadronic collisions.