Off-equilibrium non-Gaussian fluctuations near the QCD critical point: an effective field theory perspective

The non-Gaussian fluctuations of baryon density are sensitive to the presence of the conjectured QCD critical point. Their observational consequences are crucial for the ongoing experimental search for this critical point through the beam energy scan program at Relativistic Heavy Ion Collider (RHIC). In the expanding fireball created in a heavy-ion collision, critical fluctuations would inescapably fall out of equilibrium and require a systematic description within a dynamical framework. In this paper, we employ newly developed effective field theory (EFT) for fluctuating hydrodynamics to study the real-time critical non-Gaussian fluctuations of a conserved charge density. In particular, we derive the evolution equations for multi-point correlators of density fluctuations and obtain the closed-form solutions with arbitrary initial conditions that can readily be implemented in realistic simulations for heavy-ion collisions. We find that non-linear interactions among noise fields, which are missing in traditional stochastic hydrodynamics, could potentially contribute to the quartic (fourth-order) fluctuations in the scaling regime even at tree level in off-equilibrium situations.