Freezing Out Fluctuations in Hydro+ Near the QCD Critical Point

Abstract

We introduce a freeze-out procedure to convert the critical fluctuations in a droplet of quark-gluon plasma (QGP) that has, as it expanded and cooled, passed close to a posited critical point on the phase diagram into cumulants of hadron multiplicities that can subsequently be measured. The procedure connects the out-of-equilibrium critical fluctuations described in concert with the hydrodynamic evolution of the droplet of QGP by extended hydrodynamics, known as Hydro+, with the subsequent kinetic description in terms of observable hadrons. We introduce a critical scalar isoscalar field sigma whose fluctuations cause correlations between observed hadrons due to the couplings of the sigma field to the hadrons via their masses. We match the QGP fluctuations obtained by solving the Hydro+ equations describing the evolution of critical fluctuations before freeze-out to the correlations of the sigma field. In turn, these are imprinted onto correlations and fluctuations in the multiplicity of hadrons, most importantly protons, after freeze-out via the generalization of the familiar half-century-old Cooper-Frye freeze-out prescription which we introduce. The proposed framework allows us to study the effects of critical slowing down and the consequent deviation of the observable predictions from equilibrium expectations quantitatively. We also quantify the suppression of cumulants due to conservation of baryon number. We demonstrate the procedure in practice by freezing out a Hydro+ simulation in an azimuthally symmetric and boost invariant background that includes radial flow discussed in arXiv:1908.08539.

arXiv comment67 pages, 21 figures

References in corpus (63)

• The equation of state in (2+1)-flavor QCD
• Full result for the QCD equation of state with 2+1 flavors
• Signatures of the Tricritical Point in QCD
• Event-by-Event Fluctuations in Heavy Ion Collisions and the QCD Critical Point
• Heavy Ion Collisions: The Big Picture, and the Big Questions
• Non-Gaussian fluctuations near the QCD critical point
• On the Phase Diagram of QCD
• Color Superconductivity and Chiral Symmetry Restoration at Nonzero Baryon Density and Temperature
• Static and Dynamic Critical Phenomena at a Second Order QCD Phase Transition
• On the sign of kurtosis near the QCD critical point
• Mapping the Phases of Quantum Chromodynamics with Beam Energy Scan
• The Condensed Matter Physics of QCD
• Slowing Out of Equilibrium Near the QCD Critical Point
• Dissipative Hydrodynamics and Heavy Ion Collisions
• Third moments of conserved charges as probes of QCD phase structure
• 3D Ising Model:The Scaling Equation of State
• Hydro+: hydrodynamics with parametric slowing down and fluctuations near the critical point
• Relativistic Theory of Hydrodynamic Fluctuations with Applications to Heavy Ion Collisions
• Dynamic universality class of the QCD critical point
• Initial State Fluctuations and Final State Correlations in Relativistic Heavy-Ion Collisions
• Dynamical initial state model for relativistic heavy-ion collisions
• Using Higher Moments of Fluctuations and their Ratios in the Search for the QCD Critical Point
• Baryon number conservation and the cumulants of the net proton distribution
• Net baryon diffusion in fluid dynamic simulations of relativistic heavy-ion collisions
• Cumulants and Correlation Functions of Net-proton, Proton and Antiproton Multiplicity Distributions in Au+Au Collisions at energies available at the BNL Relativistic Heavy Ion Collider
• Real time evolution of non-Gaussian cumulants in the QCD critical regime
• Causal Viscous Hydrodynamics for Central Heavy-Ion Collisions
• A kinetic regime of hydrodynamic fluctuations and long time tails for a Bjorken expansion
• Diffusive dynamics of critical fluctuations near the QCD critical point
• Acceptance dependence of fluctuation measures near the QCD critical point
• Causal Viscous Hydrodynamics for Central Heavy-Ion Collisions II: Meson Spectra and HBT Radii
• Proton number fluctuation as a signal of the QCD critical end-point
• Universal off-equilibrium scaling of critical cumulants in the QCD phase diagram
• Coupling Relativistic Viscous Hydrodynamics to Boltzmann Descriptions
• Relativistic Hydrodynamic Fluctuations
• Thermally Fluctuating Second-Order Viscous Hydrodynamics and Heavy-Ion Collisions
• Hydro+ in Action: Understanding the Out-of-Equilibrium Dynamics Near a Critical Point in the QCD Phase Diagram
• Fluctuation dynamics in a relativistic fluid with a critical point
• Bulk viscosity from hydrodynamic fluctuations with relativistic hydro-kinetic theory
• Transits of the QCD Critical Point
• Correlated fluctuations near the QCD critical point
• Hydrodynamic Fluctuations in Relativistic Heavy-Ion Collisions
• Fluctuation dynamics near the QCD critical point
• Stochastic hydrodynamics and long time tails of an expanding conformal charged fluid
• Hydrodynamic fluctuations and dissipation in an integrated dynamical model
• Searching for the QCD critical point via the rapidity dependence of cumulants
• Evolution of fluctuations near QCD critical point
• Evolution of Non-Gaussian Hydrodynamic Fluctuations
• Critical behavior of the bulk viscosity in QCD
• Modeling the diffusive dynamics of critical fluctuations near the QCD critical point
• Universality of the critical point mapping between Ising model and QCD at small quark mass
• Rapidity decorrelation of anisotropic flow caused by hydrodynamic fluctuations
• Dynamics of the $O(4)$ critical point in QCD
• Kinetic freeze-out, particle spectra and harmonic flow coefficients from mode-by-mode hydrodynamics
• Cumulants of multiple conserved charges and global conservation laws
• Relativistic fluctuating hydrodynamics with memory functions and colored noises
• Impact of resonance decays on critical point signals in net-proton fluctuations
• Thermal blurring of event-by-event fluctuations provoked by rapidity conversion
• Modified equilibrium distributions for Cooper--Frye particlization
• QCD equation of state matched to lattice data and exhibiting a critical point singularity
• Universal scaling of the sigma field and net-protons from Langevin dynamics of model A
• Net-proton number fluctuations in the presence of the QCD critical point
• Characteristic momentum of Hydro+ and a bound on the speed of sound near the QCD critical point

Cited by in corpus (20)

• Phase Transitions in Particle Physics -- Results and Perspectives from Lattice Quantum Chromo-Dynamics
• The Present and Future of QCD
• The QCD phase diagram and Beam Energy Scan physics: a theory overview
• Progress and Challenges in Small Systems
• Critical lensing and kurtosis near a critical point in the QCD phase diagram in and out-of-equilibrium
• Non-Gaussian fluctuation dynamics in relativistic fluids
• Critical net-baryon fluctuations in an expanding system
• Phase transition amplification of proton number fluctuations in nuclear collisions from a transport model approach
• Cooper-Frye sampling with short-range repulsion
• Coordinate versus momentum cuts and effects of collective flow on critical fluctuations
• Dynamical critical fluctuations near the QCD critical point with hydrodynamic cooling rate
• Rapidity scan approach for net-baryon cumulants with a statistical thermal model
• The equilibrium and dynamical cumulants of QCD chiral order parameter with parametric Landau free energy
• Simple holographic dual of the Maxwell-Cattaneo model & the fate of KMS symmetry for non-hydrodynamic modes
• Non-equilibrium cumulants within model A from crossover to first-order phase transition side
• Partonic Critical Opalescence and Its Impact on the Jet Quenching Parameter $\hat{q}$
• Conservation Laws and Hydrodynamics
• The effects of the QCD critical point on the spectra and flow coefficients of hadrons
• Cumulants of conserved charges in hydrodynamic simulations
• Fluctuations of conserved charges in hydrodynamics and molecular dynamics