Event-by-Event Fluctuations in Heavy Ion Collisions and the QCD Critical Point

Abstract

The event-by-event fluctuations of suitably chosen observables in heavy ion collisions at SPS, RHIC and LHC can tell us about the thermodynamic properties of the hadronic system at freeze-out. By studying these fluctuations as a function of varying control parameters, it is possible to learn much about the phase diagram of QCD. As a timely example, we stress the methods by which present experiments at the CERN SPS can locate the second-order critical endpoint of the first-order transition between quark-gluon plasma and hadron matter. Those event-by-event signatures which are characteristic of freeze-out in the vicinity of the critical point will exhibit nonmonotonic dependence on control parameters. We focus on observables constructed from the multiplicity and transverse momenta of charged pions. We first consider how the event-by-event fluctuations of such observables are affected by Bose-Einstein correlations, by resonances which decay after freeze-out and by fluctuations in the transverse flow velocity. We compare our thermodynamic predictions for such noncritical event-by-event fluctuations with NA49 data, finding broad agreement. We then focus on effects due to thermal contact between the observed pions and a heat bath with a given (possibly singular) specific heat, and due to the direct coupling between the critical fluctuations of the sigma field and the observed pions. We also discuss the effect of the pions produced in the decay of sigma particles just above threshold after freeze-out on the inclusive pion spectrum and on multiplicity fluctuations. We estimate the size of these nonmonotonic effects which appear near the critical point, including restrictions imposed by finite size and finite time, and conclude that they should be easily observable.

58 pages, 2 figures; to appear in Phys. Rev. D

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• Evolutionary intermittency and the QCD critical point
• Onset of Deconfinement and Critical Point: NA49 and NA61/SHINE at the CERN SPS
• The cumulants of the baryon number from central Au+Au collision at $E_{lab}$= 1.23 GeV$/$nucleon reveal the nuclear mean-field potentials
• Event-By-Event Fluctuation of Maximum Particle Density in Narrow Pseudo-Rapidity Interval at a Few AGeV/c
• Charge Conservation and Higher Moments of Charge Fluctuations
• Baryon Resonances in a Chiral Hadronic Model for the QCD Equation of State
• Beam-energy dependence of identified two-particle angular correlations in Au+Au collisions at RHIC
• Overview of the QCD phase diagram -- Recent progress from the lattice
• Far-off-equilibrium expansion trajectories in the QCD phase diagram
• Large Momenta Fluctuations Of Charm Quarks In The Quark-Gluon Plasma
• Critical exponents of the quark-gluon bags model with the critical endpoint
• STAR's measurement of Long-range forward-backward multiplicity correlations as the signature of "dense partonic matter" in the Heavy Ion collisions at $\sqrt{s_{NN}}=$200 GeV.}
• Event-by-Event Efficiency Fluctuations and Efficiency Correction for Cumulants of Superposed Multiplicity Distributions in Relativistic Heavy-ion Collision Experiments
• Dispersion and suppression of sound near QCD critical point
• Event by Event fluctuation in K/pi ratio at RHIC
• Event by Event analysis of Maximum Pseudo-rapidity Gap Fluctuation in High energy Nucleus-nucleus Collisions
• Molecular dynamics analysis of particle number fluctuations in the mixed phase of a first-order phase transition
• QGP flow fluctuations and the characteristics of higher moments
• Impact of hadronic interactions and conservation laws on cumulants of conserved charges in a dynamical model
• Anatomy of critical fluctuations in hadronic matter
• Universal scaling of conserved charge in the stochastic diffusion dynamics
• Boltzmann Distributions on a Quantum Computer via Active Cooling
• Signal of the pion string at high-energy collisions
• The Equation of State and Quark Number Susceptibility in Hard-Dense-Loop Approximation
• QCD thermodynamics on the lattice
• Mini-jet thermalization and diffusion of transverse momentum correlation in high-energy heavy-ion collisions
• Probing nuclear liquid-gas phase transition with isospin correlations
• Rapidity scan approach for net-baryon cumulants with a statistical thermal model
• Influence of Impact Parameter Fluctuations on Transverse Momentum Fluctuations
• Net-proton number fluctuations in the presence of the QCD critical point
• Coordinate versus momentum cuts and effects of collective flow on critical fluctuations
• Charged-particle multiplicity fluctuations in Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV
• Mean free path of photons in relativistic heavy ion collisions
• Multiplicity fluctuations in the Glauber Monte Carlo approach
• Conserved Charge Fluctuations in a Chiral Hadronic Model including Hadrons and Quarks
• Dynamical critical fluctuations near the QCD critical point with hydrodynamic cooling rate
• Signature of QCD critical point: Anomalous transverse velocity dependence of antiproton-proton ratio
• Heavy ion collisions: Correlations and Fluctuations in particle production
• The BEST framework for the search for the QCD critical point and the chiral magnetic effect
• Nonequilibrium pion dynamics near the critical point in a constituent quark model
• Dynamic aspect of the chiral phase transition in the mode coupling theory
• Conserved Charge Fluctuations and Susceptibilities in Strongly Interacting Matter
• Fluctuations and clustering of multiplicity in collisions of relativistic ions
• Multiplicity fluctuations in relativistic nuclear collisions
• RMF models with $\sigma$-scaled hadron masses and couplings for description of heavy-ion collisions below 2A GeV
• Density correlations under global and local charge conservation
• Dilepton production from moaton quasiparticles
• Kinetics of the chiral phase transition in a linear $\sigma$ model
• Effect of finite volume on thermodynamics of quark-hadron matter
• Charge fluctuations and electric mass in a hot meson gas
• Estimation of Stopped Protons at Energies Relevant for a Beam Energy Scan at the BNL Relativistic Heavy-Ion Collider
• Highlights from STAR: probing the early medium in heavy ion collisions
• Study of dynamical charge fluctuations in the hadronic medium
• Event-by-event mean p_T fluctuations in pp and Pb-Pb collisions at the LHC
• Event-by-event mean p_T fluctuations in pp and Pb-Pb collisions measured by the ALICE experiment at the LHC
• Behavior of universal critical parameters in the QCD phase diagram
• Measurement of the ratio of the sixth order to the second order cumulant of net-proton multiplicity distributions in relativistic heavy-ion collisions
• Emergence of soft quark excitations by the coupling with a soft mode of the QCD critical point
• Lattice QCD results at finite T and μ
• Fluctuation of Gaps in Hadronization at Phase Transition
• Possible origin of HADES data on proton number fluctuations in Au+Au collisions
• The Universal Equation of State near the Critical Point of QCD
• Multiplicity Fluctuations and Correlations in Limited Momentum Space Bins in Relativistic Gases
• Hydrodynamic description of the baryon-charged quark-gluon plasma
• Stable Yang-Lee zeros in truncated fugacity series from net-baryon number multiplicity distribution
• Particle Production at the SPS and the QCD Phase Diagram
• Chiral Hadronic Mean Field Model including Quark Degrees of Freedom
• Generalized nonlinear Langevin equation from quantum nonlinear projection operator
• Experimental results on charge fluctuations in heavy-ion collisions
• Hydrodynamic results on multiplicity fluctuations in heavy-ion collisions
• Effect of correlations on cumulants in heavy-ion collisions
• Baryon production and net-proton distributions in relativistic heavy ion collisions
• Dynamical spectral structure of density fluctuation near QCD critical point
• Purity correction for cumulants of hyperon number distribution
• Arguing on entropic and enthalpic first-order phase transitions in strongly interacting matter
• Correlations of conserved number mixed susceptibilities in a hadron resonance gas model
• Conserved charge fluctuations using the $D$-measure in heavy-ion collisions
• Nonuniform-temperature effects on the phase transition in an Ising-like model
• Inflection point as a characteristic of the QCD critical point
• Chiral criticality and glue dynamics
• System size and energy dependence of the mean transverse momentum fluctuations at the LHC
• The Fluctuations of the Quark Number and of the Chiral Condensate
• Detecting a First-Order Transition in the QCD Phase Diagram with Baryon-Baryon Correlations
• Kinetic evolution and correlation of fluctuations in an expanding quark gluon plasma
• Study on higher moments of net-charge multiplicity distributions using a multiphase transport model
• Critical properties of various sizes of cluster in the Ising percolation transition
• Monte-Carlo approach to particle-field interactions and the kinetics of the chiral phase transition
• Onset of Deconfinement and Critical Point - Future Ion Program at the CERN SPS
• Beam energy dependence of cumulants of the net-baryon, net-charge and deuteron multiplicity distributions in Au+Au collisions at $\sqrt{s_{NN}}=3.0-5.0$ GeV
• Fluctuations in the Statistical Model of Relativistic Heavy Ion Collisions
• Dynamic Universality Class of Model H with Frustrated Diffusion: $\epsilon$-Expansion
• Quantum baryon number fluctuations in subsystems of a hot and dense relativistic gas of fermions
• Understanding the negative binomial multiplicity fluctuations in relativistic heavy ion collisions
• INFN What Next: Ultra-relativistic Heavy-Ion Collisions
• Thermal and Nonthermal Pion Enhancements with Chiral Symmetry Restoration
• Gas-liquid transition in the model of particles interacting at high energy
• Density Functional Equation of State and Its Application to the Phenomenology of Heavy-Ion Collisions
• Energy dependence of fluctuations in p+p and Be+Be collisions from NA61/SHINE
• Constructing probability density function of net-proton multiplicity distributions using Pearson curve method
• Multiplicity fluctuation and correlation of identified baryons in quark combination model
• Kinetics of the chiral phase transition in a quark-meson $\sigma$-model
• Chemical Freeze-out Parameters via a Non-perturbative QCD Approach
• Investigations into the characteristics and influences of nonequilibrium evolution
• Quark-Gluon Plasma: Status of Heavy Ion Physics
• Pseudorapidity Window Size Dependence of Multiplicity Fluctuations in High-Energy Collisions with System Size and Beam Energies
• Examination of background effects on light-nuclei yield ratio in relativistic heavy-ion collisions
• Chiral symmetry breaking and pion condensation in the early universe
• Quantum fluctuations of baryon number density
• Angular pattern of minijet transverse energy flow in hadron and nuclear collisions
• Behavior and finite-size effects of the sixth order cumulant in the three-dimensional Ising universality class
• Ratios of Fluctuation Observables in the Search for the QCD Critical Point
• Relativistic diffusion and heavy-ion collisions
• Off-of-equilibrium effects on Kurtosis Along Strangeness-Neutral Trajectories
• New dynamic critical phenomena in nuclear and quark superfluids
• Statistical method in quark combination model
• Exploring hadron-quark phase transition in heavy-ion collisions using particle emission ratios in heavy and light reaction systems
• Correlations and fluctuations studied with ALICE
• Non-equilibrium fluctuations at the QCD phase transition
• Beam Energy Dependence of Fifth and Sixth-Order Net-proton Number Fluctuations in Au+Au Collisions at RHIC
• Probing the QCD phase structure using event-by-event fluctuations
• Statistical Ensembles With Finite Bath: A Description for an Event Generator
• Chiral Phase Transition in an Expanding Quark System
• Cumulants of conserved charges in hydrodynamic simulations
• Baseline study for net-proton number fluctuations at top energies available at the BNL Relativistic Heavy Ion Collider and at the CERN Large Hadron Collider with the Angantyr model
• Enhancement of photon emission rate near QCD critical point
• Energy Dependence of Multiplicity Fluctuations in Heavy Ion Collisions
• Collision-energy Dependence of Deuteron Cumulants and Proton-deuteron Correlations in Au+Au collisions at RHIC
• Fluctuations in heavy ion collisions and global conservation effects
• Chiral Meson Masses at Finite Temperature and Density
• Freeze-out and thermalization in relativistic heavy ion collisions
• Transport properties of a charged drop in an external electric field
• Efficient calculation of thermodynamic properties of baryon-rich QCD matter from heavy-ion transport models
• Multiplicity fluctuation and correlation of mesons and baryons in ultra-relativistic heavy-ion collisions at LHC
• Effect of non-uniform efficiency on higher-order cumulants in heavy-ion collisions
• PHENIX results on fluctuations and Bose-Einstein correlations in Au+Au collisions from the RHIC Beam Energy Scan
• Thermalization of Nuclear Matter in Heavy-Ion Collisions at Fermi-Energies
• Photon emissivity in the vicinity of a critical point - A case study within the quark meson model
• Critical point particle number fluctuations from molecular dynamics
• The characterizing variable for critical point in momentum space
• QCD phase diagram and locating critical point using RHIC low energy scan data
• NA61/SHINE results on fluctuations and correlations in p+p and Be+Be interactions at CERN SPS energies
• Study of baryon-strangeness and charge-strangeness correlations in Pb$-$Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV with ALICE
• Study of net-baryon higher moments in PNJL model and their expectation for net-proton using the Subensemble Acceptance Method for the search of QCD critical point
• Maps of the Little Bangs Through Energy Density and Temperature Fluctuations
• Some Considerations concerning the Fluctuation of the Ratios of two Observables
• Variations of the crossover and first-order phase transition curve in modeling the QCD equation of state
• Measurement of correlations among net-charge, net-proton, and net-kaon multiplicity distributions in Pb$-$Pb collisions at $\sqrt{s_{\text{NN}}}=5.02$ TeV
• Ratio of baryon and electric-charge cumulants at second order with acceptance corrections
• On Fixed-multiplicity Corrections to Correlators
• NA61/SHINE ion program
• New results from fluctuation analysis in NA49 at the CERN SPS
• The Old New Frontier: Studying the CERN-SPS Energy Range with NA61/SHINE
• Transport properties of a charged hot spot in an external electromagnetic field
• Low-momentum Pion Enhancement Induced by Chiral Symmetry Restoration
• Centrality Dependence of Multiplicity Fluctuations in Ion-Ion Collisions from the Beam Energy Scan at FAIR
• Vorticity-induced modifications of chemical freeze-out in heavy-ion collisions
• Calculation of Power Spectrum in the Little Bangs
• Phase Fluctuations near the Chiral Critical Point
• Features of the QCD phase diagram from small, noisy, fluctuating systems
• Conserved Charge Susceptibilities in a Chemically Frozen Hadronic Gas
• Elastic parton scattering and non-statistical event-by-event mean-pt fluctuations in Au + Au collisions at RHIC
• Recent developments in particle yield fluctuation measurements
• Strange Particles and Neutron Stars - Experiments at Gsi
• Event-by-event Analysis Methods and Applications to Relativistic Heavy-ion Collision Data
• Imprints of clustering in multiplicity fluctuations
• Resonances and fluctuations in the statistical model
• Remembrance of things past: non-equilibrium effects and the evolution of critical fluctuations near the QCD critical point
• Cumulants in the 3-dimensional Ising, O(2) and O(4) spin models
• QCD Critical Point and Net-Proton Number Fluctuations at RHIC-STAR
• High-order fluctuations of temperature in hot QCD matter
• Finite-size behaviour of generalized susceptibilities in the whole phase plane of the Potts model
• How to Measure Specific Heat Using Event-by-Event Average $p_T$ Fluctuations
• Accessing proton number fluctuations in limited regions of phase space
• Particle spectra in the integrated hydrokinetic model at RHIC Beam-Energy-Scan energies
• A study of meson condensation and of the QCD critical line
• Fluctuations of conserved charges in hydrodynamics and molecular dynamics