Connecting fluctuation measurements in heavy-ion collisions with the grand-canonical susceptibilities

Abstract

We derive the relation between cumulants of a conserved charge measured in a subvolume of a thermal system and the corresponding grand-canonical susceptibilities, taking into account exact global conservation of that charge. The derivation is presented for an arbitrary equation of state, with the assumption that the subvolume is sufficiently large to be close to the thermodynamic limit. Our framework -- the subensemble acceptance method (SAM) -- quantifies the effect of global conservation laws and is an important step toward a direct comparison between cumulants of conserved charges measured in central heavy ion collisions and theoretical calculations of grand-canonical susceptibilities, such as lattice QCD. As an example, we apply our formalism to net-baryon fluctuations at vanishing baryon chemical potentials as encountered in collisions at the LHC and RHIC.

7 pages, 2 figures, published version

References in corpus (4)

• The QCD Equation of State to $\mathcal{O}({\mu }_B^6)$ from Lattice QCD
• The QCD crossover at finite chemical potential from lattice simulations
• Rapidity dependence of proton cumulants and correlation functions
• Critical point fluctuations: Finite size and global charge conservation effects

Cited by in corpus (38)

• Relativistic nuclear collisions: Establishing a non-critical baseline for fluctuation measurements
• Reaching percolation and conformal limits in neutron stars
• Hyper-order baryon number fluctuations at finite temperature and density
• QCD at finite temperature and density within the fRG approach: An overview
• The Present and Future of QCD
• Proton number cumulants and correlation functions in Au-Au collisions at $\sqrt{s_{\mathrm{NN}}}=7.7-200$ GeV from hydrodynamics
• Particlization of an interacting hadron resonance gas with global conservation laws for event-by-event fluctuations in heavy-ion collisions
• Critical lensing and kurtosis near a critical point in the QCD phase diagram in and out-of-equilibrium
• Ripples of the QCD Critical Point
• Correcting event-by-event fluctuations in heavy-ion collisions for exact global conservation laws with the generalized subensemble acceptance method
• Fluctuations near the liquid-gas and chiral phase transitions in hadronic matter
• Fluctuations and correlations of baryonic chiral partners
• Phase transition amplification of proton number fluctuations in nuclear collisions from a transport model approach
• Continuum extrapolated high order baryon fluctuations
• Interplay between chiral dynamics and repulsive interactions
• Higher order conserved charge fluctuations inside the mixed phase
• Thermodynamic approach to proton number fluctuations in baryon-rich heavy-ion matter created at moderate collision energies
• Cooper-Frye sampling with short-range repulsion
• Factorial cumulants from global baryon number conservation
• Anatomy of critical fluctuations in hadronic matter
• Molecular dynamics analysis of particle number fluctuations in the mixed phase of a first-order phase transition
• Impact of hadronic interactions and conservation laws on cumulants of conserved charges in a dynamical model
• Factorial cumulants from short-range correlations and global baryon number conservation
• Coordinate versus momentum cuts and effects of collective flow on critical fluctuations
• Rapidity scan approach for net-baryon cumulants with a statistical thermal model
• The BEST framework for the search for the QCD critical point and the chiral magnetic effect
• Density correlations under global and local charge conservation
• Acceptance dependence of factorial cumulants, long-range correlations, and the antiproton puzzle
• Conformality and percolation threshold in neutron stars
• Possible origin of HADES data on proton number fluctuations in Au+Au collisions
• Cumulants from short-range correlations and baryon number conservation - next-to-leading order
• Cumulants from fluctuating width of rapidity distribution
• Fluctuations in heavy ion collisions and global conservation effects
• Corrections to the hadron resonance gas from lattice QCD and their effect on fluctuation-ratios at finite density
• Proton number fluctuations in partial chemical equilibrium
• Critical point particle number fluctuations from molecular dynamics
• 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
• Fluctuations of conserved charges in hydrodynamics and molecular dynamics