Unified Description of Efficiency Correction and Error Estimation for Moments of Conserved Quantities in Heavy-Ion Collisions

Abstract

We provide a unified description of efficiency correction and error estimation for moments of conserved quantifies in heavy-ion collisions. Moments and cumulants are expressed in terms of the factorial moments, which can be easily corrected for the efficiency effect. By deriving the covariance between factorial moments, one can obtain the general error formula for the efficiency corrected moments based on the error propagation derived from the Delta theorem. The skellam distribution based Monto Carlo simulation is used to test the Delta theorem and Bootstrap error estimation methods. The statistical errors calculated from the two methods can well reflect the statistical fluctuations of the efficiency corrected moments.

23 pages, 5 figures

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• Non-monotonic energy dependence of net-proton number fluctuations
• 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
• Collision Energy Dependence of Moments of Net-Kaon Multiplicity Distributions at RHIC
• Fluctuations of conserved charges in relativistic heavy ion collisions: An introduction
• Acceptance dependence of fluctuation measures near the QCD critical point
• Proton number fluctuations in $\sqrt{s_{NN}}$ = 2.4 GeV Au+Au collisions studied with HADES
• A Study of the Properties of the QCD Phase Diagram in High-Energy Nuclear Collisions
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• Search for the QCD Critical Point in High Energy Nuclear Collisions
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• Higher Moments of Net-Particle Multiplicity Distributions
• Properties and uses of factorial cumulants in relativistic heavy-ion collisions
• Cumulants of Net-Proton, Net-Kaon and Net-Charge Multiplicity Distributions in Au+Au Collisions at RHIC BES Energies from UrQMD Model
• Efficient formulas for efficiency correction of cumulants
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• Effects of Nuclear Potential on the Cumulants of Net-Proton and Net-Baryon Multiplicity Distributions in Au+Au Collisions at $\sqrt{s_{\text{NN}}}=5\text{GeV}$
• Proton Cumulants and Correlation Functions in Au + Au Collisions at $\sqrt{s_{\mathrm{NN}}}$=7.7-200 GeV from UrQMD Model
• Efficiency correction for cumulants of multiplicity distributions based on track-by-track efficiency
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• Binomial acceptance corrections for particle number distributions in high-energy reactions
• Centrality selection effect on higher-order cumulants of net-proton multiplicity distributions in relativistic heavy-ion collisions
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• Cumulants of event-by-event net-strangeness distributions in Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}$=7.7-200 GeV from UrQMD model
• Effect of limited statistics on higher order cumulants measurement in heavy-ion collision experiments
• Mapping the QCD phase diagram with statistics friendly distributions
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• Beam energy dependence of net-$\Lambda$ fluctuations measured by the STAR experiment at RHIC
• Energy Dependence of Intermittency for Charged Hadrons in Au+Au Collisions at RHIC
• Non-critical fluctuations of (net) charges and (net) protons from iEBE-VISHNU hybrid model
• Measurement of cumulants of conserved charge multiplicity distributions in Au+Au collisions from the STAR experiment
• Intermittency analysis of proton numbers in heavy-ion collisions at energies available at the BNL Relativistic Heavy Ion Collider
• Baryon-Strangeness Correlations in Au+Au Collisions at $\sqrt{s_{\mathrm{NN}}}$=7.7-200 GeV from the UrQMD model
• Pileup corrections on higher-order cumulants
• Reconstructing particle number distributions with convoluting volume fluctuations
• Measurement of the Sixth-Order Cumulant of Net-Proton Distributions in Au+Au Collisions from the STAR Experiment
• Importance of separated efficiencies between positively and negatively charged particles for cumulant calculations
• Identity Method Revisited
• Event-by-Event Efficiency Fluctuations and Efficiency Correction for Cumulants of Superposed Multiplicity Distributions in Relativistic Heavy-ion Collision Experiments
• Effects of resonance weak decays and hadronic re-scattering on the proton number fluctuations in Au + Au collisions at $\sqrt{s_{\mathrm{NN}}}=5$ GeV from JAM model
• Effects of centrality fluctuation and deuteron formation on proton number cumulant in Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}$ = 3 GeV from JAM model
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• Charged-particle multiplicity fluctuations in Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV
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• Influence of kinematic cuts on the net charge distribution
• Overview of intermittency analysis in heavy-ion collisions
• Net-baryon multiplicity distribution consistent with lattice QCD
• Purity correction for cumulants of hyperon number distribution
• Measurements of charged-particle multiplicity dependence of higher-order net-proton cumulants in $p$+$p$ collisions at $\sqrt{s}=$ 200 GeV from STAR at RHIC
• Higher Moments of Net-Kaon Multiplicity Distributions at STAR
• The QCD phase diagram and statistics friendly distributions
• Fluctuations of Conserved Quantities in High Energy Nuclear Collisions at RHIC
• Efficiency corrections for mutually inclusive variables and particle identification effect for mixed-cumulants in heavy-ion collisions
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• High cumulants of conserved charges and their statistical uncertainties
• Non-Monotonicity of $p_{\mathrm{T}}$ Correlations in Au + Au Collisions at RHIC