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First Study of the Negative Binomial Distribution Applied to Higher Moments of Net-charge and Net-proton Multiplicity Distributions
Nuclear Experiment · Submitted 30 Oct 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Differences between $\kappa\sigma^{2}$ and a statistical Poisson assumption of a factor of four (for net-charge) and 40% (for net-protons) can be accounted for by the NBD/BD.
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The abstract, sentence by sentence
A study of the first four moments (mean, variance, skewness, and kurtosis) and their products ($\kappa\sigma^{2}$ and $S\sigma$) of the net-charge and net-proton distributions in Au+Au collisions at $\sqrt{\rm s_{NN}}$ = 7.7-200 GeV from HIJING simulations has been carried out. The skewness and kurtosis and the collision volume independent products $\kappa\sigma^{2}$ and $S\sigma$ have been proposed as sensitive probes for identifying the presence of a QCD critical point. A discrete probability distribution that effectively describes the separate positively and negatively charged particle (or proton and anti-proton) multiplicity distributions is the negative binomial (or binomial) distribution (NBD/BD). The NBD/BD has been used to characterize particle production in high-energy particle and nuclear physics. Their application to the higher moments of the net-charge and net-proton distributions is examined. Differences between $\kappa\sigma^{2}$ and a statistical Poisson assumption of a factor of four (for net-charge) and 40% (for net-protons) can be accounted for by the NBD/BD. This is the first application of the properties of the NBD/BD to describe the behavior of the higher moments of net-charge and net-proton distributions in nucleus-nucleus collisions.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | A study of the first four moments (mean, variance, skewness, and kurtosis) and their products ($\kappa\sigma^{2}$ and $S\sigma$) of the net-charge and net-proton distributions in Au+Au collisions at $\sqrt{\rm s_{NN}}$ = 7.7-200 GeV from HIJING simulations has been carried out. | contribution 0.94 | 0.93 | 0.07 | asserted 0.99 |
| s1 | The skewness and kurtosis and the collision volume independent products $\kappa\sigma^{2}$ and $S\sigma$ have been proposed as sensitive probes for identifying the presence of a QCD critical point. | background 1.00 | 0.07 | 0.07 | asserted 0.75 |
| s2 | A discrete probability distribution that effectively describes the separate positively and negatively charged particle (or proton and anti-proton) multiplicity distributions is the negative binomial (or binomial) distribution (NBD/BD). | background 0.99 | 0.06 | 0.04 | asserted 1.00 |
| s3 | The NBD/BD has been used to characterize particle production in high-energy particle and nuclear physics. | background 1.00 | 0.05 | 0.03 | asserted 1.00 |
| s4 | Their application to the higher moments of the net-charge and net-proton distributions is examined. | contribution 0.85 | 0.71 | 0.06 | asserted 0.49 |
| s5 | Differences between $\kappa\sigma^{2}$ and a statistical Poisson assumption of a factor of four (for net-charge) and 40% (for net-protons) can be accounted for by the NBD/BD. | result 0.88 | 0.73 | 0.46 | asserted 0.86 |
| s6 | This is the first application of the properties of the NBD/BD to describe the behavior of the higher moments of net-charge and net-proton distributions in nucleus-nucleus collisions. | contribution 0.96 | 0.87 | 0.37 | asserted 1.00 |
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The paper
Original abstract
A study of the first four moments (mean, variance, skewness, and kurtosis) and their products ($\kappa\sigma^{2}$ and $S\sigma$) of the net-charge and net-proton distributions in Au+Au collisions at $\sqrt{\rm s_{NN}}$ = 7.7-200 GeV from HIJING simulations has been carried out. The skewness and kurtosis and the collision volume independent products $\kappa\sigma^{2}$ and $S\sigma$ have been proposed as sensitive probes for identifying the presence of a QCD critical point. A discrete probability distribution that effectively describes the separate positively and negatively charged particle (or proton and anti-proton) multiplicity distributions is the negative binomial (or binomial) distribution (NBD/BD). The NBD/BD has been used to characterize particle production in high-energy particle and nuclear physics. Their application to the higher moments of the net-charge and net-proton distributions is examined. Differences between $\kappa\sigma^{2}$ and a statistical Poisson assumption of a factor of four (for net-charge) and 40% (for net-protons) can be accounted for by the NBD/BD. This is the first application of the properties of the NBD/BD to describe the behavior of the higher moments of net-charge and net-proton distributions in nucleus-nucleus collisions.
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References
How the literature uses it
5 arXiv papers cite this in 6 sentences
Papers citing it · 3 sentences without a confident label
Uses its method or tool 1 paper
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For a given NBD (BD) distribution, one can calculate the higher-order cumulants like $C_6$ and $C_8$ analytically by knowing the value of first and second cumulants [ref] .
Constructing probability density function of net-proton multiplicity distributions using Pearson curve method · Estimating higher-order cumulants · 0.85
Cites it as background 2 papers
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Additionally, experimental acceptance and efficiency corrections need to be taken into account [ref] .
Large proton cumulants from the superposition of ordinary multiplicity distributions · Introduction · 0.81
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While the measured susceptibilities are very sensitive to the phase structure of QCD they are also affected by other aspects of the dynamical evolution, many of which have been discussed in recent literature [ref] .
Effect of finite particle number sampling on baryon number fluctuations · Introduction · 0.90
What it cites · 2 sentences without a confident label
Cites as background 3 papers
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Several measurements of the higher-moments of net-proton, net-kaon, and net-charge distributions have been carried out [ref] .
Search for the QCD Critical Point by Higher Moments of Net-proton Multiplicity Distributions at STAR · Introduction · 0.88
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Several measurements of the higher-moments of net-proton, net-kaon, and net-charge distributions have been carried out [ref] .
Beam energy and centrality dependence of the statistical moments of the net-charge and net-kaon multiplicity distributions in Au+Au collisions at STAR · Introduction · 0.88
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The Relativistic Heavy Ion Collider (RHIC) recently embarked on a program to study the QCD phase diagram by colliding Au-nuclei at CMS collision energies ($√(s_NN)$) of $√(s_NN)$ = 7.7, 11.5, 19.6, 27, 39, 62.4, and 200 GeV [ref] .
An Experimental Exploration of the QCD Phase Diagram: The Search for the Critical Point and the Onset of De-confinement · Introduction · 0.89
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