cometadata/datacite-titles-descriptions-related-identifiers huggingface dataset:
DOI: 10.17182/hepdata.101356.v1/t7
title: "Reference Charged Particle Multiplicity 54.4 GeV" of "Cumulants and Correlation Functions of Net-proton, Proton and Antiproton Multiplicity Distributions in Au+Au Collisions at RHIC"

description: Reference charged particle multiplicity distributions using only pions and kaons ...
description: We report a systematic measurement of cumulants, $C_{n}$, for net-proton, proton and antiproton, and correlation functions, $\kappa_n$, for proton and antiproton multiplicity distributions up to the fourth order in Au+Au collisions at $\sqrt{s_{\mathrm {NN}}}$ = 7.7, 11.5, 14.5, 19.6, 27, 39, 54.4, 62.4 and 200 GeV. The $C_{n}$ and $\kappa_n$ are presented as a function of collision energy, centrality and kinematic acceptance in rapidity, $y$, and transverse momentum, $p_{T}$. The data were taken during the first phase of the Beam Energy Scan (BES) program (2010 -- 2017) at the Relativistic Heavy Ion Collider (RHIC) facility. The measurements are carried out at midrapidity ($|y| &lt;$ 0.5) and transverse momentum 0.4 $&lt;$ $p_{\rm T}$ $&lt;$ 2.0 GeV/$c$, using the STAR detector at RHIC. We observe a non-monotonic energy dependence ({\snn} = 7.7 -- 62.4 GeV) of the net-proton $C_{4}$/$C_{2}$ with the significance of 3.1$\sigma$ for the 0-5\% central Au+Au collisions. This is consistent with the expectations of critical fluctuations in a QCD-inspired model. Thermal and transport model calculations show a monotonic variation with \snn. For the multiparticle correlation functions, we observe significant negative values for a two-particle correlation function, $\kappa_2$, of protons and antiprotons, which are mainly due to the effects of baryon number conservation. Furthermore, it is found that the four-particle correlation function, $\kappa_4$, of protons plays a role in determining the energy dependence of proton $C_4/C_1$ below 19.6 GeV, which cannot be solely understood by the negative values of $\kappa_2$ for protons.
DOI: 10.17182/hepdata.101356.v1/t8
title: "Reference Charged Particle Multiplicity 62.4 GeV" of "Cumulants and Correlation Functions of Net-proton, Proton and Antiproton Multiplicity Distributions in Au+Au Collisions at RHIC"

description: Reference charged particle multiplicity distributions using only pions and kaons ...
description: We report a systematic measurement of cumulants, $C_{n}$, for net-proton, proton and antiproton, and correlation functions, $\kappa_n$, for proton and antiproton multiplicity distributions up to the fourth order in Au+Au collisions at $\sqrt{s_{\mathrm {NN}}}$ = 7.7, 11.5, 14.5, 19.6, 27, 39, 54.4, 62.4 and 200 GeV. The $C_{n}$ and $\kappa_n$ are presented as a function of collision energy, centrality and kinematic acceptance in rapidity, $y$, and transverse momentum, $p_{T}$. The data were taken during the first phase of the Beam Energy Scan (BES) program (2010 -- 2017) at the Relativistic Heavy Ion Collider (RHIC) facility. The measurements are carried out at midrapidity ($|y| &lt;$ 0.5) and transverse momentum 0.4 $&lt;$ $p_{\rm T}$ $&lt;$ 2.0 GeV/$c$, using the STAR detector at RHIC. We observe a non-monotonic energy dependence ({\snn} = 7.7 -- 62.4 GeV) of the net-proton $C_{4}$/$C_{2}$ with the significance of 3.1$\sigma$ for the 0-5\% central Au+Au collisions. This is consistent with the expectations of critical fluctuations in a QCD-inspired model. Thermal and transport model calculations show a monotonic variation with \snn. For the multiparticle correlation functions, we observe significant negative values for a two-particle correlation function, $\kappa_2$, of protons and antiprotons, which are mainly due to the effects of baryon number conservation. Furthermore, it is found that the four-particle correlation function, $\kappa_4$, of protons plays a role in determining the energy dependence of proton $C_4/C_1$ below 19.6 GeV, which cannot be solely understood by the negative values of $\kappa_2$ for protons.
DOI: 10.17182/hepdata.101356.v1/t9
title: "Reference Charged Particle Multiplicity 200 GeV" of "Cumulants and Correlation Functions of Net-proton, Proton and Antiproton Multiplicity Distributions in Au+Au Collisions at RHIC"

description: Reference charged particle multiplicity distributions using only pions and kaons ...
description: We report a systematic measurement of cumulants, $C_{n}$, for net-proton, proton and antiproton, and correlation functions, $\kappa_n$, for proton and antiproton multiplicity distributions up to the fourth order in Au+Au collisions at $\sqrt{s_{\mathrm {NN}}}$ = 7.7, 11.5, 14.5, 19.6, 27, 39, 54.4, 62.4 and 200 GeV. The $C_{n}$ and $\kappa_n$ are presented as a function of collision energy, centrality and kinematic acceptance in rapidity, $y$, and transverse momentum, $p_{T}$. The data were taken during the first phase of the Beam Energy Scan (BES) program (2010 -- 2017) at the Relativistic Heavy Ion Collider (RHIC) facility. The measurements are carried out at midrapidity ($|y| &lt;$ 0.5) and transverse momentum 0.4 $&lt;$ $p_{\rm T}$ $&lt;$ 2.0 GeV/$c$, using the STAR detector at RHIC. We observe a non-monotonic energy dependence ({\snn} = 7.7 -- 62.4 GeV) of the net-proton $C_{4}$/$C_{2}$ with the significance of 3.1$\sigma$ for the 0-5\% central Au+Au collisions. This is consistent with the expectations of critical fluctuations in a QCD-inspired model. Thermal and transport model calculations show a monotonic variation with \snn. For the multiparticle correlation functions, we observe significant negative values for a two-particle correlation function, $\kappa_2$, of protons and antiprotons, which are mainly due to the effects of baryon number conservation. Furthermore, it is found that the four-particle correlation function, $\kappa_4$, of protons plays a role in determining the energy dependence of proton $C_4/C_1$ below 19.6 GeV, which cannot be solely understood by the negative values of $\kappa_2$ for protons.
DOI: 10.17182/hepdata.101356.v1/t12
title: "Net-Proton Multiplicity 7.7 70-80%" of "Cumulants and Correlation Functions of Net-proton, Proton and Antiproton Multiplicity Distributions in Au+Au Collisions at RHIC"

description: $\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...
description: We report a systematic measurement of cumulants, $C_{n}$, for net-proton, proton and antiproton, and correlation functions, $\kappa_n$, for proton and antiproton multiplicity distributions up to the fourth order in Au+Au collisions at $\sqrt{s_{\mathrm {NN}}}$ = 7.7, 11.5, 14.5, 19.6, 27, 39, 54.4, 62.4 and 200 GeV. The $C_{n}$ and $\kappa_n$ are presented as a function of collision energy, centrality and kinematic acceptance in rapidity, $y$, and transverse momentum, $p_{T}$. The data were taken during the first phase of the Beam Energy Scan (BES) program (2010 -- 2017) at the Relativistic Heavy Ion Collider (RHIC) facility. The measurements are carried out at midrapidity ($|y| &lt;$ 0.5) and transverse momentum 0.4 $&lt;$ $p_{\rm T}$ $&lt;$ 2.0 GeV/$c$, using the STAR detector at RHIC. We observe a non-monotonic energy dependence ({\snn} = 7.7 -- 62.4 GeV) of the net-proton $C_{4}$/$C_{2}$ with the significance of 3.1$\sigma$ for the 0-5\% central Au+Au collisions. This is consistent with the expectations of critical fluctuations in a QCD-inspired model. Thermal and transport model calculations show a monotonic variation with \snn. For the multiparticle correlation functions, we observe significant negative values for a two-particle correlation function, $\kappa_2$, of protons and antiprotons, which are mainly due to the effects of baryon number conservation. Furthermore, it is found that the four-particle correlation function, $\kappa_4$, of protons plays a role in determining the energy dependence of proton $C_4/C_1$ below 19.6 GeV, which cannot be solely understood by the negative values of $\kappa_2$ for protons.
DOI: 10.17182/hepdata.101356.v1/t13
title: "Net-Proton Multiplicity 11.5 0-5%" of "Cumulants and Correlation Functions of Net-proton, Proton and Antiproton Multiplicity Distributions in Au+Au Collisions at RHIC"

description: $\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...
description: We report a systematic measurement of cumulants, $C_{n}$, for net-proton, proton and antiproton, and correlation functions, $\kappa_n$, for proton and antiproton multiplicity distributions up to the fourth order in Au+Au collisions at $\sqrt{s_{\mathrm {NN}}}$ = 7.7, 11.5, 14.5, 19.6, 27, 39, 54.4, 62.4 and 200 GeV. The $C_{n}$ and $\kappa_n$ are presented as a function of collision energy, centrality and kinematic acceptance in rapidity, $y$, and transverse momentum, $p_{T}$. The data were taken during the first phase of the Beam Energy Scan (BES) program (2010 -- 2017) at the Relativistic Heavy Ion Collider (RHIC) facility. The measurements are carried out at midrapidity ($|y| &lt;$ 0.5) and transverse momentum 0.4 $&lt;$ $p_{\rm T}$ $&lt;$ 2.0 GeV/$c$, using the STAR detector at RHIC. We observe a non-monotonic energy dependence ({\snn} = 7.7 -- 62.4 GeV) of the net-proton $C_{4}$/$C_{2}$ with the significance of 3.1$\sigma$ for the 0-5\% central Au+Au collisions. This is consistent with the expectations of critical fluctuations in a QCD-inspired model. Thermal and transport model calculations show a monotonic variation with \snn. For the multiparticle correlation functions, we observe significant negative values for a two-particle correlation function, $\kappa_2$, of protons and antiprotons, which are mainly due to the effects of baryon number conservation. Furthermore, it is found that the four-particle correlation function, $\kappa_4$, of protons plays a role in determining the energy dependence of proton $C_4/C_1$ below 19.6 GeV, which cannot be solely understood by the negative values of $\kappa_2$ for protons.
DOI: 10.17182/hepdata.101356.v1/t14
title: "Net-Proton Multiplicity 11.5 30-40%" of "Cumulants and Correlation Functions of Net-proton, Proton and Antiproton Multiplicity Distributions in Au+Au Collisions at RHIC"

description: $\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...
description: We report a systematic measurement of cumulants, $C_{n}$, for net-proton, proton and antiproton, and correlation functions, $\kappa_n$, for proton and antiproton multiplicity distributions up to the fourth order in Au+Au collisions at $\sqrt{s_{\mathrm {NN}}}$ = 7.7, 11.5, 14.5, 19.6, 27, 39, 54.4, 62.4 and 200 GeV. The $C_{n}$ and $\kappa_n$ are presented as a function of collision energy, centrality and kinematic acceptance in rapidity, $y$, and transverse momentum, $p_{T}$. The data were taken during the first phase of the Beam Energy Scan (BES) program (2010 -- 2017) at the Relativistic Heavy Ion Collider (RHIC) facility. The measurements are carried out at midrapidity ($|y| &lt;$ 0.5) and transverse momentum 0.4 $&lt;$ $p_{\rm T}$ $&lt;$ 2.0 GeV/$c$, using the STAR detector at RHIC. We observe a non-monotonic energy dependence ({\snn} = 7.7 -- 62.4 GeV) of the net-proton $C_{4}$/$C_{2}$ with the significance of 3.1$\sigma$ for the 0-5\% central Au+Au collisions. This is consistent with the expectations of critical fluctuations in a QCD-inspired model. Thermal and transport model calculations show a monotonic variation with \snn. For the multiparticle correlation functions, we observe significant negative values for a two-particle correlation function, $\kappa_2$, of protons and antiprotons, which are mainly due to the effects of baryon number conservation. Furthermore, it is found that the four-particle correlation function, $\kappa_4$, of protons plays a role in determining the energy dependence of proton $C_4/C_1$ below 19.6 GeV, which cannot be solely understood by the negative values of $\kappa_2$ for protons.
DOI: 10.17182/hepdata.101356.v1/t15
title: "Net-Proton Multiplicity 11.5 70-80%" of "Cumulants and Correlation Functions of Net-proton, Proton and Antiproton Multiplicity Distributions in Au+Au Collisions at RHIC"

description: $\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...
description: We report a systematic measurement of cumulants, $C_{n}$, for net-proton, proton and antiproton, and correlation functions, $\kappa_n$, for proton and antiproton multiplicity distributions up to the fourth order in Au+Au collisions at $\sqrt{s_{\mathrm {NN}}}$ = 7.7, 11.5, 14.5, 19.6, 27, 39, 54.4, 62.4 and 200 GeV. The $C_{n}$ and $\kappa_n$ are presented as a function of collision energy, centrality and kinematic acceptance in rapidity, $y$, and transverse momentum, $p_{T}$. The data were taken during the first phase of the Beam Energy Scan (BES) program (2010 -- 2017) at the Relativistic Heavy Ion Collider (RHIC) facility. The measurements are carried out at midrapidity ($|y| &lt;$ 0.5) and transverse momentum 0.4 $&lt;$ $p_{\rm T}$ $&lt;$ 2.0 GeV/$c$, using the STAR detector at RHIC. We observe a non-monotonic energy dependence ({\snn} = 7.7 -- 62.4 GeV) of the net-proton $C_{4}$/$C_{2}$ with the significance of 3.1$\sigma$ for the 0-5\% central Au+Au collisions. This is consistent with the expectations of critical fluctuations in a QCD-inspired model. Thermal and transport model calculations show a monotonic variation with \snn. For the multiparticle correlation functions, we observe significant negative values for a two-particle correlation function, $\kappa_2$, of protons and antiprotons, which are mainly due to the effects of baryon number conservation. Furthermore, it is found that the four-particle correlation function, $\kappa_4$, of protons plays a role in determining the energy dependence of proton $C_4/C_1$ below 19.6 GeV, which cannot be solely understood by the negative values of $\kappa_2$ for protons.
DOI: 10.17182/hepdata.101356.v1/t16
title: "Net-Proton Multiplicity 14.5 0-5%" of "Cumulants and Correlation Functions of Net-proton, Proton and Antiproton Multiplicity Distributions in Au+Au Collisions at RHIC"

description: $\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...
description: We report a systematic measurement of cumulants, $C_{n}$, for net-proton, proton and antiproton, and correlation functions, $\kappa_n$, for proton and antiproton multiplicity distributions up to the fourth order in Au+Au collisions at $\sqrt{s_{\mathrm {NN}}}$ = 7.7, 11.5, 14.5, 19.6, 27, 39, 54.4, 62.4 and 200 GeV. The $C_{n}$ and $\kappa_n$ are presented as a function of collision energy, centrality and kinematic acceptance in rapidity, $y$, and transverse momentum, $p_{T}$. The data were taken during the first phase of the Beam Energy Scan (BES) program (2010 -- 2017) at the Relativistic Heavy Ion Collider (RHIC) facility. The measurements are carried out at midrapidity ($|y| &lt;$ 0.5) and transverse momentum 0.4 $&lt;$ $p_{\rm T}$ $&lt;$ 2.0 GeV/$c$, using the STAR detector at RHIC. We observe a non-monotonic energy dependence ({\snn} = 7.7 -- 62.4 GeV) of the net-proton $C_{4}$/$C_{2}$ with the significance of 3.1$\sigma$ for the 0-5\% central Au+Au collisions. This is consistent with the expectations of critical fluctuations in a QCD-inspired model. Thermal and transport model calculations show a monotonic variation with \snn. For the multiparticle correlation functions, we observe significant negative values for a two-particle correlation function, $\kappa_2$, of protons and antiprotons, which are mainly due to the effects of baryon number conservation. Furthermore, it is found that the four-particle correlation function, $\kappa_4$, of protons plays a role in determining the energy dependence of proton $C_4/C_1$ below 19.6 GeV, which cannot be solely understood by the negative values of $\kappa_2$ for protons.
DOI: 10.17182/hepdata.101356.v1/t17
title: "Net-Proton Multiplicity 14.5 30-40%" of "Cumulants and Correlation Functions of Net-proton, Proton and Antiproton Multiplicity Distributions in Au+Au Collisions at RHIC"

description: $\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...
description: We report a systematic measurement of cumulants, $C_{n}$, for net-proton, proton and antiproton, and correlation functions, $\kappa_n$, for proton and antiproton multiplicity distributions up to the fourth order in Au+Au collisions at $\sqrt{s_{\mathrm {NN}}}$ = 7.7, 11.5, 14.5, 19.6, 27, 39, 54.4, 62.4 and 200 GeV. The $C_{n}$ and $\kappa_n$ are presented as a function of collision energy, centrality and kinematic acceptance in rapidity, $y$, and transverse momentum, $p_{T}$. The data were taken during the first phase of the Beam Energy Scan (BES) program (2010 -- 2017) at the Relativistic Heavy Ion Collider (RHIC) facility. The measurements are carried out at midrapidity ($|y| &lt;$ 0.5) and transverse momentum 0.4 $&lt;$ $p_{\rm T}$ $&lt;$ 2.0 GeV/$c$, using the STAR detector at RHIC. We observe a non-monotonic energy dependence ({\snn} = 7.7 -- 62.4 GeV) of the net-proton $C_{4}$/$C_{2}$ with the significance of 3.1$\sigma$ for the 0-5\% central Au+Au collisions. This is consistent with the expectations of critical fluctuations in a QCD-inspired model. Thermal and transport model calculations show a monotonic variation with \snn. For the multiparticle correlation functions, we observe significant negative values for a two-particle correlation function, $\kappa_2$, of protons and antiprotons, which are mainly due to the effects of baryon number conservation. Furthermore, it is found that the four-particle correlation function, $\kappa_4$, of protons plays a role in determining the energy dependence of proton $C_4/C_1$ below 19.6 GeV, which cannot be solely understood by the negative values of $\kappa_2$ for protons.
DOI: 10.17182/hepdata.101356.v1/t18
title: "Net-Proton Multiplicity 14.5 70-80%" of "Cumulants and Correlation Functions of Net-proton, Proton and Antiproton Multiplicity Distributions in Au+Au Collisions at RHIC"

description: $\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...
description: We report a systematic measurement of cumulants, $C_{n}$, for net-proton, proton and antiproton, and correlation functions, $\kappa_n$, for proton and antiproton multiplicity distributions up to the fourth order in Au+Au collisions at $\sqrt{s_{\mathrm {NN}}}$ = 7.7, 11.5, 14.5, 19.6, 27, 39, 54.4, 62.4 and 200 GeV. The $C_{n}$ and $\kappa_n$ are presented as a function of collision energy, centrality and kinematic acceptance in rapidity, $y$, and transverse momentum, $p_{T}$. The data were taken during the first phase of the Beam Energy Scan (BES) program (2010 -- 2017) at the Relativistic Heavy Ion Collider (RHIC) facility. The measurements are carried out at midrapidity ($|y| &lt;$ 0.5) and transverse momentum 0.4 $&lt;$ $p_{\rm T}$ $&lt;$ 2.0 GeV/$c$, using the STAR detector at RHIC. We observe a non-monotonic energy dependence ({\snn} = 7.7 -- 62.4 GeV) of the net-proton $C_{4}$/$C_{2}$ with the significance of 3.1$\sigma$ for the 0-5\% central Au+Au collisions. This is consistent with the expectations of critical fluctuations in a QCD-inspired model. Thermal and transport model calculations show a monotonic variation with \snn. For the multiparticle correlation functions, we observe significant negative values for a two-particle correlation function, $\kappa_2$, of protons and antiprotons, which are mainly due to the effects of baryon number conservation. Furthermore, it is found that the four-particle correlation function, $\kappa_4$, of protons plays a role in determining the energy dependence of proton $C_4/C_1$ below 19.6 GeV, which cannot be solely understood by the negative values of $\kappa_2$ for protons.
DOI: 10.17182/hepdata.101356.v1/t19
title: "Net-Proton Multiplicity 19.6 0-5%" of "Cumulants and Correlation Functions of Net-proton, Proton and Antiproton Multiplicity Distributions in Au+Au Collisions at RHIC"

description: $\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...
description: We report a systematic measurement of cumulants, $C_{n}$, for net-proton, proton and antiproton, and correlation functions, $\kappa_n$, for proton and antiproton multiplicity distributions up to the fourth order in Au+Au collisions at $\sqrt{s_{\mathrm {NN}}}$ = 7.7, 11.5, 14.5, 19.6, 27, 39, 54.4, 62.4 and 200 GeV. The $C_{n}$ and $\kappa_n$ are presented as a function of collision energy, centrality and kinematic acceptance in rapidity, $y$, and transverse momentum, $p_{T}$. The data were taken during the first phase of the Beam Energy Scan (BES) program (2010 -- 2017) at the Relativistic Heavy Ion Collider (RHIC) facility. The measurements are carried out at midrapidity ($|y| &lt;$ 0.5) and transverse momentum 0.4 $&lt;$ $p_{\rm T}$ $&lt;$ 2.0 GeV/$c$, using the STAR detector at RHIC. We observe a non-monotonic energy dependence ({\snn} = 7.7 -- 62.4 GeV) of the net-proton $C_{4}$/$C_{2}$ with the significance of 3.1$\sigma$ for the 0-5\% central Au+Au collisions. This is consistent with the expectations of critical fluctuations in a QCD-inspired model. Thermal and transport model calculations show a monotonic variation with \snn. For the multiparticle correlation functions, we observe significant negative values for a two-particle correlation function, $\kappa_2$, of protons and antiprotons, which are mainly due to the effects of baryon number conservation. Furthermore, it is found that the four-particle correlation function, $\kappa_4$, of protons plays a role in determining the energy dependence of proton $C_4/C_1$ below 19.6 GeV, which cannot be solely understood by the negative values of $\kappa_2$ for protons.
DOI: 10.17182/hepdata.101356.v1/t20
title: "Net-Proton Multiplicity 19.6 30-40%" of "Cumulants and Correlation Functions of Net-proton, Proton and Antiproton Multiplicity Distributions in Au+Au Collisions at RHIC"

description: $\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...
description: We report a systematic measurement of cumulants, $C_{n}$, for net-proton, proton and antiproton, and correlation functions, $\kappa_n$, for proton and antiproton multiplicity distributions up to the fourth order in Au+Au collisions at $\sqrt{s_{\mathrm {NN}}}$ = 7.7, 11.5, 14.5, 19.6, 27, 39, 54.4, 62.4 and 200 GeV. The $C_{n}$ and $\kappa_n$ are presented as a function of collision energy, centrality and kinematic acceptance in rapidity, $y$, and transverse momentum, $p_{T}$. The data were taken during the first phase of the Beam Energy Scan (BES) program (2010 -- 2017) at the Relativistic Heavy Ion Collider (RHIC) facility. The measurements are carried out at midrapidity ($|y| &lt;$ 0.5) and transverse momentum 0.4 $&lt;$ $p_{\rm T}$ $&lt;$ 2.0 GeV/$c$, using the STAR detector at RHIC. We observe a non-monotonic energy dependence ({\snn} = 7.7 -- 62.4 GeV) of the net-proton $C_{4}$/$C_{2}$ with the significance of 3.1$\sigma$ for the 0-5\% central Au+Au collisions. This is consistent with the expectations of critical fluctuations in a QCD-inspired model. Thermal and transport model calculations show a monotonic variation with \snn. For the multiparticle correlation functions, we observe significant negative values for a two-particle correlation function, $\kappa_2$, of protons and antiprotons, which are mainly due to the effects of baryon number conservation. Furthermore, it is found that the four-particle correlation function, $\kappa_4$, of protons plays a role in determining the energy dependence of proton $C_4/C_1$ below 19.6 GeV, which cannot be solely understood by the negative values of $\kappa_2$ for protons.