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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

M. S. Abdallah et al. (STAR Collaboration)
Phys. Rev. C 104, 024902 – Published 5 August 2021
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  • INTRODUCTION
  • EXPERIMENTAL DATA ANALYSIS
  • RESULTS
  • SUMMARY AND OUTLOOK
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    We report a systematic measurement of cumulants, Cn, for net-proton, proton, and antiproton multiplicity distributions, and correlation functions, κn, for proton and antiproton multiplicity distributions up to the fourth order in Au+Au collisions at sNN=7.7, 11.5, 14.5, 19.6, 27, 39, 54.4, 62.4, and 200 GeV. The Cn and κn are presented as a function of collision energy, centrality and kinematic acceptance in rapidity, y, and transverse momentum, pT. The data were taken during the first phase of the Beam Energy Scan (BES) program (2010–2017) at the BNL Relativistic Heavy Ion Collider (RHIC) facility. The measurements are carried out at midrapidity (|y|< 0.5) and transverse momentum 0.4<pT<2.0GeV/c, using the STAR detector at RHIC. We observe a nonmonotonic energy dependence (sNN = 7.7–62.4 GeV) of the net-proton C4/C2 with the significance of 3.1σ 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, κ2, 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, κ4, of protons plays a role in determining the energy dependence of proton C4/C1 below 19.6 GeV, which cannot be understood by the effect of baryon number conservation.

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    • Received 31 January 2021
    • Accepted 12 July 2021

    DOI:https://doi.org/10.1103/PhysRevC.104.024902

    ©2021 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Particle correlations & fluctuationsRelativistic heavy-ion collisions
    Nuclear Physics

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    Vol. 104, Iss. 2 — August 2021

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    Images

    • Figure 1
      Figure 1

      Top left panel: The mass squared (m2) versus rigidity for charged tracks in Au+Au collisions at sNN=39 GeV. The rigidity is defined as momentum/z, where z is the dimensionless ratio of particle charge to the electron charge magnitude. Bottom left panel: The specific ionization energy loss (dE/dx) as a function of rigidity measured in the TPC for the same data set. Also shown as solid lines are the theoretical expectations for each particle species. Right panels: Rapidity (y) versus transverse momentum (pT). The color reflects the relative yields of protons (top) and antiprotons (bottom) using the TPC PID for Au+Au collisions at sNN=39 GeV. The dashed boxes represent the acceptance used in the current analysis. Two blobs at large rapidities are contaminated by particles other than (anti)protons. This contamination is rejected in later steps of the analysis.

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    • Figure 2
      Figure 2

      The uncorrected reference charged particle multiplicity (Nch) distributions within pseudorapidity |η|< 1 by excluding protons and antiprotons in Au+Au collisions at sNN=7.7–200 GeV. These distributions are used for centrality determination. The shaded region at each sNN corresponds to 0–5% central collisions. The dashed line corresponds to Monte Carlo Glauber model simulations [89].

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    • Figure 3
      Figure 3

      Net-proton multiplicity (ΔNp) distributions in Au+Au collisions at various sNN for 0–5%, 30–40%, and 70-80% collision centralities at midrapidity. The statistical errors are small and within the symbol size. The distributions are not corrected for either the finite-centrality-width effect or for the reconstruction efficiencies of protons and antiprotons.

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    • Figure 4
      Figure 4

      Cn of net-proton distributions in Au+Au collisions at sNN=7.7, 19.6, and 62.4 GeV as a function of 〈Npart〉. The results are shown for 10%, 5%, and 2.5% centrality bins without CBWC and for nine centrality bins (0–5%, 5–10%, 10–20%, ..., 70–80%) with CBWC. The bars are the statistical uncertainties.

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    • Figure 5
      Figure 5

      κσ2 as a function of collision energy for Au+Au collisions for 0–5% centrality. The data have been corrected for volume fluctuation effects using CBWC, a data driven approach, and a model-dependent volume fluctuation correction method. The bars are the statistical uncertainties.

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    • Figure 6
      Figure 6

      Efficiency-uncorrected Cn of net-proton, proton, and antiproton multiplicity distributions in Au+Au collisions at sNN=7.7–200 GeV as a function of 〈Npart〉. The results are CBW corrected. The bars are the statistical uncertainties.

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    • Figure 7
      Figure 7

      Efficiencies of proton and antiproton as a function of 〈Npart〉 in Au+Au collisions for various sNN. For the lower pT range (0.4<pT<0.8 GeV/c), only the TPC is used. For the higher pT range (0.8<pT< 2.0 GeV/c), both the TPC and TOF are used.

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    • Figure 8
      Figure 8

      Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions. Red lines are fits to the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using the α that gives the minimum χ2/ndf. Each panel presents results for a different combination of the number of embedded protons and antiprotons as labeled in the legend. The ratio of the fits to the embedding data is shown for each panel at the bottom.

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    • Figure 9
      Figure 9

      Unfolded net-proton multiplicity distributions for sNN= 200 GeV Au+Au collisions where the binomial distribution (black circle), beta-binomial distributions with α+σ (green triangle), α (red square), and α−σ (blue triangle) are utilized in response matrices. Ratios of the beta-binomial unfolded distributions to that from binomial response matrices are shown in the bottom panel.

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    • Figure 10
      Figure 10

      Comparison of the statistical uncertainties on Cn of net-proton distributions in Au+Au collisions at sNN = 19.6 GeV from the delta theorem and bootstrap methods. The results are presented as a function of 〈Npart〉.

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    • Figure 11
      Figure 11

      Ratios of cumulants (Cn) as a function of 〈Npart〉, for net-proton distributions in Au+Au collisions at sNN=200 GeV obtained by varying the analysis criteria in terms of track selection criteria, particle identification criteria, and efficiency. Since variations with respect to default selection criteria are used to obtain the systematic uncertainties on the measurements, the errors are shown only for the default case.

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    • Figure 12
      Figure 12

      Collision centrality dependence of proton (open squares), antiproton (open triangles), and net-proton (filled circles) cumulants from (7.7–200 GeV) Au+Au collisions at RHIC. The data are from |y|<0.5 and 0.4<pT<2.0 GeV/c. Statistical and systematic uncertainties are shown as the narrow black and wide grey bands, respectively. Note that the net-proton and proton C4 from 0–5% and 5–10% central Au+Au collisions at 7.7 GeV have been scaled down by a factor of 2, indicated in the yellow box.

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    • Figure 13
      Figure 13

      Collision centrality dependence of the cumulant ratios of proton, antiproton and net-proton multiplicity distributions for Au+Au collisions at sNN = 7.7, 11.5, 14.5, 19.6, 27, 39, 54.4, 62.4, and 200 GeV. The bars and caps represent the statistical and systematic uncertainties, respectively.

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    • Figure 14
      Figure 14

      Collision centrality dependence of normalized correlation functions κn/κ1 (n=2,3,4) for proton and antiproton multiplicity distributions in Au+Au collisions at sNN = 7.7, 11.5, 14.5, 19.6, 27, 39, 54.4, 62.4, and 200 GeV. The bars and caps represent the statistical and systematic uncertainties, respectively. For clarity, the X-axis values for protons are shifted and the values of proton and antiproton κ4/κ1 at sNN = 7.7 GeV are scaled down by a factor of 2.

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    • Figure 15
      Figure 15

      Rapidity acceptance dependence of cumulants of proton, antiproton, and net-proton multiplicity distributions in 0–5% central Au+Au collisions at sNN = 7.7, 11.5, 14.5, 19.6, 27, 39, 54.4, 62.4, and 200 GeV. The bars and caps represent statistical and systematic uncertainties, respectively. For clarity, the X-axis values for protons are shifted and the values of proton, antiproton, and net-proton C4 at sNN = 7.7 GeV are scaled down by a factor of 2.

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    • Figure 16
      Figure 16

      Rapidity acceptance dependence of normalized correlation functions up to fourth order (κn/κ1, n=2, 3, 4) for proton and antiproton multiplicity distributions in 0–5% central Au+Au collisions at sNN = 7.7, 11.5, 14.5, 19.6, 27, 39, 54.4, 62.4, and 200 GeV. The X-axis rapidity cut ymax is applied as |y|<ymax. The bars and caps represent statistical and systematic uncertainties, respectively. For clarity, the X-axis values for protons are shifted and the values of proton and antiproton κ4/κ1 at sNN = 7.7 GeV are scaled down by a factor of 2.

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    • Figure 17
      Figure 17

      Rapidity-acceptance dependence of cumulant ratios of proton, antiproton and net-proton multiplicity distributions in 0–5% central Au+Au collisions at sNN = 7.7, 11.5, 14.5, 19.6, 27, 39, 54.4, 62.4, and 200 GeV. The bars and caps represent statistical and systematic uncertainties, respectively. For clarity, the X-axis values for net protons and protons are shifted.

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    • Figure 18
      Figure 18

      pT-acceptance dependence of cumulants of proton, antiproton, and net-proton multiplicity distributions for 0–5% central Au+Au collisions at sNN = 7.7, 11.5, 14.5, 19.6, 27, 39, 54.4, 62.4, and 200 GeV. The bars and caps represent statistical and systematic uncertainties, respectively. For clarity, the X-axis values for net protons are shifted and the values of proton, antiproton, and net-proton C4 at sNN = 7.7 GeV are scaled down by a factor of 2.

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    • Figure 19
      Figure 19

      The pT-acceptance dependence of the normalized correlation functions up to fourth order (κn/κ1, n=2, 3, 4) for proton and antiproton multiplicity distributions in 0–5% central Au+Au collisions at sNN = 7.7, 11.5, 14.5, 19.6, 27, 39, 54.4, 62.4, and 200 GeV. The bars and caps represent statistical and systematic uncertainties, respectively. For clarity, the X-axis values for protons are shifted and the values of proton and antiproton κ4/κ1 at sNN = 7.7 GeV are scaled down by a factor of 2.

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    • Figure 20
      Figure 20

      pT-acceptance dependence of cumulant ratios of proton, antiproton, and net-proton multiplicity distributions for 0–5% central Au+Au collisions at sNN = 7.7, 11.5, 14.5, 19.6, 27, 39, 54.4, 62.4, and 200 GeV. The bars and caps represent statistical and systematic uncertainties, respectively. For clarity, the X-axis values for net protons are shifted.

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    • Figure 21
      Figure 21

      Left panel: Collision energy dependence of C2B/C1B, C3B/C2B, and C4B/C2B for various pT acceptances from the hadron resonance gas model. Right panel: The variation of net-proton and net-baryon C2/C1, C3/C2, and C4/C2 within the experimental acceptance [117]. Note: this simulation is done within a pseudorapidity window in order to make comparison between baryons of different mass.

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    • Figure 22
      Figure 22

      Left panel: UrQMD results on pT acceptance dependence of C2/C1, C3/C2, and C4/C2 ratios as a function of sNN for net baryons. Right panel: Same ratios within the experimental acceptance for net protons and net baryons. Note: similar to Fig. 21, this simulation is done within a pseudorapidity window in order to make comparison between baryons of different mass.

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    • Figure 23
      Figure 23

      Upper panel: (a) σ2/M, (b) Sσ, and (c) κσ2 of net-proton distributions for 0–5% central Au+Au collisions from sNN=7.7–62.4 GeV. The error bars on the data points are statistical and systematic uncertainties added in quadrature. The black solid lines are polynomial fit functions which well describe the cumulant ratios. The legends also specify the values of chi squared per degree of freedom for the respective fits. The black dashed lines are the Poisson baselines. Lower panel: Derivative of the fitted polynomial as a function of collision energy. The bar and the gold band on the derivatives represent the statistical and systematic uncertainties, respectively.

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    • Figure 24
      Figure 24

      Collision energy dependence of C2/C1, C3/C2, and C4/C2 for net-proton multiplicity distributions in 0–5% central Au+Au collisions. The experimental net-proton measurements are compared to corresponding values from UrQMD and HRG models within the experimental acceptances. The bars and caps represent the statistical and systematic uncertainties of the experimental data, respectively. The widths of the bands reflect the statistical uncertainties for the model calculations.

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    • Figure 25
      Figure 25

      Collision energy dependence of the scaled (anti)proton cumulants and correlation functions in 0–5% central Au+Au collisions at sNN = 7.7, 11.5, 14.5, 19.6, 27, 39, 54.4, 62.4, and 200 GeV. The error bars and bands represent the statistical and systematic uncertainties, respectively. The results from UrQMD model calculation are also shown for comparison.

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