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Universal relations between non-Gaussian fluctuations in heavy-ion collisions

Jiunn-Wei Chen, Jian Deng, Hiroaki Kohyama, and Lance Labun
Phys. Rev. D 95, 014038 – Published 31 January 2017
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  • INTRODUCTION
  • INTERPLAY BETWEEN SKEWNESS AND KURTOSIS
  • SCENARIOS IN ENERGY SCAN EXPERIMENTS
  • SUMMARY
  • ACKNOWLEDGMENTS
    • References

    Abstract

    We show that universality near a critical end point implies a characteristic relation between third- and fourth-order baryon susceptibilities χ3 and χ4, resulting in a banana-shaped loop when χ4 is plotted as a function of χ3 along a freeze-out line. This result relies only on the derivative relation between χ3 and χ4, the enhancement of the correlation length and the scaling symmetry near a critical point, and the freeze-out line near the critical point not too parallel to the μB axis. Including the individual enhancements of χ3 and χ4 near a critical point, these features may be a consistent set of observations supporting the interpretation of baryon fluctuation data as arising from criticality.

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    • Received 2 April 2016

    DOI:https://doi.org/10.1103/PhysRevD.95.014038

    © 2017 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Critical phenomenaParticle correlations & fluctuationsQCD phase transitionsRelativistic heavy-ion collisions
    Nuclear PhysicsStatistical Physics & Thermodynamics

    Authors & Affiliations

    Jiunn-Wei Chen1,2,*, Jian Deng3,†, Hiroaki Kohyama1,‡, and Lance Labun4,§

    • 1Department of Physics, CTS and LeCosPA, National Taiwan University, Taipei 10617, Taiwan
    • 2Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
    • 3Key Laboratory of Particle Physics and Particle Irradiation (MOE), School of Physics, Shandong University, Jinan 250100, China
    • 4Department of Physics, The University of Texas, Austin, Texas 78746, USA

    • *jwc@phys.ntu.edu.tw
    • †jdeng@sdu.edu.cn
    • ‡kohyama.hiroaki@gmail.com
    • §labun@utexas.edu

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    Vol. 95, Iss. 1 — 1 January 2017

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    Images

    • Figure 1
      Figure 1

      Upper panel: κ2,3,4(H) at fixed t>0. Lower panel: The Ising model phase diagram with line A the maximum of κ3 (also κ4=0), and line B the maximum of κ4. The curved lines are example freeze-out lines, drawn to model how they may pass through the scaling region in QCD.

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    • Figure 2
      Figure 2

      Upper left (right): Density plot of κ3(κ4) in the Ising model. Regions of κi>0 are in blue and κi<0 are in red. The dotted (black) line is the same as line A in Fig. 1 and the dot-dashed (red) line is the same as line B. Lower panel: A sketch of the peaks in χ3 and χ4 on a plausible phase diagram of QCD together with a hypothetical freeze-out line. Comparison to the location of the maxima in χ3 and χ4 in Fig. 1 suggests how the freeze-out line may be mapped onto the Ising coordinates.

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    • Figure 3
      Figure 3

      κ4 versus κ3 on example freeze-out lines passing through the universal region as shown in Fig. 1. Temperature decreases in the anticlockwise direction.

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    • Figure 4
      Figure 4

      Inset: The phase diagram of the NJL model with K=K0, a value chosen to reproduce QCD observables, and three hypothetical freeze-out lines tracking the phase boundary (see text). Larger frame: m2 versus m1 on the freeze-out lines plotted in the inset.

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    • Figure 5
      Figure 5

      Same as Fig. 4 but with K=0.65K0. The critical end point is at TCEP=0.

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    • Figure 6
      Figure 6

      Same as Fig. 5 with K=0.4K0. The critical end point would be formally at TCEP<0. Note the difference in scale of the axes.

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    • Figure 7
      Figure 7

      Same as Fig. 4 but with all quark masses zero mu=md=ms=0. The phase boundary is the first-order line. There is no critical point in the first quadrant μB,T>0, or the critical end point can be considered in the second quadrant with μCEP<0.

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    • Figure 8
      Figure 8

      From STAR preliminary data for the net-proton distribution in 0%–5% centrality of Au+Au collisions [23], κσ2 versus Sσ forms an anticlockwise loop from high to low, sNN=200, 62.4, 39, 27, 19.6, 11.5, 7.7 GeV.

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