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Recent development of hydrodynamic modeling in heavy-ion collisions

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Abstract

We present a concise review of the recent development of relativistic hydrodynamics and its applications to heavy-ion collisions. Theoretical progress on the extended formulation of hydrodynamics toward out-of-equilibrium systems is addressed, with emphasis on the so-called attractor solution. Moreover, recent phenomenological improvements in the hydrodynamic modeling of heavy-ion collisions with respect to the ongoing beam energy scan program, the quantitative characterization of transport coefficients in three-dimensionally expanding quark–gluon plasma, the fluid description of small colliding systems, and certain other interdisciplinary connections are discussed.

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Notes

  1. We normalize the four-velocity as \(U^\mu U_\mu =1\), corresponding to the mostly negative metric convention: \(g_{\mu \nu }=(+,-,-,-)\).

  2. Causality and stability can be achieved in first-order viscous hydrodynamics as well but within a frame other than the choice by Landau and Lifshitz or Eckart [43].

  3. These transport coefficients have different evaluations for a strongly coupled system. From the \({\mathcal {N}}=4\) super-YM field theory, they are [45]

    $$\begin{aligned} C_\tau = \frac{2-\log 2}{2\pi },\quad C_\lambda = \frac{1}{2\pi }. \end{aligned}$$
    (11)

    .

  4. The convergence of the hydrogradient expansion also depends on the detailed identification of the expansion parameter. For instance, the dispersion relation consisting of perturbations around equilibrium gives rise to a series expansion in terms of the wave number, which is convergent [cf. Ref [54]]. On the contrary, for series expansion in real space over spatial gradients, the convergence property may depend on the initial condition [55].

  5. Note that this recursion relation differs from that in [47] by rescaling \(w\rightarrow C_\tau w\) and \(f_n\rightarrow 1-f_n/4\).

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Acknowledgements

We thank C. Gale, U. Heinz, J. P. Blaizot, J. F. Paquet, and B. Schenke for fruitful discussions. We thank the JETSCAPE Collaboration for providing the preliminary results shown in Fig. 11.

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Authors and Affiliations

  1. Department of Physics and Astronomy, Wayne State University, Detroit, MI, 48201, USA

    Chun Shen

  2. RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, NY, 11973, USA

    Chun Shen

  3. Key Laboratory of Nuclear Physics and Ion-Beam Application (MOE), Institute of Modern Physics, Fudan University, 220 Handan Road, Shanghai, 200433, China

    Li Yan

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Correspondence to Li Yan.

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This work was supported in part by the US Department of Energy (DOE) (No. DE-SC0013460), the National Science Foundation (NSF) (No. PHY-2012922), the National Natural Science Foundation of China (No. 11975079),  and the US Department of Energy, Office of Science, Office of Nuclear Physics, within the framework of the Beam Energy Scan Theory (BEST) Topical Collaboration.

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Shen, C., Yan, L. Recent development of hydrodynamic modeling in heavy-ion collisions. NUCL SCI TECH 31, 122 (2020). https://doi.org/10.1007/s41365-020-00829-z

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