# Viscous Hydrodynamic Description of the Pseudorapidity Density and Energy Density Estimation for Pb+Pb and Xe+Xe Collisions at the LHC

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## Abstract

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## 1. Introduction

## 2. Pseudorapidity Distribution from Hydrodynamics

## 3. Relationship between the Energy Density Estimation and Viscous Effect

## 4. Conclusions and Discussion

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**Left**): Pseudorapidity distribution from our model calculation (solid curves) compared to the LHC experimental data [16,17,18]. The black curves represent the pseudorapidity distribution for $\sqrt{{s}_{NN}}=2.76$ TeV Pb+Pb collisions, $\sqrt{{s}_{NN}}=5.02$ TeV Pb+Pb collisions and $\sqrt{{s}_{NN}}=5.44$ TeV Xe+Xe collisions. (

**Right**): the correction factor ${\u03f5}_{\mathrm{corr}}/{\u03f5}_{\mathrm{Bj}}$ as a function of the ratio of freeze-out time and thermalization time (${\tau}_{f}/{\tau}_{0}$) for different $\lambda $ and shear viscosity ratio $\eta /s$, bulk viscosity ratio $\zeta /s$. The black dashed line is the result of Bjorken model, while the red band is the result that include the viscosity effect enhancement (Equation(10)), and the blue band is the result from Equation (9). The band width comes from the uncertainty of $\lambda $ (−1.030 $\le \lambda \le $ 1.035). For the viscous fluid, the viscosity ratio is assumed to be constant [22,23] here and the statistical analysis of viscosity ratio is not discussed here.

$\sqrt{{\mathit{s}}_{\mathit{NN}}}$ | System | $\frac{\mathit{dn}}{\mathit{d}{\mathit{\eta}}_{\mathit{p}}}{|}_{{\mathit{\eta}}_{\mathit{p}}={\mathit{\eta}}_{\mathit{p}0}}$ | $\mathit{\lambda}$ | ${\mathit{\u03f5}}_{\mathbf{corr}}^{\mathbf{CNC}}/{\mathit{\u03f5}}_{\mathbf{Bj}}$ | ${\mathit{\u03f5}}_{\mathbf{corr}}^{\mathbf{viscous}}/{\mathit{\u03f5}}_{\mathbf{Bj}}$ |
---|---|---|---|---|---|

2.76 TeV | Pb+Pb | 1615 ± 39.0 | 1.035 ± 0.003 | 1.225 ± 0.022 | 1.285 ± 0.022 |

5.02 TeV | Pb+Pb | 1929 ± 47.0 | 1.032 ± 0.002 | 1.204 ± 0.012 | 1.263 ± 0.015 |

5.44 TeV | Xe+Xe | 1167 ± 26.0 | 1.030 ± 0.003 | 1.190 ± 0.021 | 1.248 ± 0.022 |

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**MDPI and ACS Style**

Gong, X.-T.; Jiang, Z.-F.; She, D.; Yang, C.B.
Viscous Hydrodynamic Description of the Pseudorapidity Density and Energy Density Estimation for Pb+Pb and Xe+Xe Collisions at the LHC. *Universe* **2019**, *5*, 112.
https://doi.org/10.3390/universe5050112

**AMA Style**

Gong X-T, Jiang Z-F, She D, Yang CB.
Viscous Hydrodynamic Description of the Pseudorapidity Density and Energy Density Estimation for Pb+Pb and Xe+Xe Collisions at the LHC. *Universe*. 2019; 5(5):112.
https://doi.org/10.3390/universe5050112

**Chicago/Turabian Style**

Gong, Xiong-Tao, Ze-Fang Jiang, Duan She, and C. B. Yang.
2019. "Viscous Hydrodynamic Description of the Pseudorapidity Density and Energy Density Estimation for Pb+Pb and Xe+Xe Collisions at the LHC" *Universe* 5, no. 5: 112.
https://doi.org/10.3390/universe5050112