# Initial Energy Density of √s = 7 and 8 TeV p–p Collisions at the LHC

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## Abstract

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## 1. Introduction

## 2. Rapidity Distributions from Hydrodynamics

## 3. Energy Density Estimation

- It has to reproduce the EoS-independent Bjorken estimate for $\lambda \to 1$.
- It should approximately reproduce the results of numerical hydro calculations; most importantly, the additional correction for $\kappa >1$ should increase the initial energy density.

## 4. Initial Energy Densities in 7 and 8 TeV LHC p–p Collisions

## 5. Uncertainty of the Estimate

## 6. Improved Initial Energy Density Using Combined TOTEM+CMS $dN/d\eta $ Data

## 7. Summary

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Charged particle $\frac{dN}{d\eta}$ distributions from the LHC TOTEM experiment, fitted with the result of the relativistic hydro solution described in this paper.

**Figure 2.**The correction factor as a function of freeze-out time versus thermalization time (${\tau}_{f}/{\tau}_{0}$). At a reasonable value of 2, the correction factor is around 25%.

**Figure 3.**Initial energy density (based on Table 1), temperature and pressure (based on the $\u03f5\propto {T}^{4}$ relationship) at 7 TeV (left) and 8 TeV (right), is indicated as a function of central charged particle multiplicity density. The Bjorken-estimate (dashed curve) is above the critical energy density of 1 GeV/fm${}^{3}$ if the multiplicity is larger than 12. Corrected initial energy density (solid curve) is above the critical value if multiplicity is larger than 9. Boxes (parallelograms) show systematic uncertainty (estimated from the 7 TeV case).

**Figure 4.**(

**a**) Charged particle $\frac{dN}{d\eta}$ distributions from CMS [51] and TOTEM [66] at 7 TeV fitted with the result of our relativistic hydrodynamical solution described in this paper, with $\lambda =1.076$; (

**b**) Charged particle $\frac{dN}{d\eta}$ distributions from CMS and TOTEM 8 TeV data of Reference [62,67] fitted with our results, with $\lambda =1.066$.

Parameter | Value | Stat. | Syst. Eff. on ϵ |
---|---|---|---|

λ | 1.073 | 0.1% | 0.4% (from data) |

${c}_{s}^{2}$ | 0.1 | - | −2% + 0.2% (if $0.05<{c}_{s}^{2}<0.5$) |

${\tau}_{f}/{\tau}_{0}$ | 2 | - | −4% + 10% (for ${\tau}_{f}/{\tau}_{0}$ in 1.5–4) |

${\tau}_{0}$ (fm$/c$) | 1 | - | underestimates ϵ |

R (fm) | 1.766 | - | 1.3% (from ${\sigma}_{\mathrm{tot}}$) |

$\langle E\rangle $ (GeV$/{c}^{2}$) | 0.562 | 0.5% | 3% |

${dN/d\eta |}_{\eta =0}$ | 5.895 | 0.2% | 3% (equivalently from ${N}_{0}$) |

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**MDPI and ACS Style**

Csanád, M.; Csörgő, T.; Jiang, Z.-F.; Yang, C.-B.
Initial Energy Density of √*s* = 7 and 8 TeV p–p Collisions at the LHC. *Universe* **2017**, *3*, 9.
https://doi.org/10.3390/universe3010009

**AMA Style**

Csanád M, Csörgő T, Jiang Z-F, Yang C-B.
Initial Energy Density of √*s* = 7 and 8 TeV p–p Collisions at the LHC. *Universe*. 2017; 3(1):9.
https://doi.org/10.3390/universe3010009

**Chicago/Turabian Style**

Csanád, Máté, Tamás Csörgő, Ze-Fang Jiang, and Chun-Bin Yang.
2017. "Initial Energy Density of √*s* = 7 and 8 TeV p–p Collisions at the LHC" *Universe* 3, no. 1: 9.
https://doi.org/10.3390/universe3010009