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Describing the Dynamics of the Quark-Gluon Plasma Using Relativistic Viscous Hydrodynamics

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DESCRIBING THE DYNAMICS OF THE QUARK-GLUON PLASMA USING RELATIVISTIC VISCOUS HYDRODYNAMICS A Thesis Submitted to the Kent State University, College of Arts and Sciences in partial fulfillment of the requirements for the degree of Master of Science. By Mohammad N. Yaseen August 2016 © Copyright, 2016 by Mohammad N. Yaseen All Rights Reserved ii A thesis written by Mohammad N. Yaseen B.S., University of Anbar, 2008 M.S., Kent State University, 2016 Approved by __________________________, Director, Master’s Thesis Committee Michael Strickland __________________________, Member, Master’s Thesis Committee Bjorn Lussem __________________________, Member, Master’s Thesis Committee Spyridon Margetis Accepted by __________________________, Chair, Department of Physics James T. Gleeson __________________________, Dean, College of Arts and Sciences James L. Blank iii YASEEN, MOHAMMAD N., M.S., August 2016 QGP Produced in Ultra Relativistic Heavy Ion Collisions DESCRIBING THE DYNAMICS OF THE QUARK-GLUON PLASMA USING RELATIVISTIC VISCOUS HYDRODYNAMICS (83 pp.) Director of Thesis: Michael Strickland, Ph.D. When heavy nuclei collide at ultra-relativistic energies, their nuclear matter will melt producing what is known as the Quark-Gluon Plasma (QGP); a new state of matter that has been produced at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory (BNL) and Super Proton Synchrotron (LHC) in European Organization for Nuclear Research (CERN). Scientists now think that this matter filled the entire universe during the first micro second after the Big Bang. According to the experimental data, this matter acts like a nearly perfect liquid. This study requires a quantitatively precise theoretical framework to describe the dynamical evolution of the fireball produced by the collision. The equations that control the fireball expansion cannot be solved analytically. As a result, scientists must solve these equations numerically. The main goal of this thesis is to find precise numerical solutions for these equations. This is complicated by the fact that when using fluctuating initial conditions, discontinuities may be present which cause problems for standard centered- differences schemes. To fix this problem, we will use the following two numerical methods: LAX and weighted LAX. ACKNOWLEDGEMENTS Here, I mainly want to thank my advisor Dr. Michael Strickland for his continuous support and patience. He showed great knowledge and interest in theoretical physics and, he is really a great educator who can introduce deep theoretical concepts in simplified way. I also want to thank my friend Ammar Kirmani who helped me to understand the principles of programming. I also want to thank my thesis defense committee members Spyridon Margetis and Bjorn Lussem for the time they granted to me. iv Preface When heavy nuclei collide at ultra-relativistic energies, their nuclear matter will melt producing what is known as the Quark-Gluon Plasma (QGP). Since QGP behaves like a nearly perfect relativistic liquid, one can use viscous hydrodynamics equations to simulate the QGP hot bulk expansion. The viscous hydrodynamics equations cannot be solved analytically. Therefore, I use the numerical method to solve them and simulate the QGP expansion and this is the main goal of this thesis. In “chapter I’’, I introduce the reader to the basic important concepts that are necessary to understand what the QGP is and how it behaves. I introduce basic concepts of QCD after taking a historical glance. After that, I introduce the QGP concept and try to simplify the main concepts related to GGP as much as possible. In “chapter II”, I derive the main equations needed in the numerical calculations. I take the zeroth, first and second moment of the Boltzmann equation to derive the necessary number of independent equations needed to evaluate the necessary variables. In “chapter III”, I introduce the numerical calculation results. To perform this simulation, I use the following two numerical methods: LAX and weighted LAX. In “Chapter IV” I introduce the link between the astronomy studies and QGP and how QGP studies with gravitational waves can help us to understand the compact star inner structure. Finally, I discuss the results of the whole experimental and theoretical work done to simulate the QGP behavior and try to take a look at the future. iv TABLE OF CONTENTS Page ACKNOWLEDGMENTS ……………………………………………………………… iv PREFACE ………………………………………………………………………………. v LIST OF FIGURES ………………………………………………………………....… vii CHAPTER I. INTRODUCTION ……………………………………………………………….… 1 Historical Glance …...………………………………………………………………. 1 Quarks, Gluons and Chromodynamics ……………………………………………... 3 Quark Model …………………………………………………………………...….3 The Experimental Evidence for Quarks ……………………………………………7 Quantum Chromodynamics (QCD), Color Charge and Strong Interaction ……… 10 Color Confinement ……………………………………………………………….. 15 Jets ……………………………………………………………………………….. 15 Jet Quenching ……………………………………………………………………. 18 Quark Gluon Plasma (QGP) ………………………………………………………... 19 What is QGP? ………………………………………………………………….…. 19 A Glance on Experimental Detection Techniques and Calculations ………….….. 19 II. ANISOTROPIC RELATIVISTIC HYDRODYNAMICS ………………………… 22 Elliptic Flow ……………………………………………..………………………… 22 Derivation of Ideal Hydrodynamics Equations from Kinetic Theory ……………... 28 Bjorken Hydrodynamics …………………………………………………………… 32 General 3+1d Anisotropic Hydrodynamics Equations for a Massless Hydrodynamics System …………………………………………………………… 34 Convention and Notation ……………………………………………………….. 35 Basic Vectors ……………………………………………………………………. 35 Distribution function …………………………………………………………….. 36 Dynamical Variables …………………………………………………………….. 37 Bulk Variables ………………………………………………………………….... 38 Dynamical Equations …………………………………………………………….. 40 v III. NUMERICAL CALCULATIONS ……………………………………….………. 44 Weighted LAX ………………………………………………………….……….. 44 What is Weighted LAX? …………………………………………….……….. 44 Mathematical Formula ……………………………………………….……….. 44 The Best Value of λ ………………………………………………….………… 45 Numerical Results……………………………………………………….………... 46 Code constant Parameters and Initial Conditions …………………….……….. 46 Longitudinal Anisotropic Momentum Parameter Graph …………….………... 47 Effective Temperature Graphs ……………………………………….………... 47 Transverse Anisotropic Momentum Parameter Graph ……………….………... 52 The Graph of the Ratio of the Transverse Parameter to the Longitudinal Parameter ………………………………………….……… 54 Pion Differential Spectra Graph ………………………………………….……. 57 Freeze-out Hypersurface Graph ………………………………………….…….. 60 IV. APPLICATIONS, DISCUSIONS AND LOOK AT THE FUTURE ……………. 65 Theoretical Discussions and Conclusions ………………………………………... 65 Why Viscous Hydrodynamics ……………………………………………………. 67 The Experimental Results of Viscous Hydrodynamics ……………...…………… 68 QGP Existence in the Compact Stars and the Big Bang …………….………….…73 APPENDIX ……………………………………………………………………………77 REFERENCES ……………………………………………………………………….. 81 vi LIST OF FIGURES Figure Page 1. The basic quark model scheme ……………………………………………………….. 4 2. The internal structure of proton and neutron in the original quark model ……………. 5 3. The interaction between incident electron and proton’s components ………………… 9 4. The three basic colors combined with each other …………………………………… 14 5. Detecting jets in laboratory ……………………………………………………….......16 6. The basic jets and color confinement phenomenon illustration …………………...… 17 7. QGP evaluation stages ….……………………………………….………………….…21 8. Collision cross-section ………………………………………………………………. 23 9. The approximate QGP bulk shape and dimensions …………………………….…… 26 10. The asymmetry of the emerging quarks …………………………………………… 27 11. The longitudinal anisotropy parameter (훂z) as a function of position at ( = 1.25 fm/c) ……………………………………………………………………. 48 12. The longitudinal anisotropy parameter (훂z) as a function of position at ( = 10.25 fm/c) …………………………………………………………………….. 49 13. The effective temperature as a function of position at ( = 1.25 fm/c) ….…………. 50 14. The effective temperature as a function of position at ( = 10.25 fm/c) …………… 51 15. The transverse anisotropy parameter (훂x) as a function of position at ( = 0.65 fm/c) …………………………………………………………………… 53 16. The transverse anisotropy parameter (훂x) and the longitudinal anisotropy parameter (훂z) as a function of position at ( = 1.25 fm/c) ……………………...… 55 vii 17. The transverse anisotropy parameter (훂x) and the longitudinal anisotropy parameter (훂z) as a function of position at ( = 10.25 fm/c) ……………………… 56 18. The pion differential spectra graph for large number of events against to the transvers angular momentum ……………………………………….. 58 19. The pion differential spectra graph for one event against to the transvers angular momentum ………………………………………………………. 59 20. The temperature spatial invariant inside QGP bulk ………………………………... 62 21. The temperature invariant with time for every point inside the QGP bulk ………… 63 22. The freeze-out hypersurface graph …………………………………………………. 64 23. Multiplicity versus centrality (%) …………………………………………………... 69 24. Average transverse momentum versus centrality (%) ….……………………..…… 70 25. Flow hadronic coefficients versus centrality (%) ………….……………………….. 71 26. Transverse momentum spectra graph (experimental and simulation data) …………. 72 27. The nowadays estimated universe history …………………………………………... 76 viii CHAPTER I INTRODUCTION Historical Glance Like many other discoveries in physics, the Quark Gluon Plasma (QGP) was theoretically predicted many decades before it was experimentally realized. There was a problem that if Quantum Chromodynamics
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