INVESTIGATION OF NUCLEAR COMPRESSION IN THE AMPT MODEL OF NUCLEUS-NUCLEUS COLLISIONS Athesissubmittedto Kent State University in partial Fulfillment of the requirements for the Degree of Master of Science by Huda Alalawi December, 2018 c Copyright All rights reserved Except for previously published materials Thesis written by Huda Alalawi B.S., Umm Al-Qura University, 2011 M.S., Kent State University, 2018 Approved by , Advisor Dr. Declan Keane , Advisor Dr. Spyridon Margetis ,Chair,DepartmentofPhysics Dr. James T. Gleeson , Dean, College of Arts and Sciences Dr. James L. Blank Table of Contents Table of Contents ................................ iii List of Figures .................................. v List of Tables ................................... vii Acknowledgments ................................ viii 1 Introduction .................................. 1 1.1 Standard Model (SM) ......................... 1 1.2 Quantum Chromodynamics QCD ................. 4 1.3 The QCD Phase Diagram ...................... 5 1.3.1 Phase transition ........................ 6 1.4 Bag Model of a Hadron ........................ 6 1.5 Quark-Gluon Plasma-Hadron Phase Transition in the Bag Model .................................. 8 1.5.1 Equation of state ....................... 8 1.6 High-Energy Heavy -Ion Collisions ................ 10 2 AMPT Model ................................. 13 2.1 Components of The AMPT Model ................. 14 2.2 Modified AMPT Code ........................ 17 3 Findings Using the Modified AMPT Code and Discussion ..... 18 iii 4 Summary and Suggestions for Future Research ............ 27 References ..................................... 29 iv List of Figures 1.1 The Standard Model of elementary particles with the three generations of matter, gauge bosons in the fourth column, and the Higgs boson in the fifth. 3 1.2 A sketch of a possible phase diagram of QCD matter. 5 1.3 MIT bag model[14] . 7 1.4 Collisions of two heavy nuclei in relativistic heavy ion collisions. The collisions are not always head-on, thus sometimes some of the nucleons become spectators while the rest become participants. 10 1.5 The space-time evolution of heavy ion collision. 11 1.6 The space-time evolution of heavy ion collision. 12 2.1 Illustration of the structure of the default AMPT model. 15 2.2 Illustration of the structure of the AMPT model with string melting. 16 3.1 A 238U+238Usemi-centralcollision,showingthechangeofbaryonden- sity versus time. 19 3.2 Snapshots of a Au + Au collision at 11.6 A GeV from AMPT/ART, showing (a) combined local baryon density for target and projectile, and (b) the density for the projectile alone [34]. Each panel plots 3 the baryon density (fm− )onagrayscalewithinay z spatial grid − over a projected area of 20 fm 20 fm, where the horizontal (z)axis ⇥ corresponds to the beam direction. Comparison of (a) and (b) suggests thatcompressionisobserver–systemdependent. 20 v 3.3 Time evolution of central baryon density for Au + Au in the CMS sys- tem (blue circles) and the target (lab) system (red circles) at psNN = 8 GeV in the AMPT model. The vertical scale gives relative density in units of ⇢ .Thehorizontalscaleistimesteps 10 fm/c........ 21 0 ⇥ 3.4 Central baryon density in multiples of ⇢0 as a function of time for 1000 Au + Au central collisions at psNN = 8 GeV. At each time-step, each magenta dot represents the density for one event. The overlaid black circles are the average densities for each time-step. 23 3.5 Average central baryon density as a function of time for di↵erent colli- sion energies. The highest value is achieved for psNN =13GeV(black circles) . 24 3.6 Maximum average central baryon density, in multiples of ground-state nuclear density, as a function of beam energy for central Au + Au collisions. 26 4.1 Average central baryon density as a function of time as predicted by five di↵erent transport model calculations for central Au+Au collision at 5 A GeV (left panel) and at 10 A GeV (right panel). 28 vi List of Tables 3.1 Maximum average central baryon density as a function of CM energy forcentralAu+Aucollisions.. 25 vii Acknowledgments First of all, I express our deep gratitude to the Almighty Allah for giving me an opportunity to do this project. This thesis could not have been possible without precious support and guidance of many people. I would like to express my special thanks of gratitude to Prof. Declan Keane. He opened the door to this study by being my research adviser. His sincere guidance and valuable advice enabled me to achieve this project. Besides my advisor, I would like to extend my deepest appreciation to Dr. Spyridon Margetis who helped me with the AMPT model and ROOT. His instruction, patience, and advice have been the cornerstone to this work. Also, I would like to thank prof. Mina Katramatou for being a member of my thesis committee. Thanks also go to my mom and my dad. Their constant prays, and encouragement reminded me I was not alone. I would like to thank my sisters and my brothers whose their support has followed me throughout my education. Finally, I can never thank enough my husband Naif. His warmth, understanding, and unwavering faith in me sustained me more than I can ever say. viii Chapter 1 Introduction All particles in the Universe are governed by four fundamental forces. In the early twentieth century, physicists believed that protons, neutrons, and electrons are the fundamental particles that constituted all matter and make up all atoms. By the mid-1960’s, physicists were beginning to realize that their prior understanding of the fundamental particles was not adequate to explain many new discovries, such as point-like particles (protons) inside the nucleon[1]. In 1964, Murray Gell-Mann and George Zweig proposed that these new pointlike objects are the subatomic particles known as quarks which as far as we know have no substructure. In the early 1970s, Murray Gell-Mann and George Zweig proposed a theory that is now an important part of the Standard Model (SM) of particle physics[2]. 1.1 Standard Model (SM) The Standard Model (SM) contains the handful of elementary particles shown in Figure 1.1. It describes a theory of fundamental particles and how they interact. Ac- cording to the Standard Model, the elementary particles exist in two primary groups. 1. Fermions: Fermions that have half-integer spin and obey the Fermi–Dirac statistics, i.e., fermions follow Pauli’s exclusion principle[3]. The fermions can be divided into three sets. Quarks : • 1 Quarks have fractional color charge and come in six flavors which refer to set of quantum numbers. These flavors with their charge are u (up), c (charm), and t 2 (top) have a charge of + 3 .Inaddition,d (down), s (strange), and b (bottom) have a charge of 1 .Theybindtogethertomakeahadronandcannotexist − 3 freely. They are a↵ected by the strong, weak, electromagnetic, and gravitational force. Leptons : • Leptons (light particles) carry integer charge. They do not have color charge and are a↵ected by all forces except the strong force[4]. The leptons consist of e the electron, µ muon, ⌧ tau, ⌫e the electron neutrino, ⌫µ muon neutrino and ⌫⌧ tau neutrino. Baryons : • Baryons (heavy particles) are not fundamental particles because they are com- posed of three quarks that can be any combination of the six quarks as long as they combine to have a baryon number of 1. Examples of baryons are protons (uud), neutrons (udd),∆++(uuu)etc. Quarks and leptons are 12 particles in total, and these particles are further classified into three generations. Two quarks and two leptons are paired into one generation. The first generation has the lightest and most stable particles, i.e. the quarks in this generation are u (up) and d (down) and leptons are e (electron) ⌫e (electron neutrino). The particles in the first generation make up 2 all stable matter in the universe[5]. In contrast, the second and third gener- ations have more massive and unstable particles. The second generation has the two quarks c (charm) and s (strange) and the two leptons µ (muon) and ⌫µ(muon neutrino) whereas the third generation has the t (top) and b (bottom) quarks and ⌧ (tau) and ⌫⌧ ( tau neutrino ) leptons. All fermions have antimatter particles with equal mass but opposite sign of electric charge. Figure 1.1: The Standard Model of elementary particles with the three generations of matter, gauge bosons in the fourth column, and the Higgs boson in the fifth. 2. Boson: Bosons have integer spin and obey the Bose-Einstein statistics, i.e. they do not follow Pauli’s exclusion principle. They are responsible for mediating the particle interac- tions, they are the force carriers. We, so far, verified the existence of the following bosons: 3 1- Photons do not carry a charge and are the mediators of the electromagnetic in- teractions. + 0 2- W ,W− and Z bosons are the mediators of the weak interactions. 3- The gluons are the mediators of the strong (nuclear) interactions. 4- The Higgs Boson as shown in Figure 1.1 was discovered at CERN in 2012[6]. It has charge and spin zero[7] and it is responsible for the mass of the quarks. 5- Mesons are not fundamental particles as they are made up of a quark–antiquark pair. Examples are the ⇡ and K-meson. The Standard Model classifies all four fundamental forces that govern our universe. In the Standard Model, a force is described as an exchange of bosons. These fun- damental forces are the strong force mediated by gluons, the electromagnetic force mediated by photons, the weak force mediated by the W and Z,andthegravitational force mediated by gravitons. 1.2 Quantum Chromodynamics QCD Quantum Chromodynamics (QCD) is a quantum field theory of strong interactions between quarks and gluons. The only fundamental particles in this theory are quarks and gluons which carry the color charge of strong interactions[8].