Higher Moments Of Event-by-Event Net-proton Multiplicity Distributions In Ultra-relativistic Heavy Ion Collision

The strong interaction, one of the four fundamental forces found in the na-ture, confines the quarks and gluons in the hadrons. Quantum Chromodynamics (QCD), which can successfully explain plenty of physics phenomena, is believed to be the correct theory to describe the strong interaction. The phase structure of nuclear matter, described by strong interaction, can be demonstrated by QCD phase diagram, which is two dimensional diagram with parameters temperature (T) and baryon chemical potential (μB). A new form of matter-Quark Gluon Plasma (QGP) dominated by quark and gluon degree of freedom is believed to exist in the early Universe after few tens microseconds of Big Bang, when the energy density and temperature is extremely high. Finite temperature Lattice QCD calculations predict a smooth cross-over transition from hadronic phase to the Quarak Gluons Plasma (QGP) phase at high temperature and smallμB region, and a first order phase transition at largeμB region. The end point of the first order phase boundary toward the cross-over region is the so called QCD Critical Point (CP). Although many efforts have been made by theorist and experimentalist to locate the CP, its location or even existence is still not confirmed yet.The Relativistic Heavy Ion Collider (RHIC) locating at Brookheaven Nation Lab (BNL) can create hot dense nuclear matter by accelerating and colliding gold nuclei up to center of mass energy SNN^1/SNN=200 GeV per nucleon pair. It provides us an ideal experimental tool to explore the phase structure of nuclear matter and study the properties of QGP. After more than ten years' experimental study, there are strong evidences that the strongly coupled QGP has already been formed in the heavy ion collisions at top energy of RHIC, such as the hydrodynamic behavior and number of quarks scaling of the elliptic flow (v2), comparable v2 of multi-strange hadrons to the light hadrons, high pT particle suppression-jet quenching.Recently, it was found that the higher order fluctuation observables-higher moments (Variance (a2), Skewness (S), Kurtosis (κ)) of conserved quantities, such as net-baryon, net-charge, and net-strangeness, distributions can be directly connected to the corresponding thermodynamic susceptibilities in Lattice QCD and Hadron Resonance Gas (HRG) model. Theoretical calculations demonstrate that the experimental measurable net-proton (proton number minus anti-proton number) number fluctuations can effectively reflect the fluctuations of the net-baryon and net-charge number in heavy ion collision experiments. Thus, it is of great interest to measure the higher moments of event-by-event net-proton mul-tiplicity distributions in the heavy ion collision experiment. It allows us to probe the bulk properties of the hot dense nuclear matter and test the QCD theory at non-perturbative domain, which is rarely tested by experiments. Meanwhile, model calculations demonstrate that the higher moments of net-proton distribu-tions are also proportional to the higher power of the QCD critical point related correlation length (ξ). It motivates us to search for the QCD critical point with the higher moments of the net-proton distributions, experimentally, as a direct application of the higher moments observable. The experimental confirmation of the QCD critical point will largely improve our knowledge and understanding of properties of the nuclear matter at finite temperature as well as the QCD theory. In this thesis, we have performed the world's first comprehensive and system-atical measurements of the higher moments of event-by-event net-proton multi-plicity distributions in heavy ion collision. It opens a completely new domain and effective way for probing the bulk properties of hot dense nuclear matter through the heavy ion collision experiments. Those higher moments are also used to search for the QCD critical point for the first time. It is indicated that the QCD critical point should not be in theμB<200 MeV region. On the other hand, by comparing the higher moments of net-proton distributions with the results from first principle Lattice QCD calculations, we can test the QCD theory in the non-perturbative domain and constrain fundamental parameters of the QCD. Based on this method, the scale for the QCD phase diagram, the tran-sition temperature Tc atμB=0, for the first time, have been extracted from our experimental data. We conclude that the transition temperature Tc atμB=0, Tc=175-7+1 MeV. This result has been accepted for publication on Science.In the year 2010 (Run 10), RHIC has started its Beam Energy Scan (BES) program and tuned the Au+Au collision energy from SNN^1/SNN=39 GeV down to 7.7 GeV with the correspondingμB coverage 112<μB< 410 MeV. This allows us to access and probe broad region of the QCD phase diagram. The character-istic signatures for the appearance of QCD critical point are the non-monotonic dependence of the observations with the collision energy (SNN^1/SNN). With our large uniform acceptance and good capability of particle identification STAR detec-tor at RHIC, it provides us very good opportunities to find the QCD critical point with sensitive observable, if the existence of QCD critical point is true. In this thesis, we will present the world's first comprehensive and systematical measurements for the higher moments of net-proton distributions in the heavy ion collision. Specifically, those are the beam energy and system size dependence results for higher moment (σ, S,κ) as well as moment products(κσ2, Sσ) of net-proton multiplicity distributions for Au+Au collisions at SNN^1/SNN=200,130,62.4, 39,19.6,11.5 and 7.7 GeV (including BES energies), Cu+Cu collisions at SNN^1/SNN = 200, 62.4 and 22.4 GeV, d+Au collisions at SNN^1/SNN=200 GeV, p+p collisions at SNN^1/SNN=200 and 62.4 GeV.To ensure the purity and similar efficiency, the protons and anti-protons are identified with the ionization energy loss (dE/dx) measured by Time Projec-tion Champer (TPC) of STAR detector within 0.41/SNN =39,19.6,11.5 and 7.7 GeV. Recent model calculations demonstrate that theκσ2 value will be always smaller than its Poisson statistical expectation value 1, when the QCD critical point is approached from the high energy cross-over side. Theκσ2 from Lattice QCD calculations at 19.6 GeV shows negative value while the experimental results of 19.6 GeV are with large errors due to the limited statistics. Fortunately, this trend can be confirmed soon by Runll 19.6 GeV data with higher statistics. The Time-Of-Flight (TOF) detector is also used to identify proton and anti-proton at higher pT, this allows us to study the phase space (pT, y) coverage dependence of our observables.Whether the matter created in the heavy ion collision is thermalization or not, is a long standing question. The Sσof net-proton distributions is found to be related to the thermodynamics parameters of T,μB in the grand canonical ensemble description of the collision system, as Sσ=tanh(μB/T). The Sσalso scale with mid-rapidity charged particle density (dNch/dη) and the collision energy(SNN^1/SNN) with a double power law form. This in turn predicts the similar scaling properties ofμB/T ratio, which is confirmed by theμB/T extracted from the thermal model fits of measured particle ratios. The particle yields and fluctuations in heavy ion collision can be seen as two sides of coin. The mutual agreements between theμB/T extracted from thermal model fits of particle ratio and from the event-by-event fluctuation observable Sa of net-proton distributions provides a further evidence of thermalization of the matter created in the heavy ion collisions.Finally, let's summarize three new results for the higher moments of net-proton distributions obtained in the heavy ion collision experiment.1. First time, those higher moments of net-proton distributions are used to search for the QCD critical point in the heavy ion collision experiments. It is observed that the moment productsκσ2 and Sσof net-proton distri-butions for Au+Au collisions are consistent with Lattice QCD and HRG model calculations at high energy 200,130 and 62.4 GeV, while deviating from the HRG model expectations at 39,19.6,11.5 and 7.7 GeV. Those deviations could potentially be related to chiral phase transition and QCD critical point. Forκσ2, the Lattice QCD calculations at 19.6 GeV shows negative value while the experimental results of 19.6 GeV are with large errors due to the limited statistics. Fortunately, this ambiguity can be clarified soon by Runll 19.6 GeV data with higher statistics.2. First time, the thermalization issue in heavy ion collision is addressed with the higher moments of net-proton number distributions measurement. The results strongly support the thermalization of the matter created in the high energy heavy ion collisions.3. First time, the transition temperature Tc atμB=0 for the QCD phase diagram is determined by comparing our experimental higher order net-proton fluctuations with first principle Lattice QCD calculations. This temperature is a basic scale for QCD phase diagram. It opens a new domain for probing the bulk properties of nuclear matters and find a new method to test the QCD theory at non-perturbative region. This research has been accepted for publication in Science.The experimental study of higher moments of net-proton distributions in heavy ion collisions open a new domain and provide a effective way for probing the bulk properties of nuclear matter. Thus, it is of great significance for nuclear physics and heavy ion collision physics research.