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Higher Moments Measurement of Net-Kaon Multiplicity Distribution in the Search for the QCD Critical Point

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Higher Moments Measurement of Net-Kaon Multiplicity Distribution in the Search for the QCD Critical Point Higher Moments Measurement of Net-Kaon Multiplicity Distribution in the Search for the QCD Critical Point Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy by Amal Sarkar (Roll No. 09412601) Supervisor Prof. Raghava Varma Department of Physics INDIAN INSTITUTE OF TECHNOLOGY, BOMBAY, INDIA December, 2015 Dedicated To My Parents & My Supervisor Scanned by CamScanner Declaration I declare that this written submission represents my ideas in my own words and where others’ ideas or words have been included, I have adequately cited and referenced the original sources. I also declare that I have adhered to all princi- ples of academic honesty and integrity and have not misrepresented or fabricated or falsified any idea/data/fact/source in my submission. I understand that any violation of the above will be cause disciplinary action by the Institute and can also evoke penal action from the sources which have thus not been properly cited or from whom proper permission has not been taken when needed. Amal Sarkar Roll No. 09412601 Date : ——————— Place : ———————- iii Abstract The Relativistic Heavy-Ion Collider (RHIC), at Brookhaven National Labora- tory (BNL), with its beam energy scan (BES) program by colliding heavy-ions has covered a wide range of baryonic chemical potential (µB) to map the QCD phase diagram. Lattice QCD calculations at finite temperature and baryon chemical potential µ 0 suggest a crossover between hadronic to quarks and gluons de- B ⇡ grees of freedom. Several QCD based calculations find the quark-hadron phase transition to be of the first order at large µB. The point in the QCD phase plane (T vs µB) where the first order line ends and phase transition becomes continuous is called the QCD critical point (CP). Current theoretical calculations are highly uncertain about location of the critical point because of numerical challenges in computing. At the critical point long range correlation and fluctuation arise at all length scales. Such properties of state open several possibilities for experimental signatures. These distinct experimental observables can be used to discover the QCD critical point. The correlation length (⇠) and the magnitude of the fluctuations of the con- served quantities (net-baryon, net-strangeness and net-charge) diverge at the crit- ical point but because of the finite size and time slowing down effects in the heavy ion collisions, ⇠ takes values in the range of 2 3fm. Higher non Gaussian mo- − ments such as skewness, S ( ⇠4.5), and kurtosis, ( ⇠7) of these conserved / / quantities can provide much better handle in location of CP as they are much more sensitive than variance ( ⇠2) to the correlation length. As these higher / order moments are system size or volume dependent moment products, such as, Sσ( ⇠2.5) and 2( ⇠5) can be constructed to cancel out the volume dependency. / / QCD-based models and Lattice calculations show that moments of net-conserved (baryons (B), strangeness (S) and charge (Q)) distributions are related to its con- iv 2 (∆Nx) h i served number susceptibilities (χx = VT ; where, x represents B, S and Q, & V is the volume). Volume independent moment products Sσ and 2 are the ratio (3) (2) (4) (2) of third (χx ) to second χx order and fourth χx to second χx order susceptibili- ties. Close to the critical point, QCD based models predict the distributions of the conserved quantities to be non-Gaussian. The susceptibilities diverge causing Sσ and 2 to fluctuate near the critical point. Experimentally measuring con- served quantum numbers on an event-by-event basis is very difficult. Hence, net proton, kaons and pions can serve as proxy for baryon, strangeness and charge conservation respectively. We calculate event-by-event the net-kaon multiplicity (∆N = N + N ) to obtain the net-kaon distribution. Simulations carried out K K − K− in this work demonstrate that net-kaon multiplicity can be taken to be a proxy for net strangeness to a reasonably good approximation. In this Thesis, we report the measurement of the moments of the net-kaon multiplicity distributions as a function of baryon chemical potential which was varied from 410 to 20 MeV by changing the psNN from 7.7, 11.5, 19.6, 27, 39, 62.4 to 200 GeV in Au + Au collisions by the STAR experiment at RHIC. The measure- ments of these higher moments of ∆NK multiplicity distributions was carried out at mid-rapidity ( ⌘ < 0.5) in 0.2 <p<1.6 GeV/c in Au + Au collisions. Higher | | moments such as Mean (M), Variance (σ2), Skewness (S) and kurtosis () of the net-kaon (∆NK ) multiplicity distributions as a function of collision centrality are presented. As these higher moments are system size dependent different combi- nation of moment product such as Sσ and 2 have been calculated (to cancel out the dependence on the volume) as a function of collision centrality and energy. QCD based calculations expect a non-monotonic dependence of these moment products near the critical point. Various methods have been used to calculate the statistical errors for this analysis. The systematic have been studied for the experimental acceptance used to select the data sample. The detector efficiency correction method have been developed and implemented in the results. The ex- perimental results have been compared with different baselines and Monte Carlo simulated model which do not include the critical point for non-critical baseline. v We observe deviation from the Poissonian behaviour for Sσ and 2 at 19.6 GeV and 27 GeV . This indicates that we are very near the critical point. Presently we are analyzing the behaviour at center of mass energy of 14 GeV to further con- firm our results. To confirm the discovery of critical point we would need much larger statistics which would be undertaken in the Beam Energy Scan Program-II of RHIC. Keywords : QGP, Phase transition, Critical Point, Higher Moments. vi Contents 1 Introduction 1 1.1 The Standard Model . 2 1.2 Strong interaction and Quantum Chromodynamics (QCD) . 5 1.3 Confinement and Asymptotic freedom . 7 1.3.1 The Quark Gluon Plasma and Heavy Ion Collisions . 10 1.4 Experimental Observables for the QGP Signature . 14 1.5 QCD Phase Diagram and Critical Point . 21 1.5.1 Phase Transition . 22 1.5.2 QCD Phase Diagram . 22 1.5.3 QCD Critical Point and its Signatures . 25 1.6 Relativistic Heavy-Ion Collisions and its Beam Energy Scan Program 28 1.7 Scope and Organization of the thesis . 33 2 Higher moments and Cumulants in Heavy Ion Collision 37 2.1 Higher Moments . 37 2.1.1 Introduction . 37 2.2 Cumulants . 40 2.2.1 Properties of Moments and Cumulants . 41 2.2.2 Relation between Moments with Cumulants . 42 2.3 Lattice QCD approach . 45 2.4 Relation between Higher Moments and Thermodynamic Quanti- ties from Lattice QCD . 46 2.5 Higher Moments in Heavy Ion Collision . 49 2.6 Relation with Correlation Length in Heavy Ion Collision . 51 3 The Experimental Set-up 55 3.1 Introduction . 55 3.2 The Relativistic Heavy-Ion Collider . 56 3.3 The STAR Detector . 59 vii CONTENTS CONTENTS 3.4 The STAR Time Projection Chamber . 60 3.5 The STAR’s Time of Flight . 66 3.6 The STAR Silicon Vertex Tracker . 71 3.7 Silicon Strip Detector . 72 3.8 Photon Multiplicity Detector . 72 3.9 Barrel Electromagnetic Calorimeter . 74 3.10 Endcap Electromagnetic Calorimeter . 75 3.11 The STAR Trigger . 75 3.12 The STAR DAQ . 77 3.13 STAR Trigger-DAQ Interface . 77 3.14 STAR Computing Facilities . 79 4 Analysis Methods 81 4.1 Data Selection . 82 4.1.1 Trigger for Data . 82 4.1.2 Run Selection . 82 4.1.3 Event Selection . 83 4.1.4 Track Quality Assurance (QA) . 88 4.2 Particle Identification . 89 4.3 Centrality Selection . 95 4.3.1 Autocorrelation Effects and Refmult2 . 97 4.3.2 Centrality Selection from MC Glauber Model . 100 4.3.3 Centrality Resolution Effects . 104 4.3.4 Centrality Bin Width Effects and it’s Corrections . 107 4.4 Error Estimation . 111 4.4.1 Statistical Error Estimation . 112 4.4.2 Systematic Error Estimation . 113 4.5 Detector Efficiency and it’s Correction . 118 4.5.1 Introduction . 118 4.5.2 Detector Efficiency Correction for Cumulants . 119 4.5.3 Efficiency Calculation . 121 4.5.4 Final Efficiency Calculation . 123 5 Models and Baseline study 127 5.1 Introduction . 127 5.2 Hadron Resonance Gas Model . 128 5.3 UrQMD . 134 5.4 Baseline Study . 138 viii CONTENTS CONTENTS 5.4.1 Poisson Baseline Study . 139 5.4.2 Negative Binomial Distribution Study . 142 5.5 Central Limit Theorem Study . 145 6 Results and Discussion 149 6.1 Kaon and Anti-Kaon Distribution . 150 6.2 Event by Event Net-Kaon Distribution . 152 6.3 Centrality Dependency of the Moments . 154 6.4 Centrality Dependence of the Moment Products . 157 6.5 Energy Dependence of Volume Independent Moment Product . 163 7 Summary and Outlook 171 7.1 Summary . 171 7.2 Future Prospective . 175 A Error Calculation 179 A.1 Statistical Error Calculation . 179 A.1.1 Sub Group Method . 179 A.1.2 Delta Theorem . 180 A.1.3 Bootstrap Method . 180 List of Publication 194 Acknowledgements 203 ix CONTENTS CONTENTS x List of Figures 1.1 (Color online) The Standard Model of the elementary particles with quarks, leptons, gauge boson and Higgs boson. 4 1.2 (Color online) A summary of coupling constant measurement from different experiments and theoretical calculations as a function of the energy scale (momentum transfer) Q. The figure is taken from Ref.[15].
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