Title Page

Abstract

Contents

Chapter 1. Introduction 13

1.1. Heavy-ion collisions 13

1.2. Nuclear matter 15

1.3. Collective motion, flow 19

1.4. Strange particle, kaons 22

1.5. Subthreshold kaon production 22

1.6. In-medium Modification 23

1.7. Neutron star 27

1.8. Transport models 29

1.8.1. HSD (Hadron String Dynamics) 30

1.8.2. Isospin Quantum Molecular Dynamics (IQMD) 33

Chapter 2. The FOPI experiment 37

2.1. Accelerator facility in GSI 37

2.2. FOPI detector 42

2.2.1. Magnet 44

2.2.2. In-beam START detector 44

2.2.3. Central drift chamber (CDC) 45

2.2.4. Helitron 50

2.2.5. Plastic barrel Time-of-Flight 50

2.2.6. MMRPC Time-of-Flight 51

2.2.7. Plastic Wall (PLAWA) 51

2.2.8. Zero-Degree Detector (ZDD) 52

2.3. MMRPC Time-of-Flight upgrade 53

2.4. S325 and S325e experiment 56

2.4.1. Beam and target 58

2.4.2. Trigger 59

Chapter 3. Data analysis 60

3.1. MMRPC calibration 60

3.2. Centrality estimation 67

3.3. Identification of K+ and K- mesons(이미지참조) 69

3.4. Flow Analysis 80

3.4.1. Reaction plane reconstruction 80

3.4.2. Finite multiplicity effect 82

3.4.3. Correction for reaction plane 82

3.4.4. Reaction plane flattening treatment 82

3.4.5. Flow measurements 87

Chapter 4. Experimental results 91

4.1. Directed charged kaon flow 91

4.2. Elliptic charged kaon flow 91

4.3. Differential directed flow of charged kaons 94

4.4. Differential elliptic flow of charged kaons 94

4.5. Centrality dependence of charged kaon flow 101

4.6. Centrality dependence of differential charged kaon flow 101

Chapter 5. Discussions 111

5.1. Comparision to prediction of HSD transport model 111

5.1.1. Charged kaon flow with HSD 111

5.1.2. Charged kaon differential flow with HSD 112

5.1.3. Centrality dependence of charged kaon flow with HSD 112

5.1.4. Centrality dependence of differential charged kaon flow with HSD 119

Chapter 6. Summary 126

Appendix 130

Appendix A : Strange particle, kaons 130

A.1. Parity violation 130

A.2. Time reversal violation 131

A.3. CP violation 131

A.4. CPT invariance 133

Appendix B : Kinematics 134

B.1. Laboratory and Center-of-Momentum Frames 134

B.2. Rapidity 135

Appendix C : Bethe-Bloch equation 136

Appendix D : Statistics 137

D.1. Error estimation of mean value 137

Bibliography 138

Table 2.1. The polar angular coverage of different FOPI sub-detectors. The target position is shifted by 40 cm upstream from its nominal position in experiments analyzed in this thesis. 42

Table 3.1. Cross sections and impact parameters estimation for experiment S325 and S325e. 69

Table 3.2. Cross sections and impact parameters estimation for the whole statistics. 69

Table 3.3. K+ and K- particle identification statistics for S325 and S325e experiments. The momentum cuts, S/B ratio and number of kaons are given.(이미지참조) 79

Table 3.4. Reaction plane correction factors for charged kaon flow. 83

Figure 1.1. (a) Formation of QGP at high temperature by means of relativistic nucleus-nucleus collision with a collider-type accelerator like in RHIC. (b) Formation of QGP at high baryon density by means of less energetic collisions... 14

Figure 1.2. Energy per nucleon as a function of density at temperature of 0 K. 'The Fermi gas' curve assumes no interaction apart from Pauli blocking The other curves show minima around the observed normal nuclear density.... 16

Figure 1.3. Sketch of the QCD phase diagram, temperature T vs. the baryon chemical potential μB associated with net baryon density ρB. The cross-hatched region indicates the expected phase transition between hadronic phase...(이미지참조) 17

Figure 1.4. Reaction plane defined by the impact parameter b and the beam axis. Figure shows out of plane elliptic flow corresponding SIS energy. 19

Figure 1.5. Kaon selfenergy in a density dependent quasi-particle mass. 26

Figure 1.6. Possible internal structures and compositions of four different type of compact stars. Condensed K- mesons may prevail in the interiors, hyperon stars if hyperons (Σ, Λ, Ξ, possibly in equilibrium with the Δ resonance) be-...(이미지참조) 28

Figure 1.7. The inclusive Lorentz-invariant cross section as a function of the kaon momentum in the nucleus- nucleus c.m.s, for K- mesons at θlab＝0˚ for Ni + Ni at 1.85 GeV/u without including K- selfenergies in comparison to...(이미지참조) 32

Figure 1.8. K-N inelastic (solid line) and elastic (dashed line) cross section as a function of kaon laboratory momentum PK as fitted to the experimental data from. The dotted line displays the elastic K+N cross section.(이미지참조) 34

Figure 1.9. IQMD parametrization of the RMF optical potential. For details see text. 35

Figure 2.1. Schematic of acceleration facility in GSI, showing sources, UNILAC(universal linear accelerator), low and high energy experimental area, SIS synchrotron, FRS (fragment separator) and ESR (experimental storage... 38

Figure 2.2. Schematic of synchrotron in GSI, SIS18 with major parameters given. 40

Figure 2.3. Development of SIS beam intensities after the installation of an electron cooler in the SIS and new high current injector at the UNILAC. 41

Figure 2.4. Setup of the FOPI detector. All sub-detectors are labeled. The target is placed inside of the central drift chamber (CDC), indicated by xyz coordinate arrows. The whole setup has cylindrical symmetry around the beam... 43

Figure 2.5. p-CVD diamond mounted together with electronics on the PCBduring the R& D phase. 45

Figure 2.6. Illustration of Ni+Ni collision measured with the CDC in rz plane. The open red squares mark the positions of reconstructed hits. Tracks which were found and accepted by the tracking routine are labelled by the closed... 47

Figure 2.7. CDC cross section drawings. the left side is longitudinal and the right side is transversal to beam direction. The target position is shifted by 40 cm upstream from nominal position. 48

Figure 2.8. (a) Invariant mass spectrum of pπ- pairs that form a secondary vertex (solid histogram) and normalized mixed event background (dashed histogram) before subtraction....(이미지참조) 49

Figure 2.9. Photo of the MMRPC installed in the FOPI superconducting magnet; CDC is taken out of the magnet. 54

Figure 2.10. Simulated π/K separation for MMRPC ToF with different time resolution, 120 ps and 80 ps. π are shown in blue and K are in red (sum in green).... 55

Figure 2.11. Time of flight time resolution of the MMRPC with diamond START detector. The non-Gaussian tail beyond ± 3σ is ≤ 1 %. 57

Figure 3.1. The plots on the left side are correlation plots of dt and start detector timing, energy before the MMRPC calibration is applied. The plots on the right side are after the MMRPC calibration. 62

Figure 3.2. From the top, deutron, proton, π+ and π- have shown. the dashed lines are kinematic lines, p ＝ mβγ. The proton distribution is off from its kinematic line, additional calibration process has to be applied.(이미지참조) 63

Figure 3.3. From the left to the right, π±, K±, proton and deutron. the proton peak mean value is 0.917 GeV/c which is 20 MeV off from the ideal proton mass. 64

Figure 3.4. From the top, deutron, proton, π+ and π- are shown. The dashed line is kinematic line, p ＝ mβγ. The plot shows the MMRPC calibration that has converged properly.(이미지참조) 65

Figure 3.5. From the left to the right, π±, K±, proton and deutron. The proton mass peak mean value is 0.936 GeV/c which is only 2 MeV off from the proton mass.(이미지참조) 66

Figure 3.6. Multiplicity distributions of S325e and S325 experiment are shown. The observed difference in shape in lower multiplicities is presumably due to the slightly different trigger conditions. 68

Figure 3.7. Momentum velocity correlation plot of particles with Z ＝ ±1. All particle species are indicated. 71

Figure 3.8. MMRPC mass vs. CDC mass correlation plot for Z ＝ 1, K+ island is indicated by red ellipse.(이미지참조) 72

Figure 3.9. MMRPC mass vs. CDC mass correlation plot for Z ＝ - 1, K- island is indicated by red ellipse.(이미지참조) 73

Figure 3.10. MMRPC mass for Z ＝ 1, the peaks from left are π, K+ and proton. The number of kaons and S/B ratio are indicated.(이미지참조) 74

Figure 3.11. MMRPC mass for Z ＝ - 1, the peaks from left are π- and K-. The number of kaons and S/B ratio are indicated.(이미지참조) 75

Figure 3.12. Geometrical acceptance of K+ with plab ＝ 0.13, 0.2, 0.55, 0.9 GeV/c and θ ＝ 30, 55, 110˚; plab is plotted in dot-dashed line and θ in full line. 256803 K+ are identified.(이미지참조) 77

Figure 3.13. Geometrical acceptance of K- with plab ＝ 0.13, 0.2, 0.45, 0.7 GeV/c and θ ＝30, 55, 110˚; plab is plotted in dot-dashed line and θ in full line. 5454 K- are identified.(이미지참조) 78

Figure 3.14. Schematic picture of the distribution of Q. The details are given in text. 81

Figure 3.15. Uncorrected reaction plane distribution in Φ before flattening. 84

Figure 3.16. Corrected reaction plane distribution in Φ after flattening. 85

Figure 3.17. Parameters for correction up to 4th order of Fourier expansion. 86

Figure 3.18. K+ v₁ with (blue) and without (red) reaction plane flattening correction.(이미지참조) 88

Figure 3.19. The four major types of azimuthal anisotropies, viewed in the transverse plane. The target is denoted by T and the projectile by P. Top. Directed in the projectile rapidity region, positive (left) and negative (right).... 89

Figure 3.20. 2-dimensional v₁ vs. rapidity, upper part of the plot are for proton and lower part are for K+.(이미지참조) 90

Figure 4.1. K+ directed flow in red, proton in black. K+ are identified in Prpc 〈0.9 GeV/c and Pbar 〈0.55 GeV/c.(이미지참조) 92

Figure 4.2. K- directed flow in blue. K- are identified in Prpc 〈0.7 GeV/cand Pbar 〈0.45 GeV/c.(이미지참조) 93

Figure 4.3. K+ elliptic flow in red. K+ are identified in Prpc〈0.9 GeV/c and Pbar 〈0.55 GeV/c.(이미지참조) 95

Figure 4.4. K- elliptic flow in blue. K- are identified in Prpc 〈0.7 GeV/c and Pbar 〈0.45 GeV/c.(이미지참조) 96

Figure 4.5. K+ differential directed flow in red within rapidity range -1.3 〈y0 〈-0.5. K+ are identified in Prpc 〈0.9 GeV/c and Pbar 〈0.55 GeV/c.(이미지참조) 97

Figure 4.6. K+ differential directed flow in red within rapidity range -0.5 〈y0 〈-0.2. K+ are identified in Prpc 〈0.9 GeV/c and Pbar 〈0.55 GeV/c.(이미지참조) 98

Figure 4.7. K- directed flow as a function of pT differential directed flow in blue within rapidity range -1.3 〈y0 〈-0.5. K- are identified in Prpc 〈0.7 GeV/c and Pbar 〈0.45 GeV/c.(이미지참조) 99

Figure 4.8. K- differential directed flow as a function of pT differential directed flow in blue within rapidity range -0.5 〈y0 〈-0.2. K- are identified in Prpc 〈0.7 GeV/c and Pbar 〈0.45 GeV/c.(이미지참조) 100

Figure 4.9. K+ differential elliptic flow in red within rapidity range -1.3〈y0 〈-0.5. K+ are identified in Prpc 〈0.9 GeV/c and Pbar 〈0.55 GeV/c.(이미지참조) 102

Figure 4.10. K+ differential elliptic flow in red within rapidity range -0.5 〈y0 〈-0.2. K+ are identified in Prpc 〈0.9GeV/c and Pbar 〈0.55 GeV/c.(이미지참조) 103

Figure 4.11. K+ directed flow in blue. K+ are identified in Prpc 〈0.9 GeV/c and Pbar 〈0.55 GeV/c.(이미지참조) 104

Figure 4.12. K+ elliptic flow in blue K+ are identified in Prpc 〈0.9 GeV/c and Pbar 〈0.5 GeV/c.(이미지참조) 105

Figure 4.13. K- directed flow in blue.K- are identified in Prpc 〈0.7 GeV/c and Pbar 〈0.45 GeV/c.(이미지참조) 106

Figure 4.14. K+ differential directed flow as a function of pT. differential directed flow in blue within rapidity range -0.3 〈y0 〈-0.5. K+ are identified in Prpc 〈0.9 GeV/c and Pbar 〈0.55 GeV/c.(이미지참조) 108

Figure 4.15. K+ differential directed flow as a function of pT differential directed flow in blue within rapidity range -0.5 〈y0 〈-0.2. K+ are identified in Prpc 〈0.9 GeV/c and Pbar 〈0.55 GeV/c.(이미지참조) 109

Figure 4.16. K+ differential directed flow as a function of pT differential directed flow in blue. within rapidity range -0.3 〈y0 〈-0.5. K- are identified in Prpc 〈0.7 GeV/c and Pbar 〈0.45 GeV/c.(이미지참조) 110

Figure 5.1. K+ directed flow with HSD calculations. The circle points are data point and the bands are HSD calculation. The red band is with 20 MeV K+N potential while the sky blue band is without K+N potential.(이미지참조) 113

Figure 5.2. K+ elliptic flow with HSD calculations. The circle points are data point and the bands are HSD calculation. The red band is with 20 MeV K+N potential while the sky blue band is without K+N potential.(이미지참조) 114

Figure 5.3. K- directed flow with HSD calculations. The circle points are data point and the bands are HSD calculation. The blue band is with -100 MeV K-N potential while the sky blue band is without K-N potential.(이미지참조) 115

Figure 5.4. K- elliptic flow with HSD calculations. The circle points are data point and the bands are HSD calculation. The blue band is with -100 MeV K-N potential while the sky blue band is without K-N potential.(이미지참조) 116

Figure 5.5. K+ differential directed flow with HSD calculations. The circle points are data point and the bands are HSD calculation. The red band is with 20 MeV K+N potential while the sky blue band is with out K+N potential.(이미지참조) 117

Figure 5.6. K- differential directed flow with HSD calculations. The circle points are data point and the bands are HSD calculation. The blue band is with -100 MeV K-N potential while the sky blue band is without K+N potential.(이미지참조) 118

Figure 5.7. Centrality dependence of K+ directed flow with HSD calculations. The circular points are for peripheral collisions, 3 〈b 〈7 fm, and the triangular points are for central collisions, 0 〈b 〈3 fm....(이미지참조) 120

Figure 5.8. Centrality dependence of K+ elliptic flow with HSD calculations. The circular points are for peripheral collisions, 3 〈b 〈7 fm, and the triangular points are for central collisions, 0 〈b3 fm....(이미지참조) 121

Figure 5.9. Centrality dependence of K- directed flow with HSD calculations. The circular points are for peripheral collisions, 3 〈b 〈7 fm, and the triangular points are for central collisions, 0 〈b 〈3 fm....(이미지참조) 122

Figure 5.10. Centrality dependence of K- elliptic flow with HSD calculations. The circular points are for peripheral collisions, 3 〈b 〈7 fm, and the triangular points are for central collisions, 0 〈b 〈3 fm....(이미지참조) 123

Figure 5.11. Centrality dependence of K+ differential directed flow with HSD calculations. The circular points are for peripheral collisions, 3 〈b 〈7 fm, and the triangular points are for central collisions, 0 〈b 〈3 fm....(이미지참조) 124

Figure 5.12. Centrality dependence of K- differential directed flow with HSD calculations. The circular points are for peripheral collisions, 3 〈b 〈7 fm, and the triangular points are for central collisions, 0 〈b 〈3 fm....(이미지참조) 125

The charged kaon flow measurements in Ni + Ni collisions at beam energy 1.91 AGeV are shown in this thesis. The directed flow, elliptic flow and its differential flow are investigated in different rapidity bins and centrality selections.

The anisotropic flow measurements of kaons are a good tool to deduce equation-of-state and KN in-medium potential in dense nuclear matter. This can be made by comparison with microscopic transport model. In this thesis flow results are compared with Hardron String Dynamics transport model to examine the strength of KN in-medium potential and dynamics of kaons in dense nuclear matter. Due to the very low production rate the kaon production at subthreshold energy is very difficult to investigate, therefore there is a small set of data in existence. Obtained results could give a valuable input for development of the microscopic transport models: HSD and IQMD.