1. 1 本審査・公開発表 (10/31/2007) 金野正裕 （数理物質科学研究科） Proton and Antiproton Production in High Energy Heavy Ion Collisions at RHIC (RHIC での高エネルギー重イオン衝突における陽子反陽子生成）

2. 2 1. Introduction 2. Motivation - Baryon/Meson difference - Hadron production in heavy ion collisions 3. Methods - PHENIX detector - Charged hadron measurement & PID 4. Results & Discussions - Freeze-out properties - (Anti-)Proton production at intermediate p T 5. Conclusion Outline

3. 3 - Quarks can exist as an apparent degree of freedom? => Quark Gluon Plasma (QGP) - Matter under high temperature and high energy density. - Quarks and gluons are freely moving in a large volume. - Relativistic heavy ion collisions is a method to approach the QGP. - QCD transition : Hadron gas QGP T c ~ 175 MeV ε c ~ 0.6 GeV/fm 3 Introduction - QGP (predicted by lattice QCD calculations) QCD phase diagram JHEP 04 (2004) 050 PLB 478 (2000) 447

4. 4 Relativistic Heavy Ion Collider (RHIC) RHIC located at Brookhaven National Lab (USA) A first collider for heavy ion beam 2 circulating rings (circumference: 3.83 km) Colliding nuclei: Au+Au, Cu+Cu, d+Au, p+p Top energy (Au+Au):  s NN = 200 GeV Peak luminosity: ~ 3x10 27 cm -2 s -1 Experiments: PHENIX, STAR, BRAHMS, PHOBOS

5. 5 Space-time evolution of a heavy-ion collision (time scale: ~10 fm/c) Picture of Relativistic Heavy Ion Collisions Hadron gas QGP Pre equilibrium Incoming nuclei Freeze-out Hadronic scatterings Hadronization Expansion & Cooling Thermalization Hard scattering Initial collision There are some stages and dynamic changes.

6. 6 - Longitudinal expansion (parallel to beam axis) is dominant. - Longitudinal boost invariance partly holds at mid-rapidity. Phys. Rev. C 67 (03) 044903, Phys.Rev.Lett.91 182301 (2003) RHIC Findings (1) A bulk system is expanding longitudinally & transversely. Rapidity distributions of charged hadron multiplicity (PRL 91, 052303 (2003)) - Hydrodynamic calculations reproduce elliptic flow behavior at low p T. - Small viscosity (  /s) estimated => Nearly perfect fluid

7. 7 RHIC Findings (2) Jet Quenching - In central Au+Au collisions, hadrons are suppressed at high p T. - The suppression is a final state effect (parton energy loss). - Away-side jet peak disappeared in central Au+Au collisions.

8. 8 0.5 1.0 Particles & Medium Effects - Suppression/Enhancement has particle-type dependence. => Baryon/Meson difference in yields and emission patterns at intermediate p T (2-5 GeV/c). 0 Baryon enhancedB/M Splitting of v 2 RHIC Findings (3)

9. 9 Hadron Production in RHI Collisions Hadronization Interactions in the medium Low-p T (soft) Thermal emission Quark recombination Thermalization Collective flow High-p T (hard)Jet fragmentation Hard scattering Jet quenching - There are multiple hadronization mechanisms at intermediate p T. - The relative contributions and particle-type dependence are not yet fully understood. Current understanding:

10. 10 Motivation - Measurement of Proton and Antiproton p T Spectra - Sensitive to collective flow due to its relatively large mass. - Indicator of baryon number transport at lower energies. => Enhance the high-p T PID capability with new detector. - Systematic Study - Au+Au/Cu+Cu/p+p collision systems at √s NN = 62.4/200 GeV (system size, energy dependence). - What p T does hydrodynamic contribution exist up to? - Quark recombination process is really necessary? - Can we separate hadron radial flow and quark radial flow ? - Understanding Baryon/Meson difference at intermediate p T. => What is the origin? What we should do: Outstanding questions:

11. 11 My Activities - Construction and Installation of Aerogel Cherenkov detector in PHENIX for high-p T PID upgrade (2002~2004) - Participation in PHENIX experiment during data taking periods (Run3-Run7) - Staying at BNL for ~2 years - Data analysis (2005~current) : + Calibrations, Software developments + Proton spectra using Aerogel detector - Presentations (QM05, HQ06, QM06, etc.) - Papers, proceedings (NPA 774 (2006) 461, EPJC 49, 29 (2007)) (Preparing full papers)

12. 12 Aerogel Cherenkov (PID) EM Calorimeter (PID) TOF (PID) Drift Chamber (momentum meas.) Pad Chambers (tracking) - Global detectors (event characterization) - Central Arm Detectors (|  |<0.35) (magnetic spectrometer) PHENIX Beam Beam Counter (trigger, centrality, t0, z-vertex, RP) (efficiency: A+A: ~90%, p+p: ~50%) Zero Degree Calorimeter (centrality) Global detectors:

13. 13 Data Analysis Data sets: Au+Au at  s NN = 62.4, 200 GeV (Run-4) Cu+Cu at  s NN = 62.4, 200 GeV (Run-5) p+p at  s NN = 200 GeV (Run-5) p+p at  s NN = 62.4 GeV (Run-6) Analysis methods: (1) Event selection (z-vertex, centrality) (2) Tracking, Momentum determination (3) Track selection (4) Particle Identification (TOF, ACC) (5) MC corrections (acceptance, efficiency) => Invariant yield p T distributions (  /K/p) at mid rapidity |  |<0.35

14. 14 - Minimum Bias Trigger (BBC coin.) - Centrality determination (BBC, ZDC) Event Selection Participant-Spectator model Participant Spectator ZDC BBC

15. 15 Track Reconstruction - Drift chamber provides 12 hits in (x,y) plane - Giving the bending angle  (R=220cm) after passing in magnetic field - Giving p T with field-integral value - PC1 hits and collision z-vertex fix the polar angle  - Momentum resolution: - Find intersection points between the trajectory and outer detectors. Projected points are then matched to measured points. x y R  z r 

16. 16 Track Selection - Residual distribution between hit point and projection point. - Centroid and width are parameterized as a function of p T (  position ~8 mm at r = 5m). - Require tracks to be within 2 . Background subtraction for charged hadron measurement Background sources (dominant at high p T ): - e +, e - from  conversion in materials - Weak decays mostly K +, K - - Matching residual distribution has a tail. - Asymmetric shape comes from residual bend. - Background is subtracted with shape of the distribution. MC study was done. DC tracks at PC3

17. 17 Particle Identification Time of Flight (  ~120 ps), p(  p) ID up to 4 GeV/c Aerogel Cherenkov (n=1.011), p(  p) ID up to 7 GeV/c m 2 distributions (3.5-4.0 GeV/c) Veto for proton ID ++ K+K+ p Clear proton line 02468 p T [GeV/c] TOF ACC proton & antiproton ID

18. 18 Corrections for: - Geometrical acceptance - Decays in flight - Momentum resolution - Detector efficiency - Occupancy effect (tracking efficiency is reduced in high multiplicity environment.) Real data / MC matching: - Dead areas are removed - Detector stability is checked - Same cuts are applied to obtain efficiency Acceptance (TOF) Acceptance (ACC) Occupancy (TOF, ACC) Monte Carlo Corrections * MC simulation based on Geant-3.

19. 19 Feed-down: Weak decays take place very close to the vertex. Since heavier particles take most of the decay momentum, these tracks are inseparable from tracks coming from the vertex of a collision. Feed-down from weak decays Evaluation of the fraction: - Effective lambda spectra measured including higher resonances (~33%) - Decays in PHENIX acceptance (MC) - Fraction in measured p(  p) : ~15% p+p 200 GeV TOF Proton and Lambda p T spectra Fraction of Feed-down ( from  ’s)

20. 20 Evaluation: Systematic errors are evaluated by varying cut conditions in data analysis. Some parts can be canceled when taking particle ratios etc. Systematic Errors Systematic errors (TOF) Systematic errors (ACC)

21. 21 Proton and Antiproton p T spectra p T reach extended up to 6 GeV/c for p(  p) with fine centrality bins. (1) Aerogel Cherenkov (2) High statistics NOTE: No weak decay feed-down correction applied. Au+Au  s NN = 200 GeVCu+Cu  s NN = 200 GeV p+p  s NN = 200 GeV

22. 22 Freeze-out Properties Characterizing bulk properties: - Chemical Freeze-out - Kinetic Freeze-out

23. 23 Particle Yield dN/dy at mid rapidity - Particle yields are (roughly) scaled with N part btw. Au+Au and Cu+Cu. - dN/dy(Cu+Cu) >~ dN/dy(Au+Au) at smaller N part. - Statistical model describes their ratios with few parameters (T,  ). Au+Au/Cu+Cu/p+p (  s NN = 200 GeV) Au+Au/Cu+Cu/p+p (  s NN = 62.4 GeV)  K p

24. 24 Statistical Model Fit - Extracting chemical freeze-out properties with statistical model fit. - Fitting particle ratios of dN/dy (  /K/p) at y~0. - Assuming local chemical equilibrium of light quarks (u,d,s),  s =1. - Partial feed-down correction taken into account. - T ch,  q : relatively stable -  s,  s : not determined with this set of ratios (  /K/p). Strangeness info is short. Phys. Rev. C71 054901, 2005 nucl-th/0405068 Au+Au 200 GeV (0-5%)  -/  +: 1.02 +/- 0.05 K+/K-: 1.09 +/- 0.05  p/p: 0.74 +/- 0.05 K-/  -: 0.16 +/- 0.02  p/  -: 0.08 +/- 0.01 1.00 +/- 0.01 1.09 +/- 0.08 0.74 +/- 0.08 0.16 +/- 0.02 0.08 +/- 0.02 T ch : 157 +/- 8 MeV  q : 9 +/- 1 MeV  2/ndf: 1.1/2 datamodel Au+Au 62.4 GeV (0-5%)  -/  +: 0.84 +/- 0.04 K+/K-: 1.19 +/- 0.06  p/p: 0.48 +/- 0.03 K-/  -: 0.17 +/- 0.02  p/  -: 0.08 +/- 0.01 1.01 +/- 0.01 1.20 +/- 0.13 0.48 +/- 0.09 0.17 +/- 0.02 0.08 +/- 0.02 T ch : 167 +/- 10 MeV  q : 24 +/- 3 MeV  2/ndf: 9.2/2 datamodel

25. 25 p  p annihilation rate thermal motion (+ collective flow) T = 120 MeV p ~ 500 MeV,  ~ 0.4  ann ~ 100 mb dN ch /d  ~ 700 at mid rapidity dN p /d  ~ 18 (2.5 %) V = 8.4 x 10 3 fm 3 (freeze-out, 10 fm/c)  ~ 8 n = dN p /d  /(V/  ) ~ 1.7 x 10 -2 fm -3 = 1/n  ~ 5.9 fm exp(- (  t)/ ) = exp(- (0.4x4)/5.9) ~ 0.76 survival rate (hadronic phase) cross section particle density limiting case small for high-p particles

26. 26 - T ch ~160 MeV, flat centrality dependence. - N part scaling of T ch between Au+Au and Cu+Cu. - Almost same T ch at √s NN = 62.4, 200 GeV. Au+Au/Cu+Cu/p+p (  s NN = 200 GeV) Au+Au/Cu+Cu/p+p (  s NN = 62.4 GeV) Chemical Freeze-out Temperature T ch ~160 MeV

27. 27 - Clear hadron mass dependence: larger for heavier particles. => Consistent with radial flow picture. - increases with N part. it is clearly seen for (anti)proton. Mean Transverse Momentum  K p Au+Au/Cu+Cu/p+p (  s NN = 200 GeV) Au+Au/Cu+Cu/p+p (  s NN = 62.4 GeV)

28. 28 Blast-wave model is a parameterization within a simple boost-invariant model with transverse collective flow. p T spectra reflecting thermal freeze-out temperature and transverse flow at final state. * Ref: PRC48(1993)2462 (* Resonance decay feed-down correction not applied. Instead, tighter p T fitting range used.  ; 0.6-1.2 GeV/c K; 0.4-1.4 GeV/c, p/pbar; 0.6-1.7 GeV/c) Spectra for heavier particles has a convex shape due to radial flow.  2 map Blast-wave Model Fit T fo ~120 MeV,  T ~0.7

29. 29 - : increasing with N part. - N part scaling of between Au+Au and Cu+Cu. - Almost same at √s NN = 62.4, 200 GeV. ~0.5 Transverse Flow Velocity Au+Au/Cu+Cu/p+p (  s NN = 200 GeV) Au+Au/Cu+Cu/p+p (  s NN = 62.4 GeV)

30. 30 - T fo : decreasing with N part. - N part scaling of T fo between Au+Au and Cu+Cu. - Almost same T fo at √s NN = 62.4, 200 GeV. T fo ~120 MeV Kinetic Freeze-out Temperature Au+Au/Cu+Cu/p+p (  s NN = 200 GeV) Au+Au/Cu+Cu/p+p (  s NN = 62.4 GeV)

31. 31 Summary - Freeze-out properties Characterizing bulk properties: - Chemical freeze-out - Kinetic freeze-out => Hadron production at low p T : “Thermal emission + Radial flow” Scaling properties between different systems: - Chemical/kinetic freeze-out properties show similarities between different collision systems. - N part scaling of freeze-out properties (Au+Au, Cu+Cu), * even though the overlapped region has a different shape. => System volume N part is a control parameter. * Particle yield: (Cu+Cu) > (Au+Au) at smaller N part - Similarity at  s NN = 200 and 62.4 GeV.

32. 32 Baryon Enhancement

33. 33 - (Anti-)proton enhancement observed/confirmed in 200 GeV Au+Au/Cu+Cu. - Larger than expected from jet fragmentation (measured in pp, e + e - ). - p/  (  p/  ) ratios turn over at 2~3 GeV/c,and fall towards the ratio in p+p. Baryon enhancement at  s NN = 200 GeV p/  p/p/

34. 34 Baryon enhancement at  s NN = 62.4 GeV p/  p/p/ - (Anti-)proton enhancement observed/confirmed in 62.4 GeV Au+Au/Cu+Cu. - Similar p T dependence as at 200 GeV.

35. 35 Cu+Cu vs. Au+Au (200 GeV) - N part scaling of p/  (  p/  ) at same √s NN. - The ratios are controlled by the initial overlap size of colliding nuclei, even though overlap region has a different geometrical shape. p/  ratio vs. N part 1/3 Cu+Cu vs. Au+Au (62.4 GeV)

36. 36 - Comparison with p+p spectra (reference) in binary collision scaling. - Proton, antiproton are enhanced at 1.5 - 4 GeV/c for all centralities. - Suppression is seen for , K. Nuclear Modification Factor R AA

37. 37 - Proton is enhanced for all centralities, while  /K are suppressed. Comparison of R AA in Au+Au/Cu+Cu Pion R AA (p T =2.25 GeV/c)Proton R AA (p T =2.25 GeV/c) R AA (Cu+Cu) > R AA (Au+Au)

38. 38 (Cu+Cu: b=0.0 fm, Au+Au: b=8.6 fm) ~117 Comparison of Au+Au and Cu+Cu ~100 Cu+Cu: good resolution at smaller N part Glauber model calculation Even though N coll -N part relation is almost same between Au+Au and Cu+Cu, the geometrical overlap shape is different. - R AA (Cu+Cu) > R AA (Au+Au) - Geometrical shape : Au+Au more deformed - No. of N-N scatterings per N : narrow peak in Cu+Cu

39. 39 Beam energy dependence

40. 40 Beam energy dependence of enhancement - p/  + ratio : decreasing as a function of  s NN. -  p/  - ratio : increasing as a function  s NN. -Antiproton is a good probe to study the baryon enhancement. * No weak decay feed-down correction applied. p/  p/p/

41. 41 - No N part scaling of p/  (  p/  ) in Au+Au between 62.4 and 200 GeV. - Transverse energy density dE T /d  scaling of p/  is favored. - dE T /d  is a connection key between different √s NN. p/  ratio vs. (dE T /d  ) 1/3 Proton production at 62.4 GeV is partly from baryon number transport, not only proton-antiproton pair production.

42. 42 Energy loss per nucleon: 73±6 GeV Net proton distribution it drastically changes with beam energy. BRAHMS, PRL 93 (2004) 102301

43. 43 Au+Au/Cu+Cu/p+p (  s NN = 200 GeV) Au+Au/Cu+Cu/p+p (  s NN = 62.4 GeV) Chemical Potential -  q (200 GeV) : ~8 MeV, independent of N part -  q (62.4 GeV) : increasing with N part => more baryon stopping at central

44. 44 Summary - Baryon enhancement Baryon enhancement: - Proton and antiproton enhancement confirmed at intermediate p T (2-5 GeV/c) in Au+Au/Cu+Cu. A turnover of p/  ratio seen at p T = 2-3 GeV/c. - In terms of binary collision scaling, (anti)protons are enhanced while pions/kaons are suppressed. Low energy 62.4 GeV data: - At lower energy 62.4 GeV, proton production seems to be more affected by baryon number transport process. => Antiproton is a good indicator of the baryon enhancement. Scaling properties between different systems: - N part scaling of p/  (  p/  ) - dE T /d  scaling of  p/ 

45. 45 Two-component model (Soft+Hard)

46. 46 high-p T particles low-p T particles Particle production in expanding matter z-axis time x-axis time

47. 47 Soft component : Thermal emission + Radial flow - Described by Blast-wave model - N part scaling seen - Thermal distribution extrapolated up to high p T Hard component : Jet fragmentation + Jet suppression - Measured p+p spectra - N coll scaling - Constant suppression factor (power-law distribution & fractional energy loss) Two-component Model (Soft+Hard)

48. 48 - Hard component (in p+p) at high p T depends on  s. - In Au+Au, suppression effect should be taken into account. Hard component in p+p and Au+Au p+p  s NN = 200 GeV 200 GeV 62.4 GeV Au+Au 200 GeV (pi0: diamond, h+h-: circle)

49. 49 Pion p T spectra Au+Au 200 GeV ++ -- Soft LineHard Line Reproduce the measured pion p T spectra.

50. 50 Pion fraction vs. p T Au+Au 200 GeV ++ -- Soft Hard Residual

51. 51 Proton p T spectra Au+Au 200 GeV p pp Soft LineHard Line Reproduce the measured proton p T spectra.

52. 52 Proton fraction vs. p T Au+Au 200 GeV p pp Soft Hard Residual R AA vs. N part

53. 53 Proton p T spectra Au+Au 200 GeV p pp Soft LineHard Line Using pion’s R AA for suppression factor.

54. 54 Proton fraction vs. p T Au+Au 200 GeV p pp Soft Hard Residual Need 3rd component ?

55. 55 Fraction of soft and hard components ++ -- p pp - Both soft and hard components are necessary to reproduce the hadron spectra at intermediate p T (2-5 GeV/c). - Soft component is extended to higher p T in central. - Intermediate p T : Hard pions vs. Soft protons - Cross point (S=H) vs. p T -

56. 56 Summary - Two-component model Two-component model: - Reproduce the measured p T spectra for pions and protons with a consistent way. - Identify crossover region from soft to hard hadron production at intermediate p T (2-5 GeV/c). Baryon/Meson difference: - Intermediate pT: “Hard” pions vs. “Soft” protons - Origin of baryon enhancement is radial flow. It pushes heavier particles to higher p T. Baryon/Meson difference is trivial? => Next question: Radial flow developed at partonic or hadronic phases? Energy loss & Fragmentation function: - Quarks and gluons have similar energy loss when traversing the nuclear medium, and parton fragmentation function does not change.

57. 57 Quark Flow vs. Hadron Flow

58. 58 Quark recombination - One of the hadronization mechanisms. - Recombination of thermal quarks in local phase space: q  q  Meson, qqq  Baryon - At intermediate p T, (recombination) > (fragmentation) because quark distribution is thermal: ~exp(-m T /T). - At high p T, fragmentation (power-law shape) would be dominant. Fries, R et al PRC 68 (2003) 044902 Greco, V et al PRL 90 (2003) 202302 Hwa, R et al PRC 70(2004) 024905

59. 59 p/  vs. p T - Baryon enhancement & quark number scaling of v 2 explained by “Quark recombination” - v 2 at quark level => Collective flow at quark level Applicability of quark recombination model - In a simple recombination picture, radial flow cannot be distinguished between hadron and quark phases. => Can we separate hadron flow and quark flow ? v 2 /n vs. KE T /n

60. 60 - Ideal gas: P=(1/3)  - Entropy conservation - Longitudinal expansion & Transverse expansion z x y 1+1D Adiabatic Expansion  bj vs. N p - cooling curves - t fo fixed at 10 fm/c at most central T scaled with (  bj ) 1/4 at t = 1 fm/c Cooling stopped at T fo

61. 61 - More central collisions freeze-out later at lower temperature. - Consistent with freeze-out condition: (t)=R(t) - Even if quark phase is created before hadronization, hadronic scattering should be taken into account. Freeze-out Time & Temperature Freeze-out time vs. N p - As expected, T fo is lower than T ch. Different centrality dependences. - T fo dropping is consistent with 1+1D adiabatic expansion. Freeze-out temperature vs. N p

62. 62 Summary - Quark flow & Hadron flow Quark recombination: - In a simple recombination picture, hadron and quark radial flow effects cannot be separated. Since the constituent quark number scaling of elliptic flow v 2 is indicative, quark recombination process is thought to be a possible hadronization mechanism. Quark flow vs. Hadron flow: - We see the sum of quark and hadron flow. - The difference of chemical and kinetic freeze-out temperatures shows a finite expansion time at hadronic stage. => Hadron radial flow should exist even though quark flow exist before hadronization.

63. 63 Conclusions - Systematic measurement of proton and antiproton p T spectra (Au+Au, Cu+Cu, p+p at  s NN = 200/62.4 GeV) - Proton and antiproton enhancement confirmed at intermediate p T (2-5 GeV/c). - Antiproton is a good indicator for study of the baryon enhancement. - p/  ratio & freeze-out properties show N part scaling between Au+Au and Cu+Cu at same  s NN. The Initial volume (~N part ) of colliding nuclei is a control parameter. - Baryon enhancement is caused by transverse radial flow - p T and centrality dependences are described by two-component model. - Intermediate p T (2-5 GeV/c): hard pions vs. soft protons - Chemical/Kinetic Freeze-out temperatures provide a hint for further expansion at hadronic stage.