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Study of Single Particle Spectra and Two Particle Correlations in Au+Au Collisions at 4-11 A GeV

Study of Single Particle Spectra and Two Particle Correlations in Au+Au Collisions at 4-11 A GeV. 筑波大学 物理学研究科５年　中條達也. Outline. 1) Introduction Physics of High Energy Heavy-Ion Collisions Features Observed in Pb+Pb at 158 A GeV Thesis Motivation

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Study of Single Particle Spectra and Two Particle Correlations in Au+Au Collisions at 4-11 A GeV

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  1. Study of Single Particle Spectra and Two Particle Correlations in Au+Au Collisions at 4-11 A GeV 筑波大学 物理学研究科５年　中條達也

  2. Outline 1) Introduction • Physics of High Energy Heavy-Ion Collisions • Features Observed in Pb+Pb at 158 A GeV • Thesis Motivation 2) AGS-E866 Experiment (Setup & Data Reduction) 3) Experimental Results • Single Particle Spectra(4, 11 A GeV) • π+π+Two-Particle Correlations (11 A GeV) 4) Discussions • Finite Expanding Source Model • Excitation Function of Transverse Velocity and Temperature 5) Summary

  3. Physics of High Energy Heavy-Ion Collisions ◎Prediction of lattice QCD calculation QGP phase transition at ε～2 GeV/fm3, Tc = 140 ～200 MeV ◆ Relativistic Heavy Ion Collisions BNL-AGS (Au+Au 11 A GeV) & CERN-SPS (Pb+Pb 158 A GeV) ● Proposed Signatures of QGP formation (1) J/ψ suppression by Debye screening effect of color charge (2) enhancement of low-mass dilepton (3) reduction of βt by disappearing of pressure gradient in QGP ⇔ HG etc…. Interesting results in Pb+Pb at SPS have been reported ( indication of QGP formation)

  4. potential V(r) r (1) J/ψ suppression in Pb+Pb @ SPS ●J/ψ suppression as a signature of QGP formation Proposed by Matsui and Satz (1986) M. C. Abreu et al., Phys. Lett. B450 (1999) 456 ★Debye screening effects NA50 above Tc confinement J/ψ rD : Debye radius deconfinement if rD < r J/ψ, no bound state Strong J/ψ suppression is observed in Pb+Pb central at SPS cannot be explained by hadronic scenario J/ψ production is suppressed by QGP formation QGP formation ?

  5. (2) Enhancement of low-mass dilepton @ SPS ● Lepton pair production nucl-ex/9910015 QM99 Proceedings → reflect initial temperature of system QGP : or HG : chiral symmetry restoration →ρ decay with reduced mass → enhancement at low-mass region ■Systematic e+e- measurements by CERES/NA45 Enhancement at low-mass (0.2 < mee < 0.8 GeV/c2) region compared to the hadronic decay contribution formation of QGP ? chiral symmetry restoration?

  6. (3) Softening of EoS by QGP formation ● Equation of State (EoS) from parameterization of lattice QCD data D. H. Rischke, Nucl. Phys. A610 (1996) 88c HG Mixed QGP Critical temperature : Tc Pressure P ΔT = 0 (1st. Order transition ) ΔT = 0.1 Tc (smooth transition) ideal hadron gas (no transition) Sound of velocity (squared) || pressure gradient transverse expansion velocity βt “Softening” of EoS in mixed phase can be considered as a signature of QGP formation

  7. Collective behavior in Pb+Pb @ SPS H.Appelshauser et al. (NA49), Eur. Phys. J C2 (1998) 661 T = 120±12 MeV bt = 0.55 ±0.12 How determine βt and T of the system ? ● Simultaneous analysis with the expansion model Single particle spectra 　　　　　　＋ Two particle correlations 1) consistent picture of expansion 2) less ambiguity in βｔ – T plane ★ NA49 (Pb+Pb central @ 158 A GeV) Allowed region of T, bt at CERN energy ・How evaluate obtained T and βｔ ? ・Consistent with QGP formation ? Comparison of SPS with AGS is essential, but no (T, βt) point at AGS so far !

  8. Thesis Motivation BNL-AGS-E866 Au+Au collisions DATA ・Possibility to determine T, bt at AGS using the expansion source model ・Behavior of T and bt at AGS energy ・Comparison AGS with SPS from the viewpoint of QGP formation (qualitative argument) ① Single Particle Spectra for p±, K+, p, d (4, 11 A GeV) ② Two Particle Correlations for p+ p+ pairs (11 A GeV)

  9. Contributions of Author • Calibrated the TPC, TOF. • Analyzed single particle spectra at 4 A GeV beam energy • and published the results. • Analyzed single particle spectra and two-particle • correlations at 11 A GeV beam energy.

  10. 2. AGS-E866 Experimental Setup ● Two Spectrometer System : (1)Forward Spectrometer (ycm coverage) (2) Henry Higgins Spectrometer (not used in this analysis) ● Beam : 4.04 and 10.8 GeV per nucleon (in terms of kinetic energy) Henry Higgins Spectrometer Forward Spectrometer

  11. Global Detectors ■ New Multiplicity Array (NMA) ■ Beam Counters (BTOT, HOLE) Define centrality by pion multiplicity at target Beam trigger and time-zero for TOF BTOT – Cherenkov counter (200 mm thick.) HOLE – Scintillation counter for beam halo rejection (10 mm diameter hole) ・Cherenkov counter array ・346 modules ・Polar angle coverage : 7°-112° ■ Bull’s Eye (BE) ■ Zero-degree Calorimeter (ZCAL) Define centrality by total kinetic energy of beam fragments Define INT trigger by Z of beam fragments ・9.5 m down stream ・Quartz (300 mm thickness) Cherenkov radiator ・8 PMT readout ・Fe-Scint. Sandwiched-type hadronic calorimeter ・11 m down stream

  12. Event Characterization ■ ZCAL energy distribution in INT trigger ■Participants – Spectator Picture Kinetic energy of beam 197×E beam (10.8 GeV) Beam Fragment beam ZCAL b target 50-100% = impact parameter 0-10% 10-30% 30-50% 0 1000 2000 3000 Software sum of ZCAL (GeV) Central Peripheral Provide the collision geometry event by event ■ NMA multiplicity distribution in INT trigger ●Centrality Cut ① ZCAL (Etotal of beam fragments) ② NMA (multiplicity of pions at target) 50-100% 30-50% 10-30% 0-10 % Pion multiplicity Peripheral Central

  13. Forward Spectrometer (FS) sweeping magnet (2kG) analyzing magnet (4 or 6 kG) From Event-display ● Movable spectrometer : 6°< θlab < 30°, 5 msr solid angle ● 2 tracking stations (DC+TPC+DC) + TOF (σTOF ～75 ps) ● 2 dipole Magnets : two different polarities →　＋/－ charge favor ○ TPC (Time Projection Chamber) resolution : 0.5 ～1.2 mm ○ FT (Drift Chamber) resolution : ～0.3 mm

  14. Single and Two-Particle Acceptance in y-pT (Y-KT) Space : average pT of pair ■ Single Particle Acceptance (FS) ■ p+-p+ Two Particle Acceptance Ycm at 11 A GeV p+p+ HBT analysis range 0.1 < KT < 0.6 GeV/c 1.6 < Ypp< 2.3 ycm=1.17 @ Ebeam = 4 A GeV ycm=1.6 @ Ebeam = 11 A GeV

  15. Track Finding and Reconstruction ■ Track matching Procedure m plane P1 Raw data P2 TPC1 track (clustering) TPC2 track (clustering) FTR1 track A B x FT1,2 projection FT3,4 projection FTR2 track M2 magnet z y (upward) FTR1 track FTR2 track Effective Edges Top view of FS Track matching Dx, D y, Dangle < 3s Good track selection Dx, D y < 3s TOF and Target association

  16. Momentum Resolution Momentum resolution for protons Momentum reconstruction low momentum cut off Momentum kick of track in B σp/p 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Momentum p (GeV/c) Check for the absolute momentum ■ L → p-p Invariant Mass Gaussian fitting result mL= 1116.0±0.1 [MeV/c2] 4 A GeV data Error ～0.3 MeV/c2 →1.5% in momentum FTR2 track FTR1 track 1.1 1.11 1.12 1.13 1.14 1.15 Invariant Mass [GeV/c2]

  17. Particle Identification 6 4 m : particle mass p : momentum TOF : time-of-flight L : flight-path length Signed Momentum p (GeV/c) deuteron proton 2 p+ 0 p- K+ -2 ■ Momentum cut off deuteron: 0.45 - 5.00 GeV/c proton : 0.45 - 5.00 GeV/c kaon : 0.45 - 3.00 GeV/c pion : 0.45 - 4.00 GeV/c -4 -6 -1 0 1 2 3 4 5 6 Squared Mass m2 (GeV2/c4)

  18. Trigger Conditions ① BEAM trigger pile-up rejection < 500 nsec ② INT trigger (interaction trig.) beam fragments charge Z < Z(Au) = 79 (minimum bias) Two particle correlation analysis (central 10% of σINT) ③ ZCAL trigger (central event trig.) ④ FSPEC trigger (spectrometer trig.) Single particle analysis

  19. 3. Experimental Results in Au+Au @ 4 and 11 A GeV • Single Particle Spectra for p±, K+, p, d at 4 and 11 A GeV • 1-1. Centrality dependence of mt spectra • 1-2. Centrality dependence of <mt > - m0 • 2) Two-Particle Correlations for p+p+ at 11 A GeV • 2-1. Cut criteria and Coulomb correction • 2-2. YKP parameterization and KT dependence of RT

  20. Correction Factor for Single Particle Spectra ■ Invariant Cross Section ●parameterization T : inverse slope parameter Corrections • Good beam selection → 3σ cut by ADC spectra of beam counter • Geometrical acceptance → Δφfrom Monte Carlo simulation • PID 　　　　　　　　　　　　 → in m2 vs. momentum plot • Decay correction (p, K) → from flight path length and momentum • TPC hardware efficiency • Track reconstruction software efficiency typical correction factor • TOF occupancy correction ～12% (inclusive)

  21. 1-1) Centrality Dependence of mt Spectrum p d p d p- p+ K+ K+ 4 A GeV (mid-rapidity) 11 A GeV (mid-rapidity) ・ Centrality up → increase of inverse slope “T”, deviation from exponential shape (p, p) ・ Tp < TK < Tp < Td , (4 GeV < 11 GeV) ・ Shape of spectra in most central → p = shoulder arm shape ; p = convex shape

  22. ・Thermal motion ; <E> thermal～Tthermal ・Collective motion ; <E>collective = ・Superposition ; <Ekine> = <E> thermal + <E>collective 1-2) Centrality Dependence of <mt> - m0 ■ 4 A GeV (mid-rapidity) ■ 11 A GeV (mid-rapidity) ・ Systematic increase as a function of centrality (4,11 GeV, π, K, p) ・ Most central proton, Kaon → 4GeV < 11 GeV ・ Clear mass dependence (peripheral → central) → 4 GeV < 11 GeV <mt> - m0 [GeV/c2] <mt> - m0 [GeV/c2] centrality s/strig [%] centrality s/strig [%] central peripheral central peripheral <mt> - m0 ∝ Tthermal +mass ・ <βt>2 Mass dependence of <mt> indicates the existence of bt

  23. 1/R x1 x1’ x2 x2’ x1 x1’ x2 x2’ Fourier transform of reff → 2) Two Particle Correlations (HBT) Extraction of source size “R” using quantum interferometry Formalism of HBT = Hanbury-Brown-Twis effect ● Provability amplitude for identical bosons symmetric (1 ⇔ 2) x1 p p1 X1’ R Interference term p2 ● 2 particle momentum dist. p x2 X2’ Particle emitting source C2 ● Correlation function C2 Assume Gaussian reff with width “R” C2 ; function of momentum difference

  24. 2-1) Two Particle Correlations for p+-p+ pair at 11 A GeV ■ Qinv distribution Two Particle Correlation Function C2 normalized mixed background real events with Coulomb ■ definition = Correlated / Uncorrelated ・10% central event ・2.5 M p+-p+ pairs after cuts ・Background sampling from different events

  25. ■ Correlation function in Qinv with Coulomb w/o Coulomb Cut Criteria and Coulomb Correction ● Cut criteria ・Two track separation → < 1 cm cutoff in x, y at each TPC mid-plane ・Rapidity cut 1.6 < y < 2.3 ● Coulomb correction ・Standard Gamow factor ; G Fitting Function for 1D case Coulomb interaction between charged particles in the final state

  26. with low Q||, Q0 cut [ref] U. Heinz et al., PLB 382 (1996) 181 : average pT of pair ; energy difference ; transverse p difference ; longitudinal p difference 2-2) Yano-Koonin Podgoretskii (YKP) Parameterization C2 function for QT in YKP ■ Features of this parameterization ① perfect factorization of transverse, longitudinal spatial and temporal extension of the source. ② R parameter ⇔ expanding source model ■ Definition ◎ decomposition of 3 dimensional Q value ◎ Frame : Local Centre of Mass System of pair ◎ Fitting parameters ; l, RT

  27. KT dependence of RT in YKP param. II I III |Q|||, |Q0| < 50 MeV/c projection in QT ■ KT dependence of RT ■ Correlation function in YKP as a function of QT I II III Class I : 0.1 < KT< 0.25 GeV/c Class II : 0.25 < KT< 0.35 GeV/c Class III :0.35 < KT< 0.45 GeV/c Gradual decrease of RT as a function of KT (RT : 5.21 ±0.17 fm → 3.73 ±0.26 fm)

  28. Finite Expansion Model ■Assumptions 1. Local thermal equilibration 2. Transverse/ longitudinal motion decoupling 3. Longitudinal boost invariant 4. Azimuthally symmetric source (Gaussian) 5. Freeze-out (particle emission) at temperature “T” for all particle species 6. No resonance contributions Flow velocity u(x) : unit vector where Single particle spectrum Two particle correlation function for boson ※Single particle momentum dist. : P (p1) Two particle momentum dist. : P (p1, p2) 4. Discussion – finite expansion source model ■ In general ..., emission function : S ( x, p) defines the particle distributions

  29. Expansion Model in mt Spectra ■Function shape ● Single particle momentum distribution βt=0.6 βt=0 Transverse flow velocity : Temperature at freeze-out : T ※ ■ Fitting in 11 A GeV data ●different shape of spectrum for π, p and d, if bt is large enough (bt ～0.5)

  30. Fitting Results in mt Spectra: T vs. βｔ 4 A GeV 11 A GeV deuteron K+ K+ deuteron proton p p ±2s band ±2s band proton Allowed regions of T, βt from single particle spectra 11 A GeV T = 90～100 MeV βt= 0.65～ 0.85 4 A GeV T = 80～90 MeV βt= 0.6 ～ 0.7 < without deuteron band

  31. Combine Single Particle Results with HBT’s Determine bt2/T from KT dep. of RT ■ KT dependence of RT [GeV-1] from RT in YKP ⇔ Expansion model in HBT ±3s band ■Single + HBT overlay Allowed regions of T, βt from single particle spectra and HBT deuteron K+ pp HBT E866 Au+Au 11 GeV T = 95 ±5 MeV βt= 0.77±0.06 NA49 Pb+Pb 158 A GeV T = 120 ±12 MeV βt= 0.55±0.12 < > π proton βt : AGS > SPS CL 95%

  32. SISAGSSPS SISAGSSPS Excitation Function of <bt> and T ■ Excitation function of bt ■ Excitation function of T saturation ～ <bt> = 0.5 Single spectra + HBT ● mean of bt ・ <bt> : continuous rise with Ebeam up to AGS saturation at SPS energies ・ T : continuous rise with Ebeam from SIS to SPS

  33. Comparison of βt and T between AGS and SPS Qualitative arguments ● T : AGS < SPS Lattice QCD cal. ⇒Tc = 140 ～200 MeV TSPS = 120 MeV at freeze-out ∴ Not hard to assume QGP formation at SPS, cool down and freeze-out at TSPS ● βt : AGS > SPS If QGP formed ⇒　“softening” of EoS 　⇒ pressure gradient ～ 0 ⇒ reduced βt ∴ The reduction of βt @ SPS does not contradict the hypothesis of softening of EoS by QGP formation in central Pb+Pb at SPS. Anomalous J/ψ suppression (NA50), Enhancement of low-mass dilepton (CERES) indicated by

  34. 5. Summary (1)– Experimental results 1) Single particle spectra for p±, K+, p, d at 4 and 11 A GeV and two particle correlations for p+p+ pairs at 11 A GeV in Au+Au collisions are measured. 2) Shape of spectra for protons and pions in most central event deviate from single exponential shape. ・p → convex shape at low mt ・p 　 → low mt enhancement 3) Mass dependence of <mt> -m0 is the most evident at central events. ・p, K, p, d mass splitting ; 4 GeV < 11 GeV 4) Gradual decrease of RT with increasing KT is observed in YKP parameterization. ・RT : 5.2 fm → 3.7 fm(KT : 0.1 → 0.45 GeV/c) ※In standard side-out-long parameterization, decrease of RT as a function KT is also observed. 5) These observations in single particle spectra and HBT are consistent with the expanding source scenario.

  35. E866 Au+Au 11 GeV T = 95 ±5 MeV βt= 0.77±0.06 NA49 Pb+Pb 158 A GeV T = 120 ±12 MeV βt= 0.55±0.12 < > Summary (2) –Physics interpretations • 6) T and βt of the source are extracted from mt spectra for p, K, p, d • (4, 11 A GeV) with p+p+ HBT constraint (11 A GeV) using the finite • expansion model. • 7) The expansion model reproduce the data by introducing (bt, T) • ・shapes of mt spectra for all particle species • ・KT dependence of RT • Within the model, strong transverse velocity is deduced • in central Au+Au at 11 A GeV. • 9) The reduction of βｔ at SPS does not contradict the hypothesis of • the softening of EoS by QGP formation at SPS . CL 95% indicated by J/ψ suppression (NA50) and enhancement of low-mass dilepton (CERES)

  36. Beam direction 2-2) Standard side-out-long Parameterization Standard Side-Out-Long Coordinate Beam direction

  37. KT dependence of R in side-out-long param. ■ C2 function in BP ■ KT distribution Qside Qout Qlong Class I : 0.1 < KT< 0.25 GeV/c Class II : 0.25 < KT< 0.35 GeV/c Class III :0.35 < KT< 0.45 GeV/c I (low KT) II (mid KT) ■ KT dependence of R in BP III (high KT) Fitting Function

  38. 1-3) Rapidity Density Distribution - dN/dy - 4 A GeV 11 A GeV p d p d p- p+ K+ K+

  39. L.Ahle et al. (E802), PRC 57 (1998) R466 Au+Au (central) Before ytarget ycm ybeam complete baryon stopping Si+Al (central) After 0.00 0.25 0.50 0.75 1.00 1.25 ytarget ycm ybeam Proton’s dN/dy ycm Si+Al : rapidity shift ～1 (partial transparent) Au+Au : Maximum plateau at mid-rapidity suggests strong baryon stopping ★ Possibility to create hot and dense matter at ycm

  40. Systematic Error Estimation

  41. Expanding Source Model in Single/Two Particle Dist. = finite expanding velocity field (common for all particle species) Introducing βt ■Transverse momentum dependence of RT in the expanding source model ■ Single particle dist. with βt P.B.Munzinger et al., PL B344 (1995) 43 Y.-F Wu et al., Eur. Phys. J. C1 (1998) 599 d p Si+Au 14.6 A GeV/c T= 120 MeV <βt> = 0.39 K+ p+ (MeV/c2) T=Tthermal +m <βt>2 ★ If βt is incorporated in the model, KT dependence of RT is visible ★ Successful description in Mt spectra for all particle species for individual shapes

  42. Inverse slope T 　⇔　“Temperature” Single Particle Spectra in pA at AGS ■ Transverse mass spectra for p, K, p ◆Invariant Cross section AGS-E802 data Transverse mass Rapidity T : inverse slope parameter ● Single exponential shape as a function of mt (mt scaling) with same “ T ”　～150MeV = in parallel for all particle species T : Independent on particle mass ▲T.Abbott et al. (E802), PRL 66(1991)1567 ● Consistent with the picture of the local thermal equilibrium in pp and pA at AGS = Transverse kinetic energy p+Au 14.6 GeV/c

  43. ■Mass dependence of T ・Thermal motion ; <E> thermal～Tthermal E802/866 data ・Collective motion ; <E>collective = Au+Au 11.6 A GeV/c ・Superposition ; <Ekine> = <E> thermal + <E>collective Si+Al 14.6 A GeV/c p K p d p+Au 14.6 A GeV/c Single Particle Spectra in AA ■Au+Au 11.6 A GeV/c (central) ● Shape of the spectra at low mt pion : concave shape proton : convex shape ● Clear mass dependence of T Particle mass , inverse slope ● Collision system dependence mass splitting of T : Si+Al < Au+Au L.Ahle et al. (E802), PRC 57 (1998) R466 p p E866 data T ∝ Tthermal +mass ・ <βt>2 Mass dependence of T indicates the existence of bt

  44. Summary of Results - Single Particle Spectra 1) Shape of spectra in most central event ・deviation from single exponential shape (d,p,p) ・p : shoulder-arm shape at low mt ・π：enhancement at low mt 2) Mass dependence of <mt> -m0 ・evident in most central ; p < K < p < d ・mass splitting ; 4 GeV < 11 GeV Consistent with the picture of collective flow + resonance decay contribution in low mt for pion’s spectra

  45. KT dependence of RT : average pT of pair ■Transverse momentum dependence of RT in the expanding source model Y.-F Wu et al., Eur. Phys. J. C1 (1998) 599 ● Decrease of RT as a function of KT ★ If βt is incorporated in the model, KT dependence of RT is visible (MeV/c2)

  46. Attempt to Interpret Mt spectra by Simple Models “Pion-Proton puzzle” in early ’90 ①Fireball & Firestreak Model (= simple thermal models) Thermal Equilibrium T=228 MeV, ρ/ρ0= 4.8 Firestreak Fireball ② String Model pp like string formation No equilibrium, No initial/final interaction String ★ Both simple thermal model and simple string model do not reproduce the data M.Gyulassy, HIPAGS ’90, BNL-44911 Needed more realistic treatments (+ flow?)

  47. Coulomb Correction

  48. Material (1) C2 1/R p+Au 14.6 GeV/c T.Abbott et al. (E802), PRL 66(1991)1567 E802 data POINT Finite expanding source model are used in both single particle and HBT analysis in the same framework Consistent picture of expansion MERIT Different T-βt domain between single particle and HBT analysis Determine (T,βt) uniquely

  49. ● Fitting function of mt spectra J/ψ L <mt> calculated from T or TB Single exponential func. (for p, K) Boltzmann func. (for proton, deuteron) Material (2) ● Systematic study of μ+μ- pair in p+A, S+U and Pb+Pb by NA50 Normal nuclear absorption L; mean nuclear path length

  50. Material (3) Momentum reconstruction Momentum kick of track in B FTR2 track FTR1 track

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