Study of Single Particle Spectra and Two Particle

Study of Single Particle Spectra and Two Particle Correlations in Au+Au Collisions at 4 -11 A Ge. V 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 Ge. V Thesis Motivation 2) AGS-E 866 Experiment (Setup & Data Reduction) 3) Experimental Results • • Single Particle Spectra (4, 11 A Ge. V) π+π+ Two-Particle Correlations (11 A Ge. V) 4) Discussions • • Finite Expanding Source Model Excitation Function of Transverse Velocity and Temperature 5) Summary 2

Physics of High Energy Heavy-Ion Collisions ◎Prediction of lattice QCD calculation QGP phase transition at ε～ 2 Ge. V/fm 3, Tc = 140 ～ 200 Me. V ◆ Relativistic Heavy Ion Collisions BNL-AGS (Au+Au 11 A Ge. V) & CERN-SPS (Pb+Pb 158 A Ge. V) ● 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) 3

(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. B 450 (1999) 456 ★Debye screening effects NA 50 potential V(r) above Tc confinement J/ψ r deconfinement r. D : Debye radius if r. D < r J/ψ, no bound state J/ψ production is suppressed by QGP formation 4 Strong J/ψ suppression is observed in Pb+Pb central at SPS cannot be explained by hadronic scenario QGP formation ?

(2) Enhancement of low-mass dilepton @ SPS ● Lepton pair production → reflect initial temperature of system QGP or HG nucl-ex/9910015 QM 99 Proceedings : : chiral symmetry restoration → ρ decay with reduced mass → enhancement at low-mass region ■Systematic e+e- measurements by CERES/NA 45 Enhancement at low-mass (0. 2 < mee < 0. 8 Ge. V/c 2) region compared to the hadronic decay contribution formation of QGP ? chiral symmetry restoration? 5

(3) Softening of Eo. S by QGP formation ● Equation of State (Eo. S) from parameterization of lattice QCD data D. H. Rischke, Nucl. Phys. A 610 (1996) 88 c HG Mixed QGP Critical temperature : Tc Pressure P Sound of velocity (squared) || pressure gradient 6 ΔT = 0 (1 st. Order transition ) ΔT = 0. 1 Tc (smooth transition) ideal hadron gas (no transition) transverse expansion velocity βt “Softening” of Eo. S in mixed phase can be considered as a signature of QGP formation

Collective behavior in Pb+Pb @ SPS 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 ★ NA 49 (Pb+Pb central @ 158 A Ge. V) Allowed region of T, bt at CERN energy H. Appelshauser et al. (NA 49), Eur. Phys. J C 2 (1998) 661 T = 120± 12 Me. V bt = 0. 55 ± 0. 12 ・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 ! 7

Thesis Motivation DATA BNL-AGS-E 866 Au+Au collisions ① Single Particle Spectra for p±, K+, p, d (4, 11 A Ge. V) ② Two Particle Correlations for p+ p+ pairs (11 A Ge. V) ・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) 8

Contributions of Author 1. Calibrated the TPC, TOF. 2. Analyzed single particle spectra at 4 A Ge. V beam energy and published the results. 3. Analyzed single particle spectra and two-particle correlations at 11 A Ge. V beam energy. 9

2. AGS-E 866 Experimental Setup Henry Higgins Spectrometer Forward Spectrometer ● Two Spectrometer System : (1) Forward Spectrometer (ycm coverage) (2) Henry Higgins Spectrometer (not used in this analysis) ● Beam 10 : 4. 04 and 10. 8 Ge. V per nucleon (in terms of kinetic energy)

Global Detectors ■ Beam Counters (BTOT, HOLE) Beam trigger and time-zero for TOF BTOT – Cherenkov counter (200 mm thick. ) HOLE – Scintillation counter for beam halo rejection (10 mm diameter hole) ■ Bull’s Eye (BE) Define centrality by pion multiplicity at target ・Cherenkov counter array ・ 346 modules ・Polar angle coverage : 7°-112° ■ Zero-degree Calorimeter (ZCAL) Define INT trigger by Z of beam fragments ・ 9. 5 m down stream ・Quartz (300 mm thickness) Cherenkov radiator ・ 8 PMT readout 11 ■ New Multiplicity Array (NMA) Define centrality by total kinetic energy of beam fragments ・Fe-Scint. Sandwiched-type hadronic calorimeter ・ 11 m down stream

Event Characterization ■ ZCAL energy distribution in INT trigger ■Participants – Spectator Picture Kinetic energy of beam 197×E beam (10. 8 Ge. V) Beam Fragment beam b 0 -10% 0 10 -30% 50 -100% 30 -50% 1000 2000 3000 = impact parameter target ZCAL Software sum of ZCAL (Ge. V) Central Peripheral ■ NMA multiplicity distribution in INT trigger Provide the collision geometry event by event ●Centrality Cut 50 -100% 30 -50% 10 -30% ① ZCAL (Etotal of beam fragments) ② NMA (multiplicity of pions at target) 0 -10 % Pion multiplicity Peripheral 12 Central

Forward Spectrometer (FS) sweeping magnet (2 k. G) analyzing magnet (4 or 6 k. G) 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 13

Single and Two-Particle Acceptance in y-p. T (Y-KT) Space ■ Single Particle Acceptance (FS) ■ p+-p+ Two Particle Acceptance Ycm at 11 A Ge. V ycm=1. 17 @ Ebeam = 4 A Ge. V ycm=1. 6 @ Ebeam = 11 A Ge. V 14 p+p+ HBT analysis range 0. 1 < KT < 0. 6 Ge. V/c 1. 6 < Ypp< 2. 3 : average p. T of pair

Track Finding and Reconstruction ■ Track matching P 1 Procedure m plane Raw data P 2 TPC 1 track (clustering) FTR 1 track A B x y z (upward) M 2 magnet Effective Edges FTR 2 track TPC 2 track (clustering) FT 1, 2 projection FT 3, 4 projection FTR 1 track FTR 2 track Top view of FS Track matching Dx, D y, Dangle < 3 s Good track selection Dx, D y < 3 s TOF and Target association 15

Momentum Resolution Momentum resolution for protons Momentum reconstruction Momentum kick of track in B low momentum cut off σp/p 0 0. 5 1 1. 5 2 2. 5 Momentum 3 3. 5 4 4. 5 5 p (Ge. V/c) Check for the absolute momentum ■ L → p- p Invariant Mass Gaussian fitting result m. L= 1116. 0± 0. 1 [Me. V/c 2] FTR 2 track 4 A Ge. V data FTR 1 track 1. 1 16 1. 11 1. 12 1. 13 1. 14 1. 15 Invariant Mass [Ge. V/c 2] Error ～ 0. 3 Me. V/c 2 → 1. 5% in momentum

Signed Momentum p (Ge. V/c) Particle Identification 6 4 2 proton p+ deuteron 0 K+ p-2 ■ Momentum cut off -4 -6 -1 17 m : particle mass p : momentum TOF : time-of-flight L : flight-path length 0 1 2 3 4 5 6 Squared Mass m 2 (Ge. V 2/c 4) deuteron: 0. 45 - 5. 00 Ge. V/c proton : 0. 45 - 5. 00 Ge. V/c kaon : 0. 45 - 3. 00 Ge. V/c pion : 0. 45 - 4. 00 Ge. V/c

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

3. Experimental Results in Au+Au @ 4 and 11 A Ge. V 1) Single Particle Spectra for p±, K+, p, d at 4 and 11 A Ge. V 1 -1. Centrality dependence of mt spectra 1 -2. Centrality dependence of <mt > - m 0 2) Two-Particle Correlations for p+p+ at 11 A Ge. V 2 -1. Cut criteria and Coulomb correction 2 -2. YKP parameterization and KT dependence of RT 19

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 → Δφ from Monte Carlo simulation • PID → in m 2 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) 20

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

1 -2) Centrality Dependence of <mt> - m 0 ■ 11 A Ge. V (mid-rapidity) ・ Systematic increase as a function of centrality (4, 11 Ge. V, π, K, p) <mt> - m 0 [Ge. V/c 2] ■ 4 A Ge. V (mid-rapidity) centrality s/strig central ・ Most central proton, Kaon → 4 Ge. V < 11 Ge. V centrality s/strig [%] peripheral central [%] peripheral ・ Clear mass dependence (peripheral → central) → 4 Ge. V < 11 Ge. V ・Thermal motion ; <E> thermal ～Tthermal ・Collective motion ; <E>collective = ・Superposition ; <Ekine> = <E> thermal + <E>collective 22 <mt> - m 0 ∝ Tthermal +mass ・ <βt>2 Mass dependence of <mt> indicates the existence of bt

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) x 1 p p 1 x 2 X 1 ’ R x 2 p x 1’ x 2’ Interference term ● 2 particle momentum dist. ● Correlation function C 2 1/R C 2 ; function of momentum difference 23 x 1 x 2 X 2 ’ C 2 Particle emitting source x 1’ x 2’ Fourier transform of reff → Assume Gaussian reff with width “R”

2 -1) Two Particle Correlations for p+-p+ pair at 11 A Ge. V Two Particle Correlation Function C 2 ■ Qinv distribution normalized mixed background = Correlated ■ / Uncorrelated definition ・ 10% central event ・ 2. 5 M p+-p+ pairs after cuts ・Background sampling from different events 24 real events with 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 ■ Correlation function in Qinv with Coulomb w/o Coulomb ● Coulomb correction ・Standard Gamow factor ; G Fitting Function for 1 D case Coulomb interaction between charged particles in the final state 25

2 -2) Yano-Koonin Podgoretskii (YKP) Parameterization C 2 function for QT in YKP ■ Features of this parameterization with low Q||, Q 0 cut [ref] U. Heinz et al. , PLB 382 (1996) 181 : average p. T of pair 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 ; energy difference ; transverse p difference ; longitudinal p difference ◎ Frame : Local Centre of Mass System of pair ◎ Fitting parameters ; l, RT 26

KT dependence of RT in YKP param. ■ Correlation function in YKP as a function of QT I ■ KT dependence of RT II III III |Q|||, |Q 0| < 50 Me. V/c projection in QT Gradual decrease of RT as a function of KT (RT : 5. 21 ± 0. 17 fm → 3. 73 ± 0. 26 fm) 27 Class I : 0. 1 < KT< 0. 25 Ge. V/c Class II : 0. 25 < KT< 0. 35 Ge. V/c Class III : 0. 35 < KT< 0. 45 Ge. V/c

4. Discussion – finite expansion source model ■ In general. . . , emission function : S ( x, p) defines the particle distributions Single particle spectrum Two particle correlation function for boson ※Single particle momentum dist. : P (p 1) Two particle momentum dist. : P (p 1, p 2) Finite Expansion Model Flow velocity u(x) : unit vector where 28 ■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

Expansion Model in mt Spectra ● Single particle momentum distribution ■ Function shape βt=0. 6 Transverse flow velocity : βt=0 Temperature at freeze-out : T ※ ■ Fitting in 11 A Ge. V data ●different shape of spectrum for π, p and d, if bt is large enough (bt ～ 0. 5) 29

Fitting Results in mt Spectra: T vs. βｔ 4 A Ge. V 11 A Ge. V K+ K+ deuteron proton p p ± 2 s band proton ± 2 s band Allowed regions of T, βt from single particle spectra 4 A Ge. V T = 80～ 90 Me. V βt= 0. 6 ～ 0. 7 without deuteron band 30 < 11 A Ge. V T = 90～ 100 Me. V βt= 0. 65～ 0. 85

Combine Single Particle Results with HBT’s Determine bt 2/T from KT dep. of RT ■ KT dependence of RT [Ge. V-1] from RT in YKP ⇔ Expansion model in HBT ± 3 s band ■ Single + HBT overlay K+ Allowed regions of T, βt from single particle spectra and HBT deuteron pp HBT π proton E 866 Au+Au 11 Ge. V T = 95 ± 5 Me. V βt= 0. 77± 0. 06 NA 49 Pb+Pb 158 A Ge. V < > T = 120 ± 12 Me. V βt= 0. 55± 0. 12 βt : AGS > SPS 31 CL 95%

Excitation Function of <bt> and T ■ Excitation function of bt ■ Excitation function of T Single spectra + HBT saturation ～ <bt> = 0. 5 SIS AGS SPS ● mean of bt ・ <bt> : continuous rise with Ebeam up to AGS saturation at SPS energies ・ T 32 : continuous rise with Ebeam from SIS to SPS

Comparison of βt and T between AGS and SPS Qualitative arguments ● T : AGS < SPS Lattice QCD cal. ⇒Tc = 140 ～ 200 Me. V TSPS = 120 Me. V 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 Eo. S ⇒ pressure gradient ～ 0 ⇒ reduced βt ∴ The reduction of βt @ SPS does not contradict the hypothesis of softening of Eo. S by QGP formation in central Pb+Pb at SPS. indicated by Anomalous J/ψ suppression (NA 50), Enhancement of low-mass dilepton (CERES) 33

5. Summary (1)– Experimental results 1) Single particle spectra for p±, K+, p, d at 4 and 11 A Ge. V and two particle correlations for p+p+ pairs at 11 A Ge. V 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> -m 0 is the most evident at central events. ・p, K, p, d mass splitting ; 4 Ge. V < 11 Ge. V 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 Ge. V/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. 34

Summary (2) –Physics interpretations 6) T and βt of the source are extracted from mt spectra for p, K, p, d (4, 11 A Ge. V) with p+p+ HBT constraint (11 A Ge. V) 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 8) Within the model, strong transverse velocity is deduced in central Au+Au at 11 A Ge. V. E 866 Au+Au 11 Ge. V T = 95 ± 5 Me. V βt= 0. 77± 0. 06 NA 49 Pb+Pb 158 A Ge. V < > T = 120 ± 12 Me. V βt= 0. 55± 0. 12 CL 95% 9) The reduction of βｔ at SPS does not contradict the hypothesis of the softening of Eo. S by QGP formation at SPS. 35 indicated by J/ψ suppression (NA 50) and enhancement of low-mass dilepton (CERES)

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

KT dependence of R in side-out-long param. ■ C 2 function in BP Qside I Qout ■ KT distribution Qlong Class I : 0. 1 < KT< 0. 25 Ge. V/c Class II : 0. 25 < KT< 0. 35 Ge. V/c Class III : 0. 35 < KT< 0. 45 Ge. V/c (low KT) II (mid KT) III (high KT) Fitting Function 37 ■ KT dependence of R in BP

1 -3) Rapidity Density Distribution - d. N/dy 4 A Ge. V 38 11 A Ge. V d p K+ p+ d K+ p p-

Proton’s d. N/dy L. Ahle et al. (E 802), PRC 57 (1998) R 466 Before Au+Au (central) ytarget ycm 0. 25 0. 50 0. 75 1. 00 After 1. 25 ytarget 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 39 ybeam complete baryon stopping Si+Al (central) 0. 00 ycm ybeam

Systematic Error Estimation 40

Expanding Source Model in Single/Two Particle Dist. = finite expanding velocity field (common for all particle species) Introducing βt ■ Single particle dist. with βt P. B. Munzinger et al. , PL B 344 (1995) 43 ■Transverse momentum dependence of RT in the expanding source model Y. -F Wu et al. , Eur. Phys. J. C 1 (1998) 599 d p Si+Au 14. 6 A Ge. V/c K+ T= 120 Me. V <βt> = 0. 39 p+ T=Tthermal +m <βt>2 ★ Successful description in Mt spectra for all particle species for individual shapes 41 (Me. V/c 2) ★ If βt is incorporated in the model, KT dependence of RT is visible

Single Particle Spectra in p. A at AGS ■ Transverse mass spectra for p, K, p ◆Invariant Cross section AGS-E 802 data Transverse mass Rapidity T : inverse slope parameter ● Single exponential shape as a function of mt (mt scaling) with same “ T ” ～ 150 Me. V = in parallel for all particle species ▲T. Abbott et al. (E 802), PRL 66(1991)1567 = Transverse kinetic energy p+Au 14. 6 Ge. V/c 42 T : Independent on particle mass ● Consistent with the picture of the local thermal equilibrium in pp and p. A at AGS Inverse slope T ⇔ “Temperature”

Single Particle Spectra in AA ■Au+Au 11. 6 A Ge. V/c (central) L. Ahle et al. (E 802), PRC 57 (1998) R 466 p p ● 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 E 866 data mass splitting of T : Si+Al < Au+Au ・Thermal motion ; <E> thermal ～Tthermal ■ Mass dependence of T E 802/866 data Au+Au 11. 6 A Ge. V/c Si+Al 14. 6 A Ge. V/c p K 43 p d p+Au 14. 6 A Ge. V/c ・Collective motion ; <E>collective = ・Superposition ; <Ekine> = <E> thermal + <E>collective T ∝ Tthermal +mass ・ <βt>2 Mass dependence of T indicates the existence of bt

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> -m 0 ・evident in most central ; p < K < p < d ・mass splitting ; 4 Ge. V < 11 Ge. V Consistent with the picture of collective flow + resonance decay contribution in low mt for pion’s spectra 44

KT dependence of RT ■Transverse momentum dependence of RT in the expanding source model Y. -F Wu et al. , Eur. Phys. J. C 1 (1998) 599 ● Decrease of RT as a function of KT (Me. V/c 2) : average p. T of pair 45 ★ If βt is incorporated in the model, KT dependence of RT is visible

Attempt to Interpret Mt spectra by Simple Models “Pion-Proton puzzle” in early ’ 90 ① Fireball & Firestreak Model (= simple thermal models) Firestreak Thermal Equilibrium T=228 Me. V, ρ/ρ0= 4. 8 Fireball ② String Model String pp like string formation No equilibrium, No initial/final interaction Proton yield Thermal model String model × ○ pyield × × Proton Mt dist ○ × p. Mt dist × ○ ★ Both simple thermal model and simple string model do not reproduce the data M. Gyulassy, HIPAGS ’ 90, BNL-44911 46 Needed more realistic treatments (+ flow? )

Coulomb Correction 47

p+Au 14. 6 Ge. V/c T. Abbott et al. (E 802), PRL 66(1991)1567 C 2 Material (1) E 802 data 1/R 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 48 Determine (T, βt) uniquely

Material (2) ● Systematic study of μ+μ- pair in p+A, S+U and Pb+Pb by NA 50 Normal nuclear absorption J/ψ L L; mean nuclear path length ● Fitting function of mt spectra Single exponential func. (for p, K) Boltzmann func. (for proton, deuteron) 49 <mt> calculated from T or TB

Material (3) Momentum reconstruction Momentum kick of track in B FTR 2 track 50 FTR 1 track