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

● 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….

BNL-AGS (Au+Au 11 A GeV) &CERN-SPS (Pb+Pb 158 A GeV)

◎Prediction of lattice QCD calculation QGP phase transition at ε ～ 2 GeV/fm3, Tc = 140 ～ 200 MeV

◆ Relativistic Heavy Ion Collisions

Interesting results in Pb+Pb at SPS have been reported ( indication of QGP formation)

4

(1) J/ψ suppression in Pb+Pb @ SPS

★Debye screening effects

cc potential

V(r)

r

V rr

r( ) =− +α σeff

V rr

r r( ) exp( / )=−′

−α eff

D

rD : Debye radius

above Tc

● 　 J/ψ suppression as a signature of QGP formation Proposed by Matsui and Satz (1986)

J/ψ

confinement

deconfinement if rD < r J/ψ, no bound state

J/ψ production is suppressed by QGP formation

Strong J/ψ suppression is observed in Pb+Pb central at SPS

M. C. Abreu et al., Phys. Lett. B450 (1999) 456

NA50

QGP formation ?

cannot be explained by hadronic scenario

5

(2) Enhancement of low-mass dilepton @ SPS

nucl-ex/9910015 QM99 Proceedings

Enhancement at low-mass (0.2 < mee < 0.8 GeV/c2) region compared to the hadronic decay contribution

■Systematic e+e- measurements 　 by CERES/NA45

QGP :　 or HG :

qq l l→ + −

π π+ − + −→ l l

● Lepton pair production

chiral symmetry restoration → 　 ρ decay with reduced mass→ enhancement at low-mass region

→ reflect initial temperature of system

formation of QGP ? chiral symmetry restoration?

6

(3) Softening of EoS by QGP formation

D. H. Rischke, Nucl. Phys. A610 (1996) 88c

● Equation of State (EoS) from parameterization of lattice QCD data

“Softening” of EoS in mixed phase can be considered as a signature of QGP formation

Pressure P

HG Mixed QGP

cdP

dS2 =

ε

Sound of velocity (squared) || pressure gradient

Critical temperature : Tc

ΔT = 0 (1st. Order transition )ΔT = 0.1 Tc (smooth transition) ideal hadron gas (no transition)

transverse expansion velocity βtβt

7

Collective behavior in Pb+Pb @ SPS

★ NA49 (Pb+Pb central @ 158 A GeV) Allowed region of T, t at CERN energy

T = 120±12 MeVt = 0.55 ±0.12

H.Appelshauser et al. (NA49), Eur. Phys. J C2 (1998) 661

● Simultaneous analysis with the expansion modelSingle particle spectra 　　　　　　　＋Two particle correlations

・ How evaluate obtained T and β ｔ ?・ Consistent with QGP formation ?

Comparison of SPS with AGS is essential, but no (T, βt) point at AGS so far !

1) consistent picture of expansion 2) less ambiguity in β ｔ – T plane

How determine βt and T of the system ?

8

Thesis Motivation

・ Possibility to determine T, t at AGS using the expansion source model

・ Behavior of T and t at AGS energy

・ Comparison AGS with SPS from the viewpoint of QGP formation

(qualitative argument)

DATA

① Single Particle Spectra for π, K+, p, d (4, 11 A GeV) ② Two Particle Correlations for ππ pairs (11 A GeV)

BNL-AGS-E866 Au+Au collisions

9

Contributions of Author

1. Calibrated the TPC, TOF.

2. Analyzed single particle spectra at 4 A GeV beam energyand published the results.

3. Analyzed single particle spectra and two-particle correlations at 11 A GeV beam energy.

10

2. AGS-E866 Experimental Setup

Forward Spectrometer

Henry Higgins Spectrometer

● 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)

11

Global Detectors

■ Bull’s Eye (BE)

・ 9.5 m down stream

・ Quartz (300 m thickness) 　 Cherenkov radiator

・ 8 PMT readout

■ New Multiplicity Array (NMA)

・ Cherenkov counter array ・ 346 modules・ Polar angle coverage : 7°-112°

■ Zero-degree Calorimeter (ZCAL)

・ Fe-Scint. Sandwiched-type hadronic calorimeter・ 11 m down stream

■ Beam Counters (BTOT, HOLE)

BTOT – Cherenkov counter (200m thick.)HOLE – Scintillation counter for beam halo rejection (10 mm diameter hole)

Define INT trigger by Z of beam fragments

Beam trigger and time-zero for TOF

Define centrality by total kinetic energy of beam fragments

Define centrality by pion multiplicity at target

12

Event Characterization

●Centrality CutCentrality Cut

① ZCAL (Etotal of beam fragments) ② NMA (multiplicity of pions at target)

■Participants – Spectator Picture

target

beam

ZCAL

Beam Fragment

b

■ ZCAL energy distribution in INT trigger

Software sum of ZCAL (GeV)0 　　　　　 1000 　　　　　 2000 　　　　　 3000

Kinetic energy of beam197×E beam (10.8 GeV)

0-10% 10-30% 30-50% 50-100%

Central Peripheral

= impact parameter

Provide the collision geometry event by event■ NMA multiplicity distribution in INT trigger

CentralPeripheral

Pion multiplicity

50-100% 30-50% 10-30% 0-10 %

13

Forward Spectrometer (FS)

● 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

From Event-display

sweeping magnet (2kG)analyzing magnet (4 or 6 kG)

14

Single and Two-Particle Acceptance in y-pT (Y-KT) Space

　ππ HBT analysis range 0.1 < KT < 0.6 GeV/c 1.6 < Yππ< 2.3 　 ycm=1.17 @ Ebeam = 4 A GeV

ycm=1.6 @ Ebeam = 11 A GeVK p pT T1 T2= +

12( ) : average pT of pair

Ycm at 11 A GeV

■ Single Particle Acceptance (FS) ■ ππ Two Particle Acceptance

15

Track Finding and Reconstruction

Raw data

TPC1 track(clustering)

TPC2 track(clustering)

FT1,2 projection FT3,4 projection

FTR1 track FTR2 track

Track matching

Good track selection

TOF and Target association

ProcedureProcedure

x

y (upward)

zM2 magnet

Effective Edges

FTR1 track

FTR2 track

AB

P2

P1 m plane

Top view of FS

■ Track matching

x, y, angle < 3σ

x, y < 3σ

16

Momentum Resolution

Momentum resolution for protons

σp/p

Momentum p (GeV/c)

Check for the absolute momentum

1.1 1.11 1.12 1.13 1.14 1.15 Invariant Mass [GeV/c2]

Gaussian fitting result

m= 1116.0±0.1 [MeV/c2]

Error ～ 0.3 MeV/c2

→1.5% in momentum

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

low momentum cut off

4 A GeV data

■→ π p Invariant Mass

Momentum reconstruction

p B s

B

= ⋅ ×z03. [ ]

[ ] :

q d cGeV/

T magneticfield

s [m] :path of the particle in

the magnetic field

p q B dz cx y≅ ⋅ z03. [ ]GeV/

Momentum kick of track in B

pp

p

dx dz dx dz

x

x x

x

=−

=−

tan tan

( / ) ( / )

θ θ2 1

2 1

FTR2 track FTR1 track

17

Squared Mass m2 (GeV2/c4)

-1 0 1 2 3 4 5 6

Sig

ned

Mom

entu

m p

(G

eV/c

)

6

4

2

0

-6

-4

-2

Particle Identification

■ 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

m pTOF

L2 2

2

1= FHG

IKJ −

LNMM

OQPP

m : particle mass p : momentum TOF : time-of-flight L : flight-path length

proton deuteron

K+

π

π

18

Trigger Conditions

BEAM PRE BTOT HOLE≡ I I

INT BEAM BE≡ I

ZCAL INT HZCAL≡ I

FSPEC INT FT FT≡ I I2 3

① BEAM trigger

② INT trigger (interaction trig.)

③ ZCAL trigger (central event trig.)

④ FSPEC trigger (spectrometer trig.)

Two particle correlation analysis (central 10% of σINT)

Single particle analysis

pile-up rejection < 500 nsec

beam fragments charge Z < Z(Au) = 79

(minimum bias)

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3. Experimental Results in Au+Au @ 4 and 11 A GeV

1) Single Particle Spectra for π, K+, p, d at 4 and 11 A GeV 　　　

1-1. Centrality dependence of mt spectra1-2. Centrality dependence of <mt > - m0

2) Two-Particle Correlations for ππ at 11 A GeV

2-1. Cut criteria and Coulomb correction2-2. YKP parameterization and KT dependence of RT

20

Correction Factor for Single Particle Spectra

CorrectionsCorrections

• Good beam selection → 3σ cut by ADC spectra of beam counter

• Geometrical acceptance → Δφ from Monte Carlo simulation

• PID 　　　　　　　　　　　　 → in m2 vs. momentum plot

• Decay correction (π, K) 　　→ from flight path length and momentum

• TPC hardware efficiency• Track reconstruction software efficiency typical correction factor

• TOF occupancy correction ～ 12% (inclusive)

Ed

dp

S N y p

N N p p y y pi t

t t i t

3

3

1 1σε φ

=⋅⋅

⋅ ⋅trig

beam target

( , )( , )

■ Invariant Cross Section

[ ]barn GeV-2⋅ c4

d

d d d

σφm m y

m mTt t

t∝ −−F

HGIKJexp

( )0

T : inverse slope parameter

● parameterization

21

1-1) Centrality Dependence of mt Spectrum

4 A GeV (mid-rapidity) 11 A GeV (mid-rapidity)

d

K+

p

-

・ Centrality up → increase of inverse slope “T”, deviation from exponential shape (p, π)・ Tπ< TK < Tp < Td , (4 GeV < 11 GeV)・ Shape of spectra in most central → p = shoulder arm shape ;πconvex shape

+

p

K+

d

22

1-2) Centrality Dependence of <mt> - m0

・ 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

■ 4 A GeV (mid-rapidity) ■ 11 A GeV (mid-rapidity)

central peripheral central peripheral

centrality σ/σtrig [%] centrality σ/σtrig [%]

<m

t> -

m0

[G

eV/c

2 ]

<m

t> -

m0

[G

eV/c

2 ]

・ Thermal motion ; <E> thermal ～ Tthermal

m02

2

< > t

・ Superposition ; <Ekine> = <E> thermal + <E>collective

・ Collective motion ; <E>collective = <mt> - m0 T∝ thermal +mass ・ <βt>2

Mass dependence of <mMass dependence of <mtt> indicates > indicates

the existence of the existence of t t

23

2) Two Particle Correlations (HBT)

Particle emitting source

x1

Extraction of source size “R”using quantum interferometry

x2

0 0.05 0.1 0.15 0.2

0.25

0.5

0.75

1

1.25

1.5

1.75

2

1/RC R2

2 21= + −λ (exp )q

C2

q |p p |1 2

≡ − [ / ]GεV c

p1

p2

X1’

X2’

R

CP p p

P p P p

R

eff

21 2

1 2

2

2 2

1

1

≡⋅

= +

= + −

( , )( ) ( )~ ( )

(exp )

ρ

λ

q

q

ψ 12 1 2

1

21 1 1 2 2 2 1 2 1 2 1 2( , ) ( ) ( ) ( ) ( )' ' ' '

p p e e e eip x x ip x x ip x x ip x x= +− − − − − − − −

P p p d x d x x x

P p P p d x e x p pieff

( , ) ( ) ( )

( ) ( ) ( , , )

1 24

14

2 12

2

1 2

1 24

1 2

2

1

=

= +FH IKz

zψ ρ ρ

ρqx

● Provability amplitude for identical bosons symmetric (1 ⇔ 2)

● 2 particle momentum dist.

q p p1 2≡ −

Assume Gaussian ρeff

with width “R”

Formalism of HBT = Hanbury-Brown-Twis effect

Interference term

● Correlation function C2

Fourier transform ofρeff →~ ( )ρeff q

x1 x1’ x2 x2’

x1 x1’ x2 x2’

C2 ; function of momentum difference

24

2-1) Two Particle Correlations for ππ pair at 11 A GeV

■ Qinv distribution

real events with Coulomb

normalized mixed background

・ 10% central event・ 2.5 M ππ pairs after cuts・ Background sampling from different events

Q Q Q Q Qinv x y z 0= + + −2 2 2 2

Q p p Q Q Q= − =1 2 ( , , )x y z

Q E E0 1 2= −

Two Particle Correlation Function C2

CdN d p d p

dN d p dN d p2

31

32

31

32

( )/ ( )

/ /Q p p1 2≡ − =

⋅

Uncorrelated= Correlated /

■ definition

25

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

・ Standard Gamow factor ; G

● Coulomb correction

G Qe

m Q

m Q

( )

( / )

exp( / )

inv

inv

inv

=−

=−

21

21

2

πη

π αα

πη

■ Correlation function in Qinv

with Coulomb w/o Coulomb

Fitting Function for 1D case

C Q R2 1= + −λ (exp )inv2

inv2

GdN

dQ− ×

FHG

IKJ

1

i real

Coulomb interaction between charged particles in the final state

26

2-2) Yano-Koonin Podgoretskii (YKP) Parameterization

C2 function for QT in YKP

■ Definition

Q E E

Q p p

Q p

0 1 2

2 2 1 2

= −

= +

=⊥ ( ) ( )

/

||

x y

z

; energy difference

; transverse p difference

; longitudinal p difference

◎ decomposition of 3 dimensional Q value

◎ Frame : Local Centre of Mass System of pair

C Q K R Q22 21( ; ) expT T T T= + −λ c h

[ref] U. Heinz et al., PLB 382 (1996) 181

with low Q||, Q0 cut

K p pT T1 T2= +12( ) : average pT of pair

■ Features of this parameterization

① perfect factorization of transverse, longitudinal spatial and temporal extension of the source.

② R parameter ⇔ expanding source model

◎ Fitting parameters ; λ, RT

27

KT dependence of RT in YKP param.

Gradual decrease of RGradual decrease of RTT as a function of K as a function of KTT

(R(RTT : 5.21 ±0.17 fm → 3.73 ±0.26 fm) : 5.21 ±0.17 fm → 3.73 ±0.26 fm)

■ KT dependence of RT

I II III

Class I : 0.1 < KT< 0.25 GeV/cClass II : 0.25 < KT< 0.35 GeV/cClass III :0.35 < KT< 0.45 GeV/c

I II

III

|Q|||, |Q0| < 50 MeV/c projection in QT

■ Correlation function in YKP as a function of QT

28

4. Discussion – finite expansion source model

■ In general ..., emission function : S ( S ( xx, , pp)) defines the particle distributions

Single particle spectrum

EdN

d pd x S x p P p

34

1= =z ( , ) ( )

Two particle correlation function for boson

C K Qx S x K e

x S x K

P p p

P p P p

iQ x

2

42

42

1 2

1 2

1( , )( , )

( , )

( , )

( ) ( )≅ + =

⋅zz

⋅d

d

※Single particle momentum dist. : P (p1) Two particle momentum dist. : P (p1, p2) d x d d rdr d4 =τ τ η φ

Finite Expansion ModelFinite Expansion Model

S x KK n x K u x

T

r

R( , )

( )

( )exp

( )exp=

⋅−

⋅LNM

OQP× −

LNM

OQP2 23

2

2π

u x rx

rr

y

rr rt t t t

η η ( ) cosh cosh ( ), sinh ( ), sinh ( ),sinh cosh ( )= ⋅ ⋅FHG

IKJ

t t( )rr

R= F

HGIKJ

1. Local thermal equilibration2. Transverse/ longitudinal motion decoupling3. Longitudinal boost invariant 4. Azimuthally symmetric source (Gaussian)5. Freeze-out (particle emission) at temperature “T” for all particle species6. No resonance contributions

Flow velocity u(x) : unit vector

where

■Assumptions

29

Expansion Model in mt Spectra

■ Function shape

t t( )rr

R= F

HGIKJ

● Single particle momentum distribution

Transverse flow velocity 　 :

Temperature at freeze-out : T

βt=0.6

βt=0

■ Fitting in 11 A GeV data

●different shape of spectrum for π, p and d, 　 if t is large enough (t ～ 0.5)

t ≡ v c/※

30

Fitting Results in mt Spectra: T vs. β ｔ

4 A GeV 11 A GeV

proton

deuteron

K+

πproton

deuteronK+

π

±2σband ±2σ band

Allowed regions of T, βAllowed regions of T, βt t from single particle spectrafrom single particle spectra

4 A GeVT = 80 ～ 90 MeVβt= 0.6 ～ 0.7

11 A GeVT = 90 ～ 100 MeVβt= 0.65 ～ 0.85<

without deuteron band

31

Combine Single Particle Results with HBT’s

[GeV-1]

proton

deuteronK+

π

±3σ band

Allowed regions of T, βAllowed regions of T, βtt from from

single particle spectra and HBTsingle particle spectra and HBT

E866 Au+Au 11 GeV

T = 95 ±5 MeVβt= 0.77±0.06

NA49 Pb+Pb 158 A GeV

T = 120 ±12 MeVβt= 0.55±0.12

<>

ββt t : AGS > SPS: AGS > SPS

ππ HBT

from RT in YKP ⇔ Expansion model in HBT

■ Single + HBT overlay

■ KT dependence of RT

RK m

T

T

Tt

∝

++F

HGIKJ

1

12 2

2

1 2

β

/

Determine t2/T from KT dep. of RT

CL 95%

32

Excitation Function of <t> and T

■ Excitation function of t ■ Excitation function of

SISSIS AGSAGS SPSSPS SISSIS AGSAGS SPSSPS

Single spectra + HBT saturation ～ <t> = 0.5

● mean of t

< >= =zzββ

βt

t

t

dr r r

dr r

R

R

( )0

0

2

3

・ <t> : 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

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

Lattice QCD cal. ⇒Tc = 140 ～ 200 MeV

If QGP formed ⇒ 　“ softening” of EoS 　⇒ pressure gradient ～ 0 ⇒ reduced βtreduced βt

ββt t : AGS > SPS: AGS > SPS

∴

T : AGS < SPST : AGS < SPS

∴

TSPS = 120 MeV at freeze-out

Not hard to assume QGP formation at SPS, cool down and freeze-out at TSPS

●

●

34

5. Summary (1)– Experimental results

1) Single particle spectra for π, K+, p, d at 4 and 11 A GeV and two particle 　 correlations for ππ 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 ・π → low mt enhancement

3) Mass dependence of <mt> -m0 is the most evident at central events. ・π , 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

Summary (2) –Physics interpretations

6) T and βt of the source are extracted from mt spectra for π, K, p, d (4, 11 A GeV) with ππ HBT constraint (11 A GeV) using the finite expansion model.

7) The expansion model reproduce the data by introducing (t, 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 GeV.

9) The reduction of β ｔ at SPS does not contradict the hypothesis of the softening of EoS by QGP formation at SPS .

E866 Au+Au 11 GeV

T = 95 ±5 MeVβt= 0.77±0.06

NA49 Pb+Pb 158 A GeV

T = 120 ±12 MeVβt= 0.55±0.12

<> CL 95%

indicated by J/ψ suppression (NA50) and enhancement of low-mass dilepton (CERES)

36

2-2) Standard side-out-long Parameterization

Beam direction

p2 p1

QQT

QL

Beam direction

QT

Qout

Qside KT

pT1

pT2

Q p p Q Q Q

Q Q

Q Q Q

= − =

==

1 2 ( , , )

( , )( , , )

x y z

T L

side out long

K p p

K K

= +

=

12 1 2e je jT L,

Standard Side-Out-Long Coordinate

Q Q Q Q Q

Q E E

K E E

inv x y z= + + −

= −

= +

2 2 202

0 1 2

0 1 212b g

Q

Q K

Q Q Q

long

out T

side out long

beam||

||

⊥ ⊥

37

KT dependence of R in side-out-long param.

■ KT distribution ■ C2 function in BP

Qside Qout QlongClass I : 0.1 < KT< 0.25 GeV/cClass II : 0.25 < KT< 0.35 GeV/cClass III :0.35 < KT< 0.45 GeV/c I

(low KT)

II (mid KT)

III (high KT)

■ KT dependence of R in BP

C Q R Q R Q R2 1= + − − −λ (exp )side2

side2

out2

out2

long2

long2

Fitting Function

38

1-3) Rapidity Density Distribution - dN/dy -

4 A GeV 11 A GeV d p

K+K+

pd

39

Proton’s dN/dy

ycm

y y y= −| |cm

L.Ahle et al. (E802), PRC 57 (1998) R466

Si+Al (central)

Au+Au (central)

0.00 0.25 0.50 0.75 1.00 1.25

Au+Au : Maximum plateau at mid-rapidity suggests strong baryon stopping

Si+Al : rapidity shift ～ 1 (partial transparent)

★ ★ Possibility to create hot and dense matter at yPossibility to create hot and dense matter at ycmcm

Before

After

ytarget ycm ybeam

ytarget ycm ybeam

complete baryon stopping

40

Systematic Error Estimation

41

Expanding Source Model in Single/Two Particle Dist.

★ ★ Successful description in Mt spectra for Successful description in Mt spectra for all particle species for individual shapes all particle species for individual shapes

Introducing βtIntroducing βt = finite expanding velocity field (common for all particle species)

T=Tthermal +m <βt>2

P.B.Munzinger et al., PL B344 (1995) 43

Y.-F Wu et al., Eur. Phys. J. C1 (1998) 599

■ Single particle dist. with βt ■Transverse momentum dependence of RT

　 in the expanding source model

η f = t

★ ★ If βt is incorporated in the model,If βt is incorporated in the model,

KKTT dependence of R dependence of RT T is visibleis visible

RK m

TTT

t∝ ++F

HGIKJ

−

12 2

2

1 2

β

/

Si+Au 14.6 A GeV/c

T= 120 MeV<βt> = 0.39

d

p

K+

π+

M K mT T= +2 02 (MeV/c2)

42

Single Particle Spectra in pA at AGS

● Single exponential shape as a function of mt (mt scaling) with same “ T ” 　～ 150MeV = in parallel for all particle species

m p mt t= +2 02

Ep m m y

m m

T

t t

t

d

d

d

d d d

3

3

0

σ σφ

=

∝ −−F

HGIKJexp

( )

T : inverse slope parameter yE p

E pz

z

=+−

12

ln

◆Invariant Cross section

● Consistent with the picture of the local thermal equilibrium in pp and pA at AGS

T : Independent on particle mass▲T.Abbott et al. (E802), PRL 66(1991)1567

p+Au 14.6 GeV/c

AGS-E802 data

= Transverse kinetic energy

■ Transverse mass spectra for π, K, p

Transverse mass

Rapidity

Inverse slope T 　⇔　“ Temperature”

43

Single Particle Spectra in AA

L.Ahle et al. (E802), PRC 57 (1998) R466

■Au+Au 11.6 A GeV/c (central)

E866 data

● 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

T T∝ thermal +mass ・ <βt>2

■ Mass dependence of TE802/866 data

Au+Au 11.6 A GeV/c

Si+Al 14.6 A GeV/c

p+Au 14.6 A GeV/c π K p d

π

p

　　 Mass dependence of T indicates the existence of Mass dependence of T indicates the existence of t t

・ Thermal motion ; <E> thermal ～ Tthermal

m02

2

< > t

・ Superposition ; <Ekine> = <E> thermal + <E>collective

・ Collective motion ; <E>collective =

44

Summary of Results - Single Particle Spectra

1) Shape of spectra in most central event ・ deviation from single exponential shape (d,p,π) ・ p : shoulder-arm shape at low mt ・ π ： enhancement at low mt

2) Mass dependence of <mt> -m0 ・ evident in most central ;π < K < p < d ・ mass splitting ; 4 GeV < 11 GeV

+ resonance decay contribution in low mt

for pion’s spectra

Consistent with the picture of collective flowConsistent with the picture of collective flow

45

KT dependence of RT

● Decrease of RT as a function of KT

■Transverse momentum dependence of RT in the expanding source model

RK m

TTT

t∝ ++F

HGIKJ

−

12 2

2

1 2

β

/

K p pT T1 T2= +12( ) : average pT of pair

Y.-F Wu et al., Eur. Phys. J. C1 (1998) 599

M K mT T= +2 02 (MeV/c2) ★ ★ If βt is incorporated in the model,If βt is incorporated in the model,

KKTT dependence of R dependence of RT T is visibleis visible

46

Attempt to Interpret Mt spectra by Simple Models

“Pion-Proton puzzle” in early ’90

M.Gyulassy, HIPAGS ’90, BNL-44911

① Fireball & Firestreak Model 　　 (= simple thermal models) Thermal Equilibrium T=228 MeV, ρ/ρ0= 4.8

Firestreak

Fireball

String

Proton

yield

π-

yield

Proton

Mt dist

π-

Mt dist

Thermal model × × ○ ×String model ○ × × ○

② String Model pp like string formation No equilibrium, No initial/final interaction

★ ★ Both simple thermal model and simpleBoth simple thermal model and simple string model do not reproduce the datastring model do not reproduce the data

Needed more realistic treatments (+ flow?)

47

Coulomb Correction

48

0 0.05 0.1 0.15 0.2

0.25

0.5

0.75

1

1.25

1.5

1.75

2

1/R

C Q R2 1= + ⋅(cos )C2

Q |p p |1 2

≡ − [ / ]GεV c

T.Abbott et al. (E802), PRL 66(1991)1567

p+Au 14.6 GeV/c

E802 data

Material (1)

Finite expanding source model are used in both single particle and HBT analysis in the same framework Consistent picture

of expansion

Determine (T,βt) uniquely

POINTPOINT

MERITMERIT

Different T-βt domain between single particle and HBT analysis

49

Material (2)

<mt> calculated from T or TB

● Fitting function of mt spectra

d

m dm dyN

m m

Tt t

t2

00

2

σπ

= −−F

HGIKJexp

N mm m

Ttt

B0

0exp −−F

HGIKJ

Single exponential func. (forπ, K)

Boltzmann func.(for proton, deuteron)

< >=

∞

∞

zzm

dm m f m

dm f mt

t t tm

t tm

( )

( )

0

0

J/ψJ/ψ L

L; mean nuclear path length

● Systematic study of μ+μ- pair in p+A, S+U and Pb+Pb by NA50

Normal nuclear absorption

A L L( ) exp( )= −ρ σ abs

( / ) / ( )/σ σψJ DY A L

50

Material (3)Momentum reconstruction

p B s

B

= ⋅ ×z03. [ ]

[ ] :

q d cGeV/

T magneticfield

s [m] :path of the particle in

the magnetic field

p q B dz cx y≅ ⋅ z03. [ ]GeV/

Momentum kick of track in B

pp

p

dx dz dx dz

x

x x

x

=−

=−

tan tan

( / ) ( / )

θ θ2 1

2 1

FTR2 track FTR1 track