HBT Study in PHOBOS

Willis T. LinDept. of Physics

National Central UniversityChung-Li, TAIWAN

Argonne National Laboratory, USA

Brookhaven National Laboratory, USA

Institute of Nuclear Physics, Krakow, Poland

Massachusetts Institute of Technology, USA

National Central University, Taiwan

University of Rochester, USA

University of Illinois at Chicago, USA

University of Maryland, USA

The PHOBOS Group

• Physics Results – Charged particle multiplicity near mid-rapidity in central Au+Au collisions at 56 and 130 GeV

Phys. Rev. Lett. 85, 3100 (2000)– Ratios of charged antiparticles-to-particles near mid-rapidity in Au+Au collisions at 130 GeV

Phys. Rev. Lett. 87, 102301 (2001)– Charged-particle pseudorapidity density distributions from Au+Au collisions at 130 GeV

Phys. Rev. Lett. 87, 102303 (2001)  – Energy dependence of particle multiplicities near mid-rapidity in central Au+Au collisions

Phys. Rev. Lett 88, 22302 (2002)– Centrality Dependence of Charged Particle Multiplicity at |η|<1 in Au+Au Collisions at 130 GeV

Phys. Rev. C 65, 031901R (2002)– Centrality Dependence of Charged Particle Multiplicity at |η|<1 in Au+Au Collisions at 130 and 200

GeV Phys. Rev. C 65, 061901R (2002)   

– Pseudorapidity and centrality dependence of the collective flow of charged particles in Au+Au collisions at 130 GeV Submitted to Phys. Rev. Lett. (2002) 

– Ratios of charged antiparticles to particles near mid-rapidity in Au+Au collisions at 200 GeVSubmitted to Phys. Rev. C (2002)

– The significance of the fragmentation region in ultrarelativistic heavy ion collisions  Submitted to Phys. Rev. Lett. (2002) 

• Technical– Silicon Pad Detectors for the PHOBOS Experiment at RHIC

Nucl. Instr. Meth. A461, 143-149 (2001)    – Array of Scintillator Counters for PHOBOS at RHIC

Nucl. Instr. Meth. A474, 38-45 (2001)

PHOBOS PUBLICATION

Relativistic Heavy Ion Collider

• RHIC – Highest energy density ever produced in laboratory– Species : pp, AuAu

• 12 June: 1st Collisions @ sNN = 56 GeV• 24 June: 1st Collisions @ sNN = 130 GeV• 5 Sep : end of first Au-Au Physics run• 13 Sep : 1st polarized protons in RHIC• 2001 : Looking for 1st Collisions @ sNN = 200 GeV

RHIC

To understand fundamental features of the strong interaction :

How does nuclear matter “melt” ? Where does the proton get its spin ?

3.83 km circumferenceTwo independent rings

Capable of colliding any nuclear species on any other species

Collision Energy :500 GeV for p-p200 GeV for Au-Au (per N-N collision)

Luminosity :Au-Au 2 x 1026 cm-2 s-1

p-p : 2 x 1032 cm-2 s-1 (polarized)

Ring Counters

Paddle Trigger Counter

Spectrometer

TOF

Octagon+Vertex

PHOBOS Detector

Cerenkov

• 4 Multiplicity Array

- Octagon, Vertex & Ring Counters• Mid-rapidity Spectrometer• TOF wall for high-momentum PID• Triggering

-Scintillator Paddles- Zero Degree Calorimeter

96000 Silicon Pad channels

Silicon Everywhere

Spectrometer Arm

Ring

Silicon Pad Sensors

Vertex Detector

Octagon Detector

no. of days

Silicon Sensors Performance

• S/N ratios better than 10:1 design specification• Larger pads & longer readouts lower S/N ratio • Ave. noise in entire detector setup stable over time

t (ns)

Even

ts

Negative

Paddles

Positive Paddles

ZDC N

ZDC PAu Au

x

z

PPPNPaddle Counters

Coincidence (38 ns) between paddle counters

Event Selection

PHOBOS Works

HBT Briefing – Two-Particle Correlation

Source

x

y

r1

r2

)()()()(12

22112211

2

1 xripyripyripxrip eeee

The probability to detect particles at r1 and r2

))(~1()()(2

21

2

1244

12 qPPyxyxddP eff

Probability amp. (plane wave)

More Briefing

.

.2

21

12212 )/(

)/(~1),(uncorr

correff dqdN

dqdN

PP

PkkC

Correlation function C2(k1,k2) can be defined:

What can be measured are

.

.

)/(

)/(

uncorr

corr

dqdN

dqdN

is the Fourier transformation particle density of source.eff~

1.

2.

),(),(/),(),( 221121 xkfdkxkfdkxkfxkfeff

: the distribution fn. of chaotic source),( 1 xkf

Extract HBT Correlation- Using Event Mixing Method

21

122 PP

PC

HBT, TPA, Coulomb, FSI

No Any Correlated Interactions

Pairs from same event

Pairs from “mixed” event

2

2

2

2

2

2

2

2

2222

24tzyx

t

R

z

R

y

R

x

tzyxeff e

RRR

N

Naively, assume density of the source is a Gaussian distribution

Z-Axis

Y-A

xis

X-AxisBeamAxis

KP 1

P2 q

Conventional Q Variables in LCMS

Qside

Qlong

Qout

zppQ

zKppQ

KppQ

long

side

out

ˆ)(

)ˆˆ()(

ˆ)(

21

21

21

2222222 22 1)( OLLOLLSSOO RQQRQRQRQeQC

221 TT

T

PPK

LCMS or Pratt coor.

Relationship btw Rout and Rside

txtxKR TTTout~~2~~ 2222

22 ~yKR Tside

22 ~~ tzKR LTlong

Only if x-t correlations are small and we get 22 ~~ yx

2222 ~tRR Tsideout

HBT Physics MotivationAu

Au

QGP PhaseMixed Phase

Source Size

Hadron Phase

By definition HBT sensitive to distribution at hadron’s last scattering pointa signature of QGP signal

A tool to understand the space-time evolution in heavy-ion collision

Theories predicted a large and long-livedsource if QGP is created

STARPHENIX

Two Particle Acceptance @ High mt

|Qlong| < 10 MeV , 0.8 <mt < 1 GeV

20 mr60 mr

PHOBOS TPA Cut ~ 25 mr

Two Particle Acceptance for “ideal case”

• TPAC is parameterized by (Δθ,ΔYA)

YA = 0 YA = 1

YA = 2 YA = 3

SpecP Only

Two Particle Acceptance for “ideal case”

SpecN Only

YA = 0 YA = 1

YA = 2 YA = 3

Official Cut

Used Two Particle Acceptance

If the pair’s relative quantities (YA,θ) are located in the shadowed area,it won’t be employed in our analysis.

Gamowλ = 1 Rinv = 5 fmλ = 1 Rinv = 10 fm

Gamowλ = 1 Rinv = 5 fmλ = 0.5 Rinv = 5 fmλ = 0.1 Rinv = 5 fmC

ou

lom

b C

orr

ecti

on

Co

ulo

mb

Co

rrec

tio

nQinv (GeV/c) Qinv (GeV/c)

Full-Wave Coulomb Correction “Partial” Coulomb Correction

“E866” Approximate Coulomb Correction

Coulomb Correction

We apply “partial” Coulomb correction officially

Coulomb correction is only applied to mixed pairs

vz

.025 cm

.05 cm

.025 cm

Event Mixing“Fixed classes “ : Chop up vertex space

#Real / #Mixed pairs must be larger than 3 !For each qualified domain, # of mixed pairs chosen randomlyis exact three times of real pairs

Introduce HBT into MC (Ⅰ)

NEWinv

OLDinv Q

invinvinv

Q

invinv dQQCQfdQQf00

)()()(

2222 /1)( cRQinv

invinveQC

Ideal comes from PYTHIA

We can calculate the corresponding momentum shift

NEWinv

OLDinvij QQP

i OLD

j OLD

i NEW j NEW

)....1( NiPPPN

jiij

OLDi

NEWi

Final momentum of particle i

Introduce HBT into MC (Ⅱ)

MCRecon

Introduce HBT into MC (Ⅲ)

PHOBOS HBT Results @ 200 GeV

- - 0.540.02 5.80.2

5.10.4 6.80.3

Rout Rside Rlong

++ 0.570.03 4.90.4 7.30.3

5.80.2

R2out-long

4.91.74.51.9Systematic error on radii of 1 fm, on of 0.06

-- dataHBT Excitation Function

Summary of HBT from RHIC

KT (GeV/c)

Ro

ut /

Rs

ide STAR error bars are not shown

PRELIMINARY

3 Kt bins analysis (Rout)

(Without error bar)

π-π-

PRELIMINARY

3 Kt bins analysis (Rside)

(Without error bar)

π-π-

PRELIMINARY

3 Kt bins analysis (Rlong)

(Without error bar)

π-π-

PRELIMINARY

3 Kt bins analysis (Rout/Rside)

(Without error bar)

π-π-

PRELIMINARY

Conclusion

HBT results are consistent between 130 and 200 GeV

RHIC Puzzle ! Most reasonable models still don’t agree well with RHIC HBT data

Don’t forget the x-t correlation term !

It’s possible a super-cooling source !

Predicted Rout/Rside

S. Soff et al. nucl-th/0012085 v2 (2001)

Assume a first order phase transition from a thermalized QGP to a gas of hadrons