Vitaly Okorokov

XXXII International Symposium on Multiparticle Dynamics

September 7-13, 2002, Alushta, Crimea, Ukraine

Two-particle correlation measurements with STAR detector

at RHIC

Vitaly A. Okorokov(for the STAR Collaboration)

Moscow Engineering Physics Institute (State University), Kashirskoe Ave.31, Moscow, 115409, Russian Federation

Vitaly Okorokov

Outline

Introduction– STAR detector– Physics motivation– HBT methods and techniques

STAR HBT experimental results– HBT correlations of identical particles

• Various dependences of HBT parameters• Status of the “RHIC HBT puzzle”

– Correlations of non-identical particles• K correlations• Kp and Kp HBT results and model predictions

Conclusions

Vitaly Okorokov

STAR experiment at RHIC

First Au-Au collision events at RHIC @ 100+100 GeV/c per beam recorded by STAR

Vitaly Okorokov

Physics motivation

Ultra-relativistic heavy ion physics is entering the new era of colliderexperiments with the start-up of RHIC at BNL. The basic questions and central in the goals of RHIC today are,

“What is the nature of nuclear matter at energy densities comparable to those of the early Universe?”

“What are the new phenomena and physics associated with the simultaneous collisions of hundreds of nucleons at relativistic energies?”

The study of small relative momentum correlations, a technique also known as HBT interferometry, is one of the most powerful tools at ourdisposal to study complicated space-time dynamics of heavy ion collisi-ons. It provides crucial information which helps to improve our under-standing of the reaction mechanisms and to constrain theoretical mo-dels of heavy ion collisions. It is also considered to be a promising signature of the Quark Gluon Plasma (QGP).

Vitaly Okorokov

Two-particle correlations

Single particle spectrum is sensitive to momentum distribution only

Relative momentum distribution of particle pairs is sensitive to space-time information

Intensity interferometry, HBT technique, etc….

),(4 pp

xSdxddNE

),(|),(|)/)(/(

/)( 2

2111

2122 qrqrr

pppp

q SdddNddN

dddNC

Source functionFSI

Vitaly Okorokov

Information:

•geometrical source size: Rside

•lifetime

(for simple sources!)

kRqkRqkRq

LongSideOut

LongLongSideSideOutOute

qqqkC222222

1

),,,(

Decomposition of the pair relative momentum

(measured in the longitudinal co-moving source –LCMS- frame; (p1+ p2)z=0)

Pratt-Bertsch parameterization

Rout2=Rside

2+(pair)2

beam direction

p2p1

QT

QS

QO

beam direction

p1 p2

QT

Q

QL

)T2PT1P(21

TK

Vitaly Okorokov

In search of the QGP. Naïve expectations

QGP has more degrees of freedom than pion gas

Entropy should be conservedduring fireball evolution

Hence: Look in hadronic phasefor signs of: Large size, Large lifetime, Expansion……

Vitaly Okorokov

In search of the QGP: Expectations

“Naïve” picture (no space-momentum correlations):

– Rout2=Rside

2+(pair)2

One step further:– Hydro calculation of Rischke

& Gyulassy expects Rout/Rside ~ 2->4 @ kt = 350 MeV.

– Looking for a “soft spot”

Rout

Rside

Vitaly Okorokov

Centrality and transverse mass dependences

Centrality dependence:

Larger initial size->Larger final size.

Significant expansion !

STAR Final

mT dependence:

Generally behavior isconsistent with flow andobservations at AGS, SPS

PRL 87 (8) 2001

s=130 GeV/A

Vitaly Okorokov

HBT Parameters: mT dependence

HBT radii increase with centrality (including RL).

HBT radii decrease with increasing <mT>

Experimental data at 130 GeV/A consistent with results at 200 GeV/A

According to Sinyukov fits, evolution duration:

t (central) = 10.08 fm

t (midcentral) = 9.30 fm

t (peripheral) = 7.59 fm

Au+Au (data @ S=200 GeV are preliminary) 200 GeV

Vitaly Okorokov

Excitation function of the HBT parameters

• ~10% Central AuAu(PbPb) events

• y ~ 0

• kT 0.17 GeV/c

no significant rise in spatio-temporal size of the emitting source at RHIC

RO/RS ~ 1

Note ~100 GeV gap betweenSPS and RHIC !

Vitaly Okorokov

Pion HBT: STAR, PHENIX Results @ 130 GeV

D.H.Rischke, Nucl.Phys. A610 (1996) 88c; D.H.Rischker, M.Gyulassy, Nucl.Phys. A608 (1996) 479.S.A. Bass, A. Dumitry, S. Soff PRL 86, nucl-th/0012085,December 2000 (Hydro+UrQMD).

STAR and PHENIX agree

All theoretical calculations show only Rout/Rside ratio to be greater than unity due to system lifetime effects which cause Rout to be larger than Rside. They also predict that the ratio

increases with kT. Such an increase seems to be a generic feature of the models based on the Bjorken-type, boost-invariant expansion

scenario.

Model does not reproduce the data

The top panel shows the measured Rside from identical pions for STAR and PHENIX. Lines arefits of analytical equations (1) and (2) for boost-invariant, hydrodynamically expanding source to the STAR and PHENIX data.The bottom panel shows the ratio Rout/Rside as a function of kT overlaid with theoretical predictions for a phase transition for two critical temperatures.

)1(1 2

22

Tm

RR

Tf

geomside

)2(

21

1 2

22

Tm

RR

Tf

geomside

f=0.69-the boost velocity, f=0.85-transverse rapidity boost, T=125 MeV is the temperature.

fmRPHENIXgeom 2.07.6

Fit (1) - dashed line

fmRPHENIXgeom 3.01.8

Fit (2) - solid line

fmRSTARgeom 1.04.9

Fit (2) - dot-dashed line

C. Adler et al. (STAR Col.), PRL 87 (2001) 082301.K. Adcox et al. (PHENIX Col.), nucl-ex/0201008, January 2002.S.C. Johnson, nucl-ex/0205001, May 2002.

Vitaly Okorokov

Possible solutions for RHIC HBT puzzle

One of the most dramatic results from RHIC are the STAR results for interferometry. There are at least two outstanding issues in two-particle HBT pion results that have avoided easy physical descriptions:

(i)   the absolute magnitude of the radii and their shape in kT at RHIC is strikingly similar

to lower energy measurements; (ii) the ratio of the transverse radii Rout/Rside is close to 1 over all kT.

It is not yet clear what physics leads to the kind of dependences reported by STAR Collaboration above.

Something exotic– Freeze out at critical point ?!– Sudden hadronization ?!– Non-Bjorken expansion scenario (Landau?)– ………– 3d hydro seems to be needed

In any case solution will require some sort of paradigm shift

Vitaly Okorokov

Correlations of non-identical particles

Correlations due to the final state interactions– Coulomb or strong

No symmetrization requirement ! => Pair wave function has odd terms => Sensitivity to source asymmetries Source asymmetries can be due to:

– different emmision times– Collective flow

Since particles, in general, have different mass => Correlations in small relative velocities not

momentum !

Vitaly Okorokov

Non-identical particle correlations How to reveal the asymmetries?

• Catching up: cos0• small mean separation• strong correlation

• Ratio of both scenarios allow quantitative study of the emission asymmetry

• Moving away: cos0• large mean separation• weak correlation

Crucial point:kaon begins farther in “out” direction(in this case due to time-ordering)

purple K emitted firstgreen is faster

purple K emitted firstgreen is slower

See talk by R. Lednicky

Vitaly Okorokov

1D relativistic view. What can be probed?

Source ofparticle 1 (pion)

Source ofparticle 2 (kaon)

Separation between particle 1 and particle 2 and boost to pair rest frame

2 parameters- Mean shift (<r*>)- Sigma (r*)

Separation between source 1 and 2 in pair rest frame

r

r (fm)

r* =pairr–pairtr* separation in pair rest frameFunction of pair(pair) which depend on the pair acceptance

We can assume that pions, kaons, and protons sources have different size and may be their are shifted in source frame

We measure only size and shift in pair rest frame

Vitaly Okorokov

Correlation functions and ratios K @ 130 GeV/A

Good agreement for like-sign and unlike-sign pairs points to similar emission process for K+ and K-

Clear sign of emission asymmetry

Two other ratios done as a double check – expected to be flat

CF

Out

Side

Long

a), b) pion kaon correlation functions

c), d) ratio of correlation function C-/C+

with respect to the sign of k*out

e), f) ratio of correlation function C-/C+

with respect to the sign of k*side

g), h) ratio of correlation function C-/C+

with respect to the sign of k*long

•Positive correlations forunlike sign pairs•Negative correlations for like sign pairs

Shape of correlation functionsdifferent for different cuts!

Vitaly Okorokov

K, p and Kp HBT results combined

Blast wave consistent with data

However, systematic errors need to be reduced to conclude

STAR Preliminary218.6 3

28.6 3

58.2

Parametersof source

Correlations

K @ 130 GeV/A

p @130 GeV/A

Kp @ 200 GeV/A

Fit in pair rest

frame

<r1* - r2

*>,

fm(t1 - t2),

fm/c6.4 - -

(r1 - r2), fm <4.6 - -

 

Table 1. Fit parameters for HBT correlations of non-identical particle pairs (Preliminary STAR data)

Vitaly Okorokov

Conclusions

The HBT interferometry measurements have been performed at RHIC energies and hereby extended the HBT excitation function into the new energy domain. A various dependences of the particle-emitting source parameters can be measured with high statistics in STAR.

Pion HBT results from Au-Au interactions at 130 GeV/A and 200 Gev/A are presented. The anomalously large source size or source lifetimes predicted for a long-lived mixed phase have not been observed in this study. The one of the most intriguing feature of the (preliminary) HBT results from RHIC is the KT dependence of the ROut/RSide ratio observed by the STAR Collaboration.

Evidence of space-time shift between , K, and p sources are obtained. Protons are ahead of kaons, kaons are ahead of pions (in the radial direction). Qualitative agreement is observed between experimental results and a Blast wave scenario which describes other STAR data.