Lanny RayOhio State Seminar - July 29, 20031 Large Scale Correlations and the Dissipative Medium...

Lanny Ray Ohio State Seminar - July 29, 2003 1

Large Scale Correlations and the DissipativeMedium Produced in Au+Au

Collisions at RHIC

Lanny RayUniversity of Texas at Austin

Ohio State University, July 29, 2003


Acknowledgements:STAR Collaboration

Event Structure Working Group

With special thanks to my collaboratorswhose work will be shown:

Aya Ishihara - thesis work included (U. Texas Ph.D. student)Jeff Reid - thesis work included (U. Washington, Post Doc)

Qingjun Liu - (U. Washington, Post Doc)Zubayer Ahammed - (Purdue U. Post Doc)

Tom Trainor - (U. Washington)


RHIC at BNLSTAR


E-M Calorimeter

Time of Flight

Projection Chamber

The STAR detector


PCM & clust. hadronization

NFD

NFD & hadronic TM

PCM & hadronic TM

CYM & LGT

string & hadronic TM

hadronizationinitial state pre-equilibrium

STAR Event viewedalong beam axis

decoupling

?

Graphics from Steffen Bass and John Harris

x

z

y

I. The general view of RHIC collisions

typicalminimumbias event


+-

Color string fragmentation,charge ordering,

local momentum conservation,bulk production at midrapidity

from hot, dense medium

Also hard and semi-hardpQCD processes

which punch into medium

How does the hot, dense medium respond?

What’s happening just after the nuclei collide?


STAR’s large acceptance

Short-range dynamics;non-statistical fluctuations

Large momentum scale correlations

Initial state scattering (soft & pQCD),color string fragmentation along beam

axis and transverse toward detector

Processes modified bydeveloping, dissipative

medium

Medium fluctuates as a result of semi-hard punches

We’ll measure the response of medium to learn about its properties

What’s our game plan?


II. Mean Transverse Momentum Fluctuation Analysis - Au+Au @ 130 GeV

Event cuts: event vertex |z| < 75cm,

|x|,|y| < 1cm

Track cuts: 0.1 < pt < 2 GeV

|<1.0, full 2

Principal Authors: Ahammed, LR, Reid (thesis), Trainor

183k central trigger events (15%)205k minimum bias events

x

z

y

magnitude is where,1

1ti

N

itit pp

Np

tp


tdp

dN

tptp̂

tp̂

Inclusive pt distribution,(all particles in all events) Randomly sample this

distribution n times to make “events” with multiplicity n. Compute the event-wise <pt> for these “events.”

tptp̂

ntt pp /ˆ

Reduced width given by:

Central Limit Theorem results

Statistical reference with which to compare real events


183K top 15% central eventsusing 70% of all primary particles

Both (+) and (-) charges|| < 1, full

0.1 < pt < 2.0 GeV/c

Nonstatistical fluctuationsincrease the rms width

by 13.7+1.3(syst)%

n/

p̂ p

Tp̂

tt

Centered at 0In units of

expected rmsfrom CLT

Gamma dist. with increased rms

Statistical ref. from inclusivepT spectrum*

STAR Preliminary(*) N sampled inclusive spectrum approx. equals Gamma dist.

Event-wise <pt> distribution:


(See: www.rhip.utexas.edu/projects/Star/ebye/meanpt)

Quantitative Mean pt Fluctuation Analysis

tt

tt

tt

pp

prealp

ptjtj

jp

N

ppN

nN

ˆ

2ˆ

2,

2ˆ

2

1

2

2

ˆ1

t

t

t

t pp

pp

ˆ

2

2

(removes multiplicity fluctuation bias)

(Direct application of CLT)

(Analogous to dx2 =2xdx)

This last step defines a fluctuation measure

linear in the mean pt distribution width

Relation to pt of Gazdzicki and Mrowczynski,Z. Phys. C 54, 127 (1992).

(varianceincrease)


Numerical measures of mean-pt fluctuations

CI

CD x 3

205K minbias events70% of primaries

Extrapolated to 100%+0.5 MeV/c stat. errors

+20% syst. ErrorsDCA cut < 3 cm

Strong nonstatistical fluctuationsCentrality dependenceCI larger than at SPS (more later)CD smaller at RHICPHENIX null result is not inconsistent with STAR’s measurement (more later)

STAR Preliminary

Charge-independent:CI = [(++)+(--)]+[(+-)+(-+)]

Charge-dependent:CD = [(++)+(--)]-[(+-)+(-+)]

centrality

Extrapolation to 100%

70% ofprimaries


3/1)2/(/2 partpartBC NNN

estimates averagepath length <l>

• Glauber-model : mean path length < l >

• Stochastic multiple scattering scales as (path length)

Saturation -dissipation

for most centralevents?

STAR Preliminary

Binary collisions, Path length and


Status of <pt> comparisons with SPS, PHENIX and Hijing

CERES experiment at CERN-SPS (Adamova et al., nucl-ex/0305002)measured pt = 3.3 +/- 2 MeV/c for Pb+Au at lab energy of 158 AGeV (fixed target), [17 GeV/NN (cm)] for N = 162 and 0.25.

PHENIX at RHIC [Adcox et al., PR C66, 024901 (2002)] measuredpt = 6+/-6 MeV/c for Au+Auat 130 GeV/c for 0.35 and|| = 58.5 deg. for top 5% central events.

STAR (almost submitted to PRL) measured pt=14+/-2 MeV/cfor N = 180 and ||<0.25

which is 4-5 times larger.

STAR also measured pt=9+/-1 MeV/c

at the PHENIX acceptance.

NA49 [Appelshausser et al., Phys. Lett. B459, 679 (1999)] measured pt=0.6+/-1 MeV/c for Pb+Pb at 158 AGeV for N = 270 and ycm=[1.1,2.6].

II. ptpt Charge Average (CI) Correlations

Au+Au @ 130 GeV

PAs: Ishihara (thesis), Trainor, LR


Two-Particle Correlations and Kinematics

]1),()[()(

)()(),(),(

21)2(2)1(1)1(

2)1(1)1(21)2(212

pprpp

ppppppC

Useful kinematics:

mfor E

ditypseudorapi is , ]/2)-log[tan(

rapidity is , log2

1

),,(

y

pE

pEy

ypp

z

z

t

)()( , , 2121

2211

dyddydpp ttProjection onto

2D subspaces:

z, beam

x

y tp

p

]1),()[,(1

212122112

ttttmixttttp pprppdppdppNt

Relation ofvariance tocorrelations Differential study of nonstatistical fluctuations


Projected, Two-Point Correlations

Count # pairs in () 2D binfrom same events (“siblings”)

Count # pairs in () 2D binfrom different events (“mixed”)

The 2D bin counts are easily obtained as the

product of(# in bin- x (# in bin-

Number Density

pt pt

Event 1 2 3 4 5

ttdpp

dN

pt1 pt1

pt2 pt2

Numerator Denominator

We can do this for any measure, e.g. pt, <pt>, E, net Q, ...

bins


Construct the Correlation

2,1

2,12,1 pp

ppppr

mixed

sibling

Sum numerator anddenominator over allevents in ensemble,

divide, and normalizeusing total number of sibling and mixed eventpairs.

Differences from 1.0indicate correlations.

(Ratios formed usingsimilar events, then r’ssummed over all events.)

Correlations

exampleonly, not

actual data

1.01

1.00

0.99


pt x pt two-point number density ratiosfor Au+Au at 130 GeV

Central 21% by multiplicity~100k events

0.15 < pt<2 GeV/c||<1.3, full

mass se transver,

]1,0[ ]GeV 4.0/)(exp[1)(

22

mpm

mmpX

tt

tt

(produces flat dist. on X)(1) HBT+Coul. at low pt.

(2) Stochastic semi-hard scattering and fragmentation at larger pt

(3) Overall “saddle” shape due to fluctuations in bulk medium; measured by curvature [Sum-diag (main) up - Diff-diag (off) down].

STAR Preliminary

Like sign Unlike sign


pt x pt two-point number density ratiosfor Au+Au at 130 GeV

most-central

peripheral

r[X(pt1),X(pt2)]-1 for all charges

STAR Preliminary

HBT,Coul.removed

using trackpair cuts


Fitting the pt x pt two-point number density ratiosfor Au+Au at 130 GeV

- remove HBT, Coul.- exclude higher pt peak from fit- use analytical 2D “saddle” shape derived from fluctuating

two-point temperature model

model residualProject residuals onto sum direction,

X=X(pt1)+X(pt2),and integrate peak

STAR Preliminary


pt x pt two-point number density ratiosfor Au+Au at 130 GeV - Summary

Plot curvature vs path length (concave up along X - concave down along X)x(N)Plot integral (xN) of high pt residual vs

We observe semi-hard scattering production which increases with initial state path length.We also observe increasing fluctuations in the bulk medium.A possible interpretation is that with increasing centrality dissipation of pt from initial state semi-hard scattering processes into the soft pt bulk medium is increased.

STAR Preliminary

III. CD Correlations Au+Au @130 GeV

PAs: Ishihara (thesis), Trainor, LR


Forming the CD Joint Autocorrelation

• CD = LS US• CI = LS + US

• CI - initial-state scattering• CD - final-state hadronization

LS US

individual two-point spaces joint autocorrelations

STAR PreliminarySTA

R P

relim

inary

charge ordering

elliptic flow, plus...


x CD Data

1D autocorrelation projections with fits

2D joint autocorrelations

these are two-pointnumber densities

STAR Preliminary

STAR Preliminary


x CD Summary• Short-range correlations

(SRC) well-studied in elementary collisions, this work extends such studies to A-A collisions

• Possible interpretation is that these data are consistent with correlated pairs escaping from an opaque medium - reduced mean free path - escape probability falls exponentially with opening angle

• Alternative hypothesis: e.g. distortion of opening-angle distribution by large radial flow

• Study changing geometry of hadronization - from 1D string fragmentation 2+D surface emission in A-A, which is an open issue in QCD phenomenology

IV. - Scaling of Fluctuations

PAs: Liu, Trainor

tp


1

)(

1

2ˆ

2 2 ˆ1

),;,(j

xM

kptjktjkp tt

ppn

0 0 Ref

222 ,ˆ)1(),( ddA

ApN tpt

2121 ,

What is a scaled correlation analysis?

The idea is to measure fluctuations on one kinematic variable

(e.g. pt) while binning on orthogonal directions (e.g. ):

acceptance bin sizeor scale

avg.over

events

sumoccupied.

bins

functionof scale

compute variance among pairs in all ( bins

in the acceptance

The scale dependence reveals correlations:

Invert Volterra eq. in its discrete form, obtain autocorrelation


Transverse momentum scaling analysis for Au+Au at 200 GeV

pt(CI)as function

of scale

pt auto-correlation

on axial space

peri

pher

alm

idce

ntra

lm

ost-

cent

ral

-Same side correlation-Away side p conserv.-Elliptical flow, plus ?-Away side suppression with centrality-Dissipation of away side pt into bulk

STA

R

Pre

lim

inary


Conclusions• Large, non-statistical <pt>

CI fluctuations; centrality

dependence at RHIC.

• Structure in ptpt CI and CD distributions seen; data fit with simple, analytic functions.

• CD correlations possibly suggest growth of an opaque medium

• ptpt CI correlations possibly suggest a dissipative system, with space-correlated temperature fluctuations, and a non-dissipated hard component increasing with centrality.

• Close connection between correlations and variance scale differences.

This evidence suggests that semi-hard ISS processes excite a dissipative and opaque medium, generating the observed CI, CD correlation structure.

tp


Russia:MEPHI - MoscowLPP/LHE JINR - DubnaIHEP - Protvino

U.S. Laboratories:ArgonneBerkeleyBrookhaven

U.S. Universities: UC BerkeleyUC DavisUC Los AngelesCarnegie Mellon Creighton UniversityIndiana UniversityKent State UniversityMichigan State UniversityCity College of New YorkOhio State UniversityPenn. State UniversityPurdue UniversityRice UniversityTexas A&MUT AustinU. of Washington Wayne State UniversityYale University

Brazil: Universidade de Sao Paulo

China: IHEP – BeijingIMP - LanzouIPP – WuhanUSTCSINR – ShanghaiTsinghua University

Great Britain: University of Birmingham

France:IReS StrasbourgSUBATECH - Nantes

Germany: MPI – MunichUniversity of Frankfurt

India:IOP - BhubaneswarVECC - CalcuttaPanjab UniversityUniversity of RajasthanJammu UniversityIIT - BombayVECC – Kolcata

Poland:Warsaw University of Tech.

The STAR Collaboration


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Lanny RayOhio State Seminar - July 29, 20031 Large Scale Correlations and the Dissipative Medium...

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