the geometry of hadronization in au-au collisions at s nn 1/2 = 130 and 200 gev

Jan. 13, 2004 QM 2004 Poster Session 1

The Geometry of Hadronizationin Au-Au Collisions at sNN

1/2 = 130 and 200 GeVStudied with Two-Particle, Charge-Dependent

Number Fluctuations and Correlations

R. L. Ray

For the STAR Collaboration

The University of Texas at Austin

QM 2004 Poster Session 2

Abstract:


+-

In high energy proton-proton collisions color string fragmentation is subject to local charge and momentum conservation.These symmetries lead to charge ordering seen in jet fragmentation, and local transverse momentum conservation seen in high energy elementary collisions.

In relativistic heavy ion collisions we measure the effects of the hot, dense medium on known processes such as this. We also study how these known processes affect, or probe the medium in order to measure its properties.

To do so we measure non-statistical fluctuations and large momentum scale correlations taking advantage of STAR’s large acceptance; interpretation

is in terms of short-range dynamical responses.

Introduction:

Semi-hardscattering“minijet”


Measuring Correlations & Particle Pair Density Ratio:

]1),()[,(

)()(),(),(

2121

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

pprpp

ppppppC

mix

A

zim

utha

l ang

le

Pseudorapidity

Event 1

Event 2

Count number of sibling pairs in all events in each bin in (vs

Similarly, count number of mixed pairs from different events in each bin in (vs

Normalize using total number of sibling and mixed event pairs.*(Ratios formed using similar events, then r’ssummed over all events.)

2,1

2,12,1 pp

ppppr

mixed

sibling

)(

)(

,ˆ

21

21

r


GeVsAuAu NN 130

Event ordering on vertex position and multiplicity

Centrality bins 0.15 < pt < 2 GeV

|<1.3 full 2 azimuth

•Central (15%) trigger (210k events after event cut)

•Minimum-bias trigger (124k events after event cut)

Data Selection and Cuts:

Collision system:

Pair cuts correct for track splitting and merging, and remove most of HBT/Coulomb correlations


Constructing Charge Dependent Correlations- Like- and Unlike-sign Combinations:

STAR Preliminary

LS US =

CICD

LS US Project to form “joint autocorrelations”

No correlation structure alongsum direction; projections ontodifference variables and preserve information; provides compact representation.

Charge-IndependentCharge-Dependent


Correlations for p+p at 200 GeV on ,

dE/dx electron cut

Effects of charge conservation stronger for unlike-sign than like-sign

Autocorrelations revealpeak structures near

superimposed on signals due to charge & p conservation.

conservationp

A

AN

A

AN

A

AN

A

AN

A

AN

STAR Preliminary

chargeconservation


Correlation Structures in pp CD – the reference:

Local charge conservation;

charge orderingLocal momentum

conservation

Quantuminterference(gamma conversion

electron contamination)STAR Preliminary

azimuthalsymmetry


Charge-Dependent (LS-US) Correlations for Au-Au at 130 GeV:

Development of 2D symmetric correlation shape and increased amplitude.

centralperipheral

STAR Preliminary

(Another view of same data.)


Fit CD correlations with a model:

STAR Preliminary

Deduced rms widthsversus multiplicity andpath length , where:

3/1)2/(/2 partpartBC NNN

(extrapolation range assumed)


Summary of 130 GeV Au-Au CD Correlations:

• Large-amplitude CD two-particle number correlations are observed on momentum space.

• CD joint autocorrelations show strong centrality dependencies of correlation structure: amplitude increases and saturates, widths decrease along both and .

• Results suggest a trend from 1D string fragmentation to 2D surface emission: a drastic change in the Hadronization Geometry in central Au-Au collisions.

• This points to the growth of an Opaque Medium in central collisions.

These correlations were measured by thedirect, pair-ratio method. But correlationscan be obtained another way…


Obtaining the CD auto-correlations fromnon-statistical fluctuations, or variance excess –

A Complementary Method:

• Based on the integral relationship between autocorrelations and variance excess in the measure quantity, i.e. net charge in the present application.

• Avoids the normalization ambiguities inherent in density ratio analyses within finite acceptance and allows measurement of very large scale correlations which exceed the acceptance scale.

• Numerically much faster than summing over pairs.

• Facilitates study of canonical suppression, or charge conservation effects, in finite acceptance < 4 and participant nucleon number fluctuation effects.

• This method is applied to Au-Au collisions at sNN1/2 = 200 GeV.


Event-wise net charge fluctuations:

We measure variances:

where for purely statistical fluctuations

In general N can be a conserved quantity such as charge, baryon number, etc. but, due to finite acceptance for the measurement, fluctuates from event-to-event.

Here we measure net charge: NQ = N+ N

where N+ and Nare the number of positive and negativeparticles in the acceptance for each event.

1)( 2

2

N

NNN

02 N


Relation to autocorrelation:Variance excess at some scale integrates over auto-correlation:

2

k

l

scale integral

),(),(),(00

2

A

ANKdd

),(2/1

12/1

122

),(11

2

ldkdA

AN

n

l

m

k

MMndmd

n

l

m

k

The autocorrelations are obtained from the measured variance excess via inversion of this integral equation.

Straightforward inversion results in a noise dominated autocorrelation.

The standard way to get useful solutions is to impose a smoothing constraint on the autocorrelation using Tikhonov regularization.

which is approximated with discrete sums for data,

References:http://www.phy.aukland.ac.nc/Staff/smt/453707SC.htmlhttp://www.samsi.info/inverse.htmlhttp://www.iop.org/EJ/journal/0266-5611 http://venda.uku.fi/research/FIPS

http://www.phy.aukland.ac.nc/Staff/smt/453707SC.html


200 GeV AuAu

Canonical suppression causes linear decrease in 2 with scale. Trend from central to peripheral Au-Au continues in pp with decreasing multiplicity.

Data (CD):

200 GeV pp

2

QN

STAR Preliminary


200 GeV Au-Au

Strong small scale correlations for central Au-Au, decreasing strength for more peripheral data. Local charge conservation evident. Peripheral Au-Au and high multiplicity pp have similar shapes.

Invert -- autocorrelations (CD):

200 GeV pp

2

QN

STA

R P

relim

inary


200 GeV AuAu

STA

R P

relim

inary

2

NN2

QNCompare CD and CI autocorrelations from inversion method:

Momentum conservation in both at with additional v2 (flow) in CI.Elongation in same-side CI peak, but narrowing in CD.Narrowing in both CI and CD same-side peaks for

Using Using

CD CI


Relation of CD autocorrelation to Balance function:

)(

)(

)(1),(),(

2

2121

A

AN

NAB CDNQ

BF depends onacceptance ()

and pseudorapiditydifference variables

Acceptancefunction:

Canonicalsuppressiondue to total

charge conservation

for finite, <4 acceptance

Two-particle,charge-dependent

autocorrelation

Balance function width depends on acceptance range and both the width and amplitude of the CD autocorrelation; interpretation in terms of correlation width is ambiguous.Observed reduction in BF width (Phys. Rev. Lett. 90, 172301 (2003) ) with increased centrality is consistent with the observed increase in correlation amplitude.

0


Summary of CD Correlations on () vs ():

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

• Comparisons with Hijing and RQMD in progress

the geometry of hadronization in au-au collisions at s nn 1/2 = 130 and 200 gev

Documents

poster session correlations

gev auau cd correlations

poster sessionabstract

poster sessionsummary

particle number correlations

charge p conservation

hd momentum

poster sessiondata selection