1 Observation of dramatic transition in 2D correlation data Lanny Ray For the STAR Collaboration University of Texas at Austin April 7, 2008 24 th Winter.

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Observation of dramatic transition in 2D correlation data

Lanny RayFor the STAR CollaborationUniversity of Texas at Austin

April 7, 2008

24th Winter Workshop on Nuclear Dynamics

Outline:Definitions and p-p referenceAu-Au data – surprising results Implications & Speculations

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Introduction and Overview

• Our philosophy: determine a “complete” map of the 2-particle correlations in p-p and A+A collisions, then interpret.

• Correlations are sensitive to physical processes: e.g. parton scattering and fragmentation (jets & minijets), elliptic flow, resonances, HBT, etc.

• Each source generally makes a unique contribution, facilitating decomposition and interpretation.

• A surprising trend in same-side correlations was found and first reported at QM 2008 (M. Daugherity, University of Texas, for STAR).

• The implications of these new results suggest a different scenario from the ubiquitous, rapid thermalization hydrodynamic models for the bulk collision environment at RHIC.

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Begin with Proton-Proton SpectraTwo-component soft + (semi)hard model:

PRD 74, 032006 (nucl-ex/0606028)

200 GeV

0

lnm

pmy tt

t

pt spectra for

increasing Nch

“soft” “semi-hard” + pQCD hard…

Spp

Data – Spp

semi-hard component:gaussian on yt

replot on“transverse rapidity”

4

SOFT component – Levy Distribution

HARD component – Gaussian on yt(!)

Peak yt=2.66 yt=2.66

pt ~ 0.5

pt ~ 1.0

pt ~ 2.0

refρ

Δρ

yt1

yt2

PRD 74, 032006

Proton-Proton: spectra to correlations

STAR Preliminary

0

lnm

pmy tt

t

5

)()(),(

),(),(),(

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

212121

pppp

pppppp refsib

Δρ as a histogram on bin (a,b):

),()( , baCov)n(n)n(nnnnn babababa

Normalize refbaba

ba nn

1

refρ

Δρ(n) measures number of correlated pairs per final state particle

ρ(p1,p2) = 2 particle density in momentum space

Event 1

Event 2

ρsibling(p1,p2)

ρreference(p1,p2)

yx

yxCovyxCorr

),(

),(

ε = bin width, converts density to bin counts

Start with a standard definition in statistics:

Correlation Measure

6

yt1

yt2

refρ

Δρ

p-p transverse correlations

ηΔ

φΔ

p-p axial correlations

refρ

Δρ

semi-hard component

ηΔ

φΔ

refρ

Δρ

soft component

ηΔ

φΔ

refρ

Δρ

Longitudinal Fragmentation: 1D Gaussian on ηΔ

HBT peak at origin, LS pairs only Minijets: 2D Gaussian at origin plus broad away-side peak: -cos(φΔ)

We hypothesize that this structureis caused by semi-hard partonic

scattering & fragmentation - minijets

Proton-Proton Components

STAR Preliminary21

21

7

84-93%

28-38%

74-84%

18-28%

64-74% 55-64% 46-55%

9-18% 5-9% 0-5%

proton-proton

note: 38-46% not shown

We observe the evolution of several correlation structures from peripheral to central Au+Au

refρ

Δρ

ηΔ

φΔ

ηΔ

φΔ

refρ

Δρ

Analyzed 1.2M minbias 200 GeV Au+Au events; included all tracks with pt > 0.15 GeV/c, |η| < 1, full φ

STAR Preliminary

200 GeV Au-Au Data

8

84-95%

28-37%

75-84%

18-28%

65-75% 56-65% 46-56%

9-18% 5-9% 0-5%

note: 37-46% not shown

Analyzed 13M 62 GeV Au+Au minbias events; included all tracks with pT > 0.15 GeV/c, |η| < 1, full φ

62 GeV Au-Au Data

A similar evolution appears but is delayed on centrality relative to the 200 GeV data.

STAR Preliminary

9

Proton-Proton fit function

= +

STAR Preliminary

longitudinal fragmentation1D gaussian

HBT, e+e-2D exponential

refρ

Δρ

refρ

Δρ

refρ

Δρ

ηΔφΔ ηΔ

φΔ ηΔφΔ

Au-Au fit functionUse proton-proton fit function + cos(2φΔ) quadrupole term (“flow”). This gives the simplest possible way to describe Au+Au data.

Note: from this point on we’ll include entire momentum range instead of using soft/hard cuts ηΔ

φΔ

dipole

quadrupolecos(2φΔ)

Fit Function (5 easy pieces)

Same-side “Minijet” Peak, 2D gaussian

Away-side -cos(φ)

“soft” “hard”

10

)1(1

)(

xAA ppAA

Deviations from binary scaling represent new physics unique to heavy ion

collisions

Binary scaling: Kharzeev and Nardi model

200 GeV62 GeVrefρ

Δρ

small increase before transition

constant widths

STAR Preliminary STAR Preliminary STAR PreliminaryPeak Amplitude Peak η Width Peak φ Width

binpppartpp

bin

chrg

binAA xNnNxn

N

N

NA

2/)1( Amplitude

Same-side 2D gaussian & binary scaling

Note the absenceof a transition pointin the quadrupole: v2 & elliptic flow

STAR Preliminary

Statistical and fitting errors as shown

Systematic error is 9% of correlation amplitude

2/part

bin

N

N

peripheral central

11

The observed minijet correlation is much larger than HIJING (factor of 4)

HIJING 1.382 default parameters, 200 GeV, quench offQuench on causes slight amplitude decrease

refρ

Δρ200 GeV62 GeV

STAR Preliminary STAR Preliminary STAR PreliminaryPeak Amplitude Peak η Width Peak φ Width

mid (40-50%)

very little centrality dependence

HIJING minijet predictions

HIJING 1.382

φΔ ηΔ

12

The dipole matches the centrality dependence of the same-side gaussian and shows the same transition point.

It’s origin is pt conservation: global + jets

Dipole – transverse momentum conservation

Global pt

conservation

Low

-x p

arto

n

KT ~ 1 GeV/c

p z

Q ~ 2 GeV/c minijets, nucleon KT , acoplanarity

Low-x parton

200 GeV62 GeV

φΔ

0

0

φΔ-3 - 3

KT broadening

)cos( 0

events1,2,3…

sumevents

away-side

STAR Preliminary

13Same-side gaussian amplitude and -width scale with particle density

Peripheral bins are compressed.

Peak Amplitude

Npart Npart

Npart

Peak η WidthSTAR PreliminarySTAR Preliminary

200 GeV62 GeV

Depends on formation time (assumed 1 fm/c), difficult to compare energies.

εBJ εBJ

Peak Amplitude Peak η WidthBjorken Energy Density

STAR PreliminarySTAR Preliminary200 GeV62 GeV

Transverse Particle Density

Peak Amplitude Peak η Width

Sd

dNch /2

3~

~ ~S = overlap area

(Monte Carlo Glauber)

STAR PreliminarySTAR Preliminary

200 GeV62 GeV

Does the transition point scale?

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pt correlationsfollow binary scaling

well past the transition

ba nnnnρ(n) )()( Δ bttattt pnppnpn)ρ(p )ˆ()ˆ(: Δ

Number pt

J Phys G 32 L37

= inclusive mean pttp̂

2D angular correlations for pt

This leads to the hypothesis that semi-hard partons continue to underlie thesame-side gaussian number correlations above the transition.

200 GeV Au+Au

pT minijet peak

0-30% centrality

Same-side amplitude and widths

21

21

15

Peak Volume

~

8x increase

STAR Preliminary200 GeV62 GeV

See also T. Trainor, arXiv:0710.4504, accepted to J Mod Phys E

Multiplicity fractions – same-side gaussian1) Probability that minbias p-p collision produces semi-hard parton:

2) Number of semi-hard partons in Au-Au

assuming binary scaling (pt correlations)

3) Total number of same-side 2D gaussian correlated pairs per event:

4) Number of final state particles associated with each semi-hard parton:

unit /0125.0

binpartons NN )unit /0125.0(

ddNVol ch)(

d

dN

N

Vol ch

partons

ddN

N

d

dN

N

Vol

ch

partonsch

partons /

5) Fraction of total multiplicity associated with same-side gaussian correlation:

For central Au+Au we estimate about 30%;a significant fraction of the bulk particles.

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2A

NVol

16

Sudden onset at lower yt corresponding to transition point for same-side gaussian.

proton-proton

How the correlations evolve in transverse momentum

Correlations remain at original yt – surface jets?increase at higher yt.

(yt,yt) correlations, 200 GeV Au+Au

(peripheral)

(central)

STAR Preliminary

(protons: see arXiv:0710.4504)

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Expected behavior:

Comparison with data:

Implications: Superposition model

Minijets unchanged, except amplitude increases with binary scaling; widths remain constant.

Minijet peak on (yt,yt) unchanged except for amplitude.

Superposition model approximates data to the transition pointbut radically fails at higher density, more central collisions.

STAR Preliminary

18

Expected behavior:

Comparison with data:

Implications: parton/hadron scattering model

Widths of both number and pt angular correlations increase

Amplitude of pt correlation falls below binary scaling

Minijet peak on (yt,yt) dissipates to lower momentum

widths increasebut widths decrease

pt correlation amplitude follows binary

scaling beyond transition; doesn’t decrease until here

Minijet peak dissipates, strength

remains at original yt,

increases at higher yt

1

3

2pT minijet peak

0-30% central

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Expected behavior:

Comparison with data:

Implications: opaque, thermalized medium

Semi-hard partons stopped; produce local hot spots; isotropic thermal motion - number angular correlations vanish, radially flowing hot spots

could produce correlations [e.g. +cos()].

momentum conserved - pt correlations on may persist

Minijet peak on (yt,yt) completely dissipated; saddle shape appears

at lower pt (J.Phys.G 34, 799)

Semi-hard partons persist;number correlationsdo not vanish, but

increase dramatically.

Peak Volume

~

8x increase

STAR Preliminary200 GeV62 GeV

Narrow azimuth width from p-p to central Au-Au,

no transition point.

1

2 width initially due to minijets. If more central dominated by other mechanisms, the latter

must seamlessly match minijets.

STAR Preliminary

pT minijet peak

0-30% central

20

Implications: opaque, thermalized medium

The minijet correlation

region in (yt,yt) does not

vanish, but increases

and extends to higher yt;

a saddle shape develops(see J.Phys.G 34, 799)

Comparison with data (cont.):

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The observed correlations contradict expectationsfor a rapidly thermalized system.

peripheral

central

200 GeV Au+Au

4

Boosted hot spots

produce +cos()

correlations;opposite sign to data

)cos(

)cos()cos( correl

)cos(1

21

d

dN

STAR Preliminary

21

beam

beam

z

time(lab)

pre-hadrons

hadrons

Interpretation: below the transition point

scattered parton

moderate scatteringand dissipation

minijet fragmentation

with moderate

width increase

approximate binary scaling

STAR Preliminary

What causes the reduction in azimuth width? Perhaps there is a competition between collisional broadening and an unknown narrowing mechanism which affects low-pt and depends on the first few N-N collisions.

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scattered parton

earlier, strongermomentum dissipation

parton fragments plus correlated hadronsspread over much

larger range

Interpretation: above the transition point

(personal speculation)

beam

beam

z

time

novel QCD environment

hadrons

larger width

STAR Preliminary

Why does the width remain narrow?

Somehow the scattered parton’s azimuth direction of motion is transferred to the bulk hadrons which are associated/correlated with it.

STAR Preliminary

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Implications for phenomenology

Novel, 1D Hubble expanding gluon field (in co-moving frame of parton)

• transverse momentum loss; no change in direction

• pt transfered to gluons along z-coordinate

• correlation along z maps to width increase on • pt not transferred on , azimuth width stays constant

• increased number of correlated pairs

• pt correlations preserved

But what causes the interaction with the gluon field to suddenly change at the transition ?

(personal speculation)

pz

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Summary and Conclusions Angular correlations on () were shown for Au+Au collisions at 62 and 200 GeV: large structures associated with semi-hard partons/fragments, dipole and quadrupole.

The same-side 2D peak follows binary scaling (minijets) until an abrupt transition: number of correlated pairs and -width increase dramatically; -width decreases.

The quadrupole, typically interpreted as elliptic flow, does not show the transition.

The transition point occurs at the same transverse particle density at 62 and 200 GeV.

Increased correlations appear due to more soft hadrons being correlated with scattered partons, rather than due to more correlated groups, or clusters (beyond binary scaling).

Up to ~30% of the final state hadrons in central Au+Au are associated with the same-side 2D correlation peak.

These angular correlations together with pt angular and (yt,yt) correlations contradict

expectations based on rapid thermalization; but do indicate strong modifications of parton scattering and fragmentation.

Phenomenological implications of these results are suggested.

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Extra Slides

26

200 GeV Model

26

refρ

Δρ

ηΔ

φΔ

ηΔ

φΔ

refρ

Δρ

STAR PreliminaryFit model

84-93%

28-38%

75-84%

19-28%

65-75% 55-65% 46-55%

9-19% 5-9% 0-5%

27

200 GeV Residual

27

Fit residual = data - model

We have a good fit with the simplest possible fit function. Other than adding the cos(2φΔ) quadrupole term, no other modification was necessary.

refρ

Δρ

ηΔ

φΔ

ηΔ

φΔ

refρ

Δρ

STAR Preliminary84-93%

28-38%

75-84%

19-28%

65-75% 55-65% 46-55%

9-19% 5-9% 0-5%

28

peripheral central

Observations• Amplitude and η widths start small and experience a sharp transition• Transition occurs at ~55% centrality at 200 GeV, is more central (~40%) for 62 • φ width has a very different centrality dependence

refρ

ΔρSTAR Preliminary

X-axis shows mean participant path-length

2/part

bin

N

N

200 GeV62 GeV

Statistical and fitting errors as shown

Systematic error is 9% of correlation amplitude

STAR Preliminary STAR PreliminaryPeak Amplitude Peak η Width Peak φ Width

Same-side 2D gaussian

29

29

Does interaction between same-side peak and cos(φΔ) terms cause the transition?

fix cos(φΔ) and cos(2φΔ) on away-side

then fit remaining terms

The results are consistent

Cancellation in fit terms does not cause the amplitude increases.

Two-stage fit: Result200 GeV: standard, two-stage fit

cos(φΔ) cos(2φΔ)

minijet peak minijet η widthν ν

ν ν

Consistency Check

30

30

Does the transition from narrow to broad ηΔ occur quickly or slowly?

data - fit (except same-side peak)

Shape changes little from peripheral to the transition

The transition occurs quickly

STAR Preliminary83-94% 55-65%

Large change within ~10%

centrality

46-55%

Smaller change from transition to most central

low-pt manifestation of the “ridge”

0-5%

ηΔ width

Transition – close-up

31

Suite of correlation and differential spectra measures:

Three example scenarios for RHIC collision environments:

Focus attention on the 2D same-side gaussian

Implications: measures and media

• Number of pair correlations on relative angles: ()

• pt correlations on ()

• 2D transverse momentum: (yt,yt)

• Charge independent (CI) and dependent (CD)• PID dependent (not yet explored, need TOF)

• Differential pt spectra (as in p-p analysis)

Superposition of p-p collisions Parton/hadron scattering, moderate cross sections Opaque medium, zero mean-free path

32

Centrality and Energy Trends

2/part

bin

N

N

33

Quadrupole ComponentData cos(2φΔ) component

Instead of removing a background, we can make a measurement

• 62 and 200 have the same shape• Substantial amp. change with energy

200 GeV62 GeV

refρ

Δρ

ηΔ

φΔ

refρ

Δρ

ηΔ

φΔ

}2{2

]2[ 22 Dv

n

ref

A

33

flow data from PRC 72 014904

D. Kettler, T. TrainorarXiv:0704.1674accepted to J Mod Phys E

The η-dependence of correlations separates quadrupole from other components

STAR Preliminary STAR Preliminaryv2{2}

v2{2D}

v2{4}

refρ

Δρ ]2[

Amplitudes

34

Another scenario: opaque core plus novel QCD corona

If an opaque core developed then minijet yield would decrease, but perhaps those that escape from the outer region pick up enoughassociated particles to make up for the deficitcaused by the core to account for what we see.

- pt correlations remain- ytxyt dissipates but amplitude remains at minijet yt- same-side 2D gaussian remainsBut…

However, many jets will lose their away-side partner, only tangential jets will have the broad away-

side correlations to produce the –cos().

In this scenario the ratio of dipole to 2D gaussian amplitude decreases.

In the STAR data this ratio is flat from pp to central AuAu.

35

Implications for phenomenology

• momentum loss• increased number of correlated pairs• Brownian motion induces and width broadening – the latter is not seen

Semi-hard parton traversing thermal medium:

1D Hubble expanding gluon field(in co-moving frame of parton)

• transverse momentum loss; no change in direction

• pt transfered to gluons along z-coordinate, not • correlation along z maps to width increase on • azimuth width constant• increased number of correlated pairs

• pt correlations preserved

But what causes the gluon field to suddenly change ?

(personal speculation)