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Observation of dramatic transition in 2D correlation data. Lanny Ray For the STAR Collaboration University of Texas at Austin April 7, 2008. Outline: Definitions and p-p reference Au-Au data – surprising results Implications & Speculations. 24 th Winter Workshop on Nuclear Dynamics.

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Observation of dramatic transition in 2D correlation data

Lanny Ray

For the STAR Collaboration

University of Texas at Austin

April 7, 2008

  • Outline:

  • Definitions and p-p reference

  • Au-Au data – surprising results

  • Implications & Speculations

24th Winter Workshop on Nuclear Dynamics


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.


Begin with Proton-Proton Spectra

Two-component soft + (semi)hard model:

PRD 74, 032006 (nucl-ex/0606028)

+ pQCD hard…

“semi-hard”

“soft”

200 GeV

Spp

replot on

“transverse rapidity”

Data – Spp

semi-hard component:

gaussian on yt

pt spectra for

increasing Nch


Proton-Proton: spectra to correlations

Peak yt=2.66

yt=2.66

yt2

pt ~ 2.0

pt ~ 1.0

pt ~ 0.5

yt1

STAR Preliminary

SOFT component – Levy Distribution

HARD component – Gaussian on yt(!)

PRD 74, 032006


Correlation Measure

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

ρsibling(p1,p2)

Event 1

ρreference(p1,p2)

Event 2

Start with a standard definition in statistics:

Δρas a histogram on bin (a,b):

ε = bin width, converts density to bin counts

measures number of correlated pairs per final state particle

Normalize


Proton-Proton Components

yt2

yt1

p-p transverse correlations

p-p axial correlations

STAR Preliminary

φΔ

ηΔ

We hypothesize that this structure

is caused by semi-hard partonic

scattering & fragmentation - minijets

soft component

semi-hard component

φΔ

φΔ

ηΔ

ηΔ

Longitudinal Fragmentation: 1D Gaussian onηΔ

HBT peak at origin, LS pairs only

Minijets: 2D Gaussian at origin plus

broad away-side peak: -cos(φΔ)


proton-proton

200 GeV Au-Au Data

Analyzed 1.2M minbias 200 GeV Au+Au events;

included all tracks with pt > 0.15 GeV/c,|η| <1, fullφ

note: 38-46% not shown

84-93%

74-84%

64-74%

55-64%

46-55%

φΔ

ηΔ

18-28%

9-18%

28-38%

5-9%

0-5%

φΔ

ηΔ

STAR Preliminary

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


62 GeV Au-Au Data

Analyzed 13M 62 GeV Au+Au minbias events;

included all tracks with pT > 0.15 GeV/c, |η| < 1, full φ

note: 37-46% not shown

84-95%

75-84%

65-75%

56-65%

46-56%

18-28%

28-37%

9-18%

5-9%

0-5%

STAR Preliminary

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


Fit Function (5 easy pieces)

Same-side “Minijet” Peak, 2D gaussian

Away-side

-cos(φ)

Proton-Proton fit function

STAR Preliminary

“soft”

“hard”

=

+

φΔ

φΔ

φΔ

ηΔ

ηΔ

ηΔ

dipole

longitudinal fragmentation

1D gaussian

HBT, e+e-

2D exponential

cos(2φΔ)

  • Au-Au fit function

    • Use proton-proton fit function + cos(2φΔ) quadrupole term (“flow”).

    • This gives the simplest possible way to describe Au+Au data.

quadrupole

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

φΔ

ηΔ


Same-side 2D gaussian & binary scaling

Peak Amplitude

Peak η Width

Peak φ Width

STAR Preliminary

STAR Preliminary

STAR Preliminary

Statistical and fitting errors as shown

Systematic error is 9% of correlation amplitude

200 GeV

62 GeV

constant widths

peripheral

central

small increase before transition

Binary scaling:

Kharzeev and Nardi model

STAR Preliminary

Note the absence

of a transition point

in the quadrupole:

v2 & elliptic flow

Deviations from binary scaling represent new physics unique to heavy ion collisions


HIJING minijet predictions

Peak Amplitude

Peak η Width

Peak φ Width

STAR Preliminary

STAR Preliminary

STAR Preliminary

200 GeV

62 GeV

HIJING 1.382 default parameters, 200 GeV, quench off

Quench on causes slight amplitude decrease

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

mid (40-50%)

HIJING 1.382

very little centrality dependence

φΔ

ηΔ


Q ~ 2 GeV/c minijets,

nucleon KT , acoplanarity

Low-x parton

KT ~ 1 GeV/c

KT broadening

pz

Low-x parton

events

1,2,3…

p

0

sum

events

φΔ

p

0

away-side

φΔ

-3p -pp 3p

0

Dipole – transverse momentum conservation

200 GeV

62 GeV

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

STAR Preliminary

Global pt

conservation


Does the transition point scale?

Peak Amplitude

Peak Amplitude

Peak η Width

Peak η Width

Bjorken Energy Density

Npart

STAR Preliminary

STAR Preliminary

STAR Preliminary

STAR Preliminary

200 GeV

62 GeV

200 GeV

62 GeV

εBJ

εBJ

Npart

Npart

Peripheral bins are compressed.

Depends on formation time (assumed

1 fm/c), difficult to compare energies.

Peak Amplitude

Peak η Width

Transverse Particle Density

STAR Preliminary

STAR Preliminary

200 GeV

62 GeV

S = overlap area

(Monte Carlo Glauber)

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


2D angular correlations for pt

pT minijet peak

0-30% centrality

= inclusive mean pt

Number

pt

200 GeV

Au+Au

Same-side amplitude and widths

pt correlations

follow binary scaling

well past the transition

J Phys G 32 L37

This leads to the hypothesis that semi-hard partons continue to underlie the

same-side gaussian number correlations above the transition.


Multiplicity fractions – same-side gaussian

1) 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:

5) Fraction of total multiplicity

associated with same-side

gaussian correlation:

Peak Volume

STAR Preliminary

200 GeV

62 GeV

For central Au+Au we estimate about 30%;

a significant fraction of the bulk particles.

8x increase

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


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

proton-proton

How the correlations evolve in transverse momentum

(peripheral)

(central)

STAR Preliminary

Sudden onset at lower yt corresponding

to transition point for same-side gaussian.

Correlations remain at original yt – surface jets?

increase at higher yt.

(protons: see arXiv:0710.4504)


Implications: Superposition model

Expected behavior:

  • Minijets unchanged, except amplitude increases with binary scaling;

    widths remain constant.

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

Comparison with data:

Superposition model approximates data to the transition point

but radically fails at higher density, more central collisions.

STAR Preliminary


1

2

3

pT minijet peak

0-30% central

Implications: parton/hadron scattering model

Expected behavior:

  • 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

Comparison with data:

pt correlation amplitude follows binary

scaling beyond transition; doesn’t decrease

until here

hwidths increase

butfwidths decrease

Minijet peak

dissipates, strength

remains at original yt,

increases at higher yt


1

2

pT minijet peak

0-30% central

Implications: opaque, thermalized medium

Expected behavior:

  • 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(fD)].

  • momentum conserved - pt correlations on h,f may persist

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

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

Comparison with data:

Semi-hard partons persist;

number correlations

do not vanish, but

increase dramatically.

Peak Volume

STAR Preliminary

200 GeV

62 GeV

STAR Preliminary

Narrow azimuth width

from p-p to central Au-Au,

no transition point.

  • width initially due to minijets.

    If more central dominated by

    other mechanisms, the latter

    must seamlessly match minijets.

8x increase


Implications: opaque, thermalized medium

b

3

4

Comparison with data (cont.):

Boosted hot spots

produce +cos(fD)

correlations;

opposite sign to data

200 GeV Au+Au

peripheral

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)

STAR Preliminary

central

The observed correlations contradict expectations

for a rapidly thermalized system.


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.

Interpretation: below the transition point

STAR Preliminary

approximate

binary scaling

time

(lab)

minijet fragmentation

with moderate hD

width increase

hadrons

moderate scattering

and dissipation

pre-hadrons

z

scattered parton

beam

beam


STAR Preliminary

Why does thefwidth remain narrow?

Somehow the scattered parton’s azimuth direction

of motion is transferred to the bulk hadrons which

are associated/correlated with it.

Interpretation: above the transition point

(personal speculation)

STAR Preliminary

larger hD width

parton fragments plus

correlated hadrons

spread over much

larger hD range

time

hadrons

earlier, stronger

momentum

dissipation

novel QCD

environment

z

scattered parton

beam

beam


Implications for phenomenology

(personal speculation)

Novel, 1D Hubble expanding gluon

field (in co-moving frame of parton)

pz

  • transverse momentum loss; no change in direction

  • pt transfered to gluons along z-coordinate

  • correlation along z maps to width increase on h

  • pt not transferred on f, 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 ?


Summary and Conclusions

  • Angular correlations on (h,f) 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 h-width increase dramatically; f-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.



200 gev model
200 GeV Model

Fit model

STAR Preliminary

84-93%

75-84%

65-75%

55-65%

46-55%

φΔ

ηΔ

19-28%

28-38%

9-19%

5-9%

0-5%

φΔ

ηΔ

26


200 gev residual
200 GeV Residual

Fit residual = data - model

STAR Preliminary

84-93%

75-84%

65-75%

55-65%

46-55%

φΔ

ηΔ

19-28%

28-38%

9-19%

5-9%

0-5%

φΔ

ηΔ

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

27


Same-side 2D gaussian

Peak Amplitude

Peak η Width

Peak φ Width

Statistical and fitting errors as shown

Systematic error is 9% of correlation amplitude

STAR Preliminary

STAR Preliminary

STAR Preliminary

200 GeV

62 GeV

peripheral

central

X-axis shows mean participant path-length

  • 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 verydifferent centrality dependence


Consistency Check

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

Result

200 GeV: standard, two-stage fit

Two-stage fit:

cos(φΔ)

cos(2φΔ)

fix cos(φΔ) and cos(2φΔ) on away-side

then fit remaining terms

ν

ν

The results are consistent

Cancellation in fit terms does not cause the amplitude increases.

minijet peak

minijet η width

ν

ν

29


Transition – close-up

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

data - fit (except same-side peak)

STAR Preliminary

83-94%

55-65%

46-55%

0-5%

ηΔ width

Large change within ~10% centrality

Smaller change from transition to most central

low-pt manifestation of the “ridge”

Shape changes little from peripheral to the transition

The transition occurs quickly

30


Implications: measures and media

Suite of correlation and differential spectra measures:

  • Number of pair correlations on relative angles: (hD,fD)

  • pt correlations on (hD,fD)

  • 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)

Three example scenarios for RHIC collision environments:

  • Superposition of p-p collisions

  • Parton/hadron scattering, moderate cross sections

  • Opaque medium, zero mean-free path

Focus attention on the 2D same-side gaussian



Quadrupole Component

Instead of removing a background, we can make a measurement

Data

cos(2φΔ) component

Amplitudes

200 GeV

62 GeV

  • 62 and 200 have the same shape

  • Substantial amp. changewith energy

φΔ

φΔ

ηΔ

ηΔ

STAR Preliminary

STAR Preliminary

v2{2}

v2{2D}

v2{4}

D. Kettler, T. Trainor

arXiv:0704.1674

accepted to J Mod Phys E

flow data from PRC 72 014904

The η-dependence of correlations separates quadrupole from other components

33


Another scenario: opaque core plus novel QCD corona

- pt correlations remain

- ytxyt dissipates but amplitude remains at minijet yt

- same-side 2D gaussian remains

But…

If an opaque core developed then minijet

yield would decrease, but perhaps those that

escape from the outer region pick up enough

associated particles to make up for the deficit

caused by the core to account for what we see.

However, many jets will lose their away-side partner, only tangential jets will have the broad away-side correlations to produce the –cos(fD).

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.


Implications for phenomenology

(personal speculation)

Semi-hard parton traversing

thermal medium:

  • momentum loss

  • increased number of correlated pairs

  • Brownian motion induces h and f

  • width broadening – the latter is not seen

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 f

  • correlation along z maps to width increase on h

  • azimuth width constant

  • increased number of correlated pairs

  • pt correlations preserved

  • But what causes the gluon field

  • to suddenly change ?


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