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The transition observed in two-dimensional correlation data from STAR

Lanny RayUniversity of Texas at Austin

STAR Collaboration

Outline: p-p phenomenology Centrality evolution Same-side structures Away-side ridge Implications

Tamura Symposium – Nov. 20-22, 2008

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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

replot on“transverse rapidity” Data – Spp

semi-hard component:gaussian on yt

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measures number of correlated pairs per final state particle

Event 1

Event 2

ρsibling(p1,p2)

ρreference(p1,p2)

Correlation measure

1

),(

),(

ba

ba

dd

dN

ref

sibch

ref

normalized ratio of 2D binned histograms;

acceptance cancellation;two-track ineff. corrections

square-rootof ref(a,b);

(for space)

Fill 2D histograms (a,b), e.g. (1,2), (1,2), (1-2,1-2), (pt1,pt2), etc.

ρ(p1,p2) = 2 particle density

Motivated by p-p superposition null hypothesis

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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: from spectra to correlations

STAR Preliminary

0

lnm

pmy tt

t

5

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

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Why minijets?Jets observed by UA1 down to 5 GeV/c in p-pbar collisions at sqrt{s} = 200 – 900 GeV; accounted for with pQCD; angular correlations and pt structures are “jet-like.”

C. Albajar (UA1) Nucl. Phys. B 309, 405 (1988)

pQCD calc.

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Why minijets?

STAR observes correlated charged hadron pairs with pt ~ 1 – 1.5 GeV/ccorresponding to typical parton pt of order >(3/2)(2)(1 – 1.5) = 3-4.5 GeV/c,well within reach of the UA1 data and pQCD descriptions.

In Au-Au we cannot hope to identify these low pt jets directly. There is alsono identifiable trigger particle at lower pt; thus we use both angular and (pt1,pt2)correlations as suggested by Xin-Nian Wang a long time ago (Phys. Rev.D 46, R1900 (1992)).

How would these low pt, minimum-bias jets, or minijets, appear in our2D () angular correlations?

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proton

proton

NN cmparton-parton cm

Jet-A

Jet-B

0

Nu

mb

er

of

pa

irsA-AB-B

A-BB-A

Nu

mb

er

of

pa

irs

0

A-AB-BA-B B-A

sum overmany events

small angle peak

large azimuth peakΦ1 -

Φ2

η1 - η2

(n)ρ

Δρ(n)

ref

p-p 200 GeV

STAR preliminary

2121 ,

Example: di-jets

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X.-N.Wang and M. Gyulassy implemented the UA1 observations intotheir Monte Carlo code HIJING (w. PYTHIA) (Phys. Rev. D 44, 3501 (1991))using standard PDFs, pQCD parton-parton cross sections, and fragmentation functions.

p + p at 200 GeV

STAR Preliminary

Minijets in HIJING & PYTHIA

In this analysis “minijets” are simply jets with no low pt cut-off.

HijingJets on

HijingJets off

additionalsharp peak:

HBT, conversionelectrons

soft pt pairsremoved

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Centrality evolution of the 2Dcorrelations

(Expectation is that minijets will be thermalized.)

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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 including the same-side low pt ridge

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

From M. Daugherity’s Ph.D Thesis (2008)

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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 function Use proton-proton fit function plus cos(2φΔ) quadrupole term (~ elliptic flow).

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

φΔ

dipole

quadrupolecos(2φΔ)

Fit function

Same-side “Minijet” Peak, 2D gaussian

Away-side -cos(φ)

“soft” “hard”

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Centrality and energy trends

2/part

bin

N

N

Au-Au at 62 and 200 GeV

200 GeV62 GeV

200 GeV62 GeV

STAR Preliminary

From M. Daugherity’s Ph.D Thesis (2008)

Transition

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Same-side correlation structure

< /2

The “soft” ridge

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)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

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 - AuAu

Statistical and fitting errors as shown

Systematic error is 9% of correlation amplitude

2/part

bin

N

N

peripheral central

HIJING 1.382 default parameters, 200 GeV, quench off

16Same-side 2D Gaussian amplitude, -width, volume 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 width aspect ratio volume

Sd

dNch /2

3~

S = overlap area(Monte Carlo

Glauber) STAR Preliminary

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

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21

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(yt1,yt2) correlations for same-side pairs

Like Sign

Unlike Sign

STAR Preliminary

Au-Au 200 GeV

HBT

peripheral

peripheral

central

central

pp

pp

minijets persist;pt dissipation

From M. Daugherity’s Ph.D Thesis (2008)

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Away-side correlation structure

> /2

The away-side ridge

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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

Away-side ridge (dipole) – local pt conservation

calculated global pt conservation

Low

-x p

arto

n

KT ~ 1 GeV/c

p z

Q ~ 2 GeV 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

Hijing – jets on(no soft pt)

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(yt1,yt2) correlations for away-side pairsAu-Au 200 GeV

Like Sign

Unlike Sign

pp

pp

STAR Preliminary

peripheral

peripheral

central

central

minijets persist;pt dissipation

minijets

From M. Daugherity’s Ph.D Thesis (2008)

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Elliptic flow measurement using2D () correlations

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Quadrupole component (~ elliptic flow)Data cos(2φΔ) component

• 62 and 200 have the same shape• Substantial amp. change with energy• no transition

200 GeV62 GeV

refρ

Δρ

ηΔ

φΔ

refρ

Δρ

ηΔ

φΔ

Amplitudes

}2{2

]2[ 22 Dv

n

ref

A

D. Kettler, T. Trainor arXiv:0704.1674

The η-dependence separates quadrupole (v2) from non-flow

STAR Preliminary

quadrupole determined by initial conditions; medium (EoS, viscosity) not relevant.

2[2]0.0045 ( ) ( )NN opt bin

ref

R s b n b

13/200log

13/log NNNN

ssR

Initial state QCD source

for v2:

Boreskov et al., arXiv:0809.0625 [hep-ph]Kopeliovich et al., arXiv:0809.4327 [hep-ph]

Au-Au

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Implications for theory and phenomenology

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Expected behavior:

Comparison with data:

Implications: superposition model

Minijet shape unchanged, amplitude follows binary scaling.

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

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Minijets & Quadrupole

Below the transition the Au-Au system appears transparent, i.e. no collisional pressure build-up, no flow,

at least up to the transition point.

What mechanism(s) produces a smooth v2?

2/ amplitude quadrupole 22vNch

expected v2?

STAR Preliminary

STAR Preliminary

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Comparisons with data:

Implications: opaque, thermalized medium

Semi-hard partons thermalize, sound waves(?) – but number correlations disperse pt correlations on disperse

Minijet peak on (yt,yt) dissipatedPeak Volume

~

8x increase

STAR Preliminary200 GeV62 GeV

Narrowing azimuth width

1

2

Any new mechanism above the transition must seamlessly match minijets.

pT minijet peak

0-30% central

Minijet correlation

region in (yt,yt)

remains strong

3

Observations contradict expectations for a rapidly thermalized system.

Semi-hard partons persist;number correlationsdo not vanish, butincrease dramatically.

Expected behavior of minijets:

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pt correlations remain (yt,yt) dissipates but amplitude remains at minijet yt

same-side 2D Gaussian remains However, same-side yield decreases unless enough hadrons from surface are correlated with minijet. Some jets will lose away-side partner, reducing –cos()

away-side pt escapes, but is dispersed among many more pairs

Implications: opaque core + hadronic coronaExpected behavior:

Comparison with data:

Ratio of away-side ridgeto same-side Gaussian

is ~constant from peripheralto most-central;

data are inconsistent with this scenario

29be

ambeam

z

time

novel QCD environment

hadrons

increasing correlation width

meansearliersource

if morecentral

is hydro

But the “soft-ridge” implies more:

For more central collisionsthe 2D Gaussian correlationmust have an earlier source when the system is supposedly opaque (Perfect Liquid). Rather than diminish, the same-side correlations increase!

Minijets & Quadrupole

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Theoretical models – same-side ridge Chiu and Hwa, Phys. Rev. C72, 034903 (2005) – Jet driven; recombination; hot spots pushed out by radial flow.

Voloshin, Nucl. Phys. A749, 287c (2005); Shuryak, Phys. Rev. C76, 047901 (2007) – beam-jet fragments pushed out by radial flow.

S. Gavin, Phys. Rev. Lett. 97, 162302 (2006) – initial state energy fluctuations spread along by shear viscosity; pushed out by radial flow.

Dumitru, Gelis, McLerran, Venugopalan, arXiv:0804.3858[hep-ph] - glasma flux tubes pushed out by radial flow.

None explain all the observations:

Majumder et al., Phys. Rev. Lett. 99, 042301 (2007); Dumitru et al., arXiv:0710.1223 [hep-ph] - Jet driven with plasma instability

C.-Y. Wong, Phys. Rev. C76, 054908 (2007) – Jet driven “momentum kick” model.

• smooth extrapolation to p-p limit• away-side ridge• transition point• narrowing width on azimuth

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Implications for phenomenology

Novel QCD field: forward scattered

debris (diffractive),glasma flux tubes,…

• Below the transition the system is transparent to semi-hard scattered partons.

• Above the transition pt transport begins suddenly.

• Correlations on z map to width increase on • Azimuth width is constant if only pt is transported.

• pt correlations are preserved.

pz

Results suggest pt transport which suddenly turns on at a critical density.

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Summary and Conclusions Same-side 2D Gaussian (minijets) follows binary scaling, then a remarkable transition occurs which scales in Au-Au with transverse particle density. The away-side ridge is crucial to understanding the RHIC data; it shows a transition, follows the minijet amplitude, and may be explained in terms of recoiling minijets. Momentum dissipation is evident yet minijet correlation structures persist to most-central. Preponderance of correlation data contradict expectations based on strong, random scattering such as in rapid thermalization scenarios.

The data suggest novel QCD processes in which

pt transport/emission suddenly increases and v2

is generated in the initial stage.