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The away-side ridge in two-dimensional correlation data from STAR

Lanny RayUniversity of Texas at Austin

STAR Collaboration

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Outline: Definitions p-p and QCD Centrality evolution Same-side structures Away-side ridge Implications

The philosophy behind the analysis presented here is based on an old and simple idea:• measure p-p and try to understand those data in terms of QCD, PDFs, FFs.• then move to p+Au (d+Au) and understand those data (initial state, sequential scattering effects)• then move to Au-Au and see if the data require anything else• interpret data with new physics mechanisms, beyond that in p-p, p-A only when the data demand it.

This is not a new idea, e.g. in Sept. 1992 at a STAR collaboration meetingMiklos Gyulassy outlined this very program.

I hope that this workshop will live up to its title of critically assessing the data and itsInterpretation.

Our Philosophy and Challenge

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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),(),(

baba

dddN

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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SS - same side

AS - away side

LS – like sign US – unlike sign

Two-component soft + semi-hard structure

away-side bumpat 1 GeV/c is

independent ofcharge pair

same-side bump at 1 GeV/c for US;soft structure varies

√

ref

√

ref

0.151.0

10.0

p t (GeV/c)

√

ref

√

ref

Transverse momentum correlations in p-p

ref

200 GeV p-p minbiastt yp

transverse rapidity

}/)ln{( 0mpmy ttt

STAR Preliminary

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yt1

yt2

refρΔρ

p-p transverse correlations

ηΔ

φΔ

p-p axial correlations

refρΔρ

semi-hard component

ηΔ

φΔ

refρΔρ

soft component

ηΔ

φΔ

refρΔρ

Longitudinal Fragmentation: 1D Gaussian on ηΔ

HBT peak at origin, LS pairs only

This looks like a jet – but is it?2D Gaussian + away-side ridge

STAR Preliminary21

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Angular correlations for p-p

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“Jets” in UA1Energy clusters were measured by UA1 down to 5 GeV/c in p-pbar collisions at sqrt{s} = 200 – 900 GeV; accounted for with pQCD; back-to-back angular correlations and pt structures are “jet-like.”

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

pQCD calc.

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Relation of UA1 jets to p-p correlationsSTAR observes angular 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.

X.-N.Wang and M. Gyulassy implemented the UA1 observations into their Monte Carlo code HIJING (PYTHIA) (Phys. Rev. D 44, 3501 (1991)) using standard PDFs, pQCD parton-parton cross sections, and standard fragmentation functions. The low-pt parton energy follows a power-law until a cut-off at Q0 ~ 2 GeV. The majority of produced jets have Q0 ~ few GeV and only produce a few hadronic fragments.

In Au-Au we cannot hope to identify these low Q0 jets directly. There is alsono identifiable trigger particle at lower pt. Thus we use both angular and (pt1,pt2)correlations for all pairs as suggested by Xin-Nian Wang a long time ago (Phys. Rev. D 46, R1900 (1992)). These soft, untriggered jets are known in the literature as minijets.

How would minijets appear in our 2D () angular correlations?

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proton

proton

NN cmparton-parton cm

Jet-A

Jet-B

0

Num

ber

of p

airs

A-AB-B

A-BB-A

Num

ber

of p

airs

0

A-AB-BA-B B-A

sum overmany events

small angle peak

large azimuth peakΦ1 - Φ

2

η1 - η2

(n)ρΔρ(n)

ref

p-p 200 GeVSTAR preliminary

2121 ,

Example: di-minijets

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p + p at 200 GeVMinijets in HIJING & PYTHIA

We conjecture that the bump at 1 GeV/c in the (yt,yt) and the above angular correlations are generated by the fragmentation of semi-hard scattered partons.

These minijets are simply jets with no low pt cut-off.

soft pt pairsremoved

STAR Preliminary

HijingJets on

HijingJets off

additionalsharp peak:

HBT, conversionelectrons

ref 4

ref

ref

~20% agreement

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Au-Au centrality evolution of the 2Dcorrelations

(Expectation is that minijets will be thermalized.)

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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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(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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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

refρΔρ

ηΔ

φΔ

ηΔ

φΔ

refρΔρ

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

refρΔρ

refρΔρ

refρΔρ

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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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

NNNA

2/)1( Amplitude

Same-side 2D Gaussian & binary scaling - AuAuStatistical and fitting errors are~5-10%

Systematic error is 9% of correlation amplitude

2/part

bin

NN

peripheral central

HIJING 1.382 default parameters, 200 GeV, quench off

172D Gaussian amplitude, -width, volume scale with particle density in Au-Au

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 /23~

S = overlap area(Monte Carlo

Glauber) STAR Preliminary

Does the transition point scale?

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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 in same-side ridge 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 (Au-Au 200 GeV)

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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 point,implying an approximately transparent system,

but 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.If a few secondary collisions (LDL) produce v2 in peripheral collisions, why aren’t the minijets affected (same pt range)?

What mechanism(s) produces a smooth v2?

2/ amplitude quadrupole 22vNch

expected v2?

STAR Preliminary

STAR Preliminary

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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

parto

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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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

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Mach Cone ?Au+Au 200 GeV 0-5% most-central

Shown are Data – Quadrupole whichisolates the away-side dipole structure

STA

R P

relim

inar

y

No indication of a double away-side ridge – no Mach cone

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Please stop using ZYAM!ZYAM method assumes non-overlapping peaks above background – questionable

Example: fake “data” generatedby same-side Gaussian + dipole

v2{2} obtainedfrom due to SS Gauss.

)2cos(

ZYAM proceduresubtracts v2 and adjusts offset.

ZYAMdeducedcorrelation

wrong amplitude!spurious shape!

nonphysical

Always plot the raw correlation data v2 is being over-subtracted; v2{2} or [v2{2} + v2{4}]/2 includes SS peak contribution, i.e. non-flow, which is larger at higher pt where this analysis is usually done.

Plots from Tom Trainor

ZYAM

input correlation

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Summary and Conclusions Correlation structures in minbias p-p collisions can be understood with pQCD, PDFs, and standard FFs.

Minijets (jets with no low-pt cut-off) are an essential component of RHIC collisions and are manifest in (yt,yt) and 2D angular correlations.

Up to the transition minijets escape from the entire collision volume (binary scaling) with little broadening as if from a transparent medium.

The transition, observed in the same-side peak, is also observed in the away-side ridge.

The transition is not manifest in v2 (quadrupole) implying that v2 is not affected by post-impact rescattering.

The minimum-bias away-side correlations do not show evidence of a double-hump structure reported in leading particle-associated analyses.