Soft Contribution to the Hard Ridge

George MoschelliWayne State University26,WWND, January 2-10, 2009

Ocho Rios, Jamaica

The Ridge• Hard Ridge: jet trigger• Soft Ridge: no trigger• Flow and jetsLong Range Correlations• Flux Tubes, Glasma, and CorrelationsComparison to Experiment• Blast Wave Flow + Glasma• pt Dependence• Soft and Hard Ridge from STAR

arXiv:0910.3590 [nucl-th] GM, Sean Gavin

Phys.Rev.C79,051902, arXiv:0806.4718 [nucl-th]Sean Gavin, Larry McLerran, G. M.

Hard Ridge: Jet + Associated Particles

Hard Ridge: Near Side Peak• Peaked near = 0 • Broad in

STAR: arXiv:0909.0191

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1

N trig

d2N

dΔφ dΔη

Measure

• High pt trigger

• Yield of associated particles per trigger

How does the formation of the ridge at large depend on jets?

Soft Ridge: Untriggered Correlationstwo particle correlations with no jet tag

central

STAR: arXiv:0806.2121

Soft and Hard Ridges Similar• Peaked near = 0 • Wider in than hard ridge• Broad in • Jet peak?

ρ(η ,φ)ρ ref

=pairs − (singles)2

singles

Measure

peripheral

Common Features• width increases with centrality• peripheral ~ proton+proton

Near Side Peak: Flow

Fluid cell

~1 fm/c Freeze out

Azimuthal correlations come from flow.

• Particles are pushed to higher pt and and focused to a smaller azimuthal angle depending on the push.

• The ridge should narrow in

with increasing pt cuts.

• Mean flow depends on position

• Opening angle for each fluid element depends on radial position

Near Side Peak: Jets + Flow

Quenched away jet

Fluid cell

~1 fm/c Freeze out

Jet Correlations With Bulk

• Correlation of flow and jet particles if produced nearby in transverse plane

• Surviving jets tend to be more radial, due to quenching.

• Bulk particles are pushed into the radial direction by flow

Claim:

Soft ridge explained by bulk flow

Hard ridge: additional jet-bulk contribution

E. Shuryak, Phys. Rev. C 76, 047901 (2007)

Flow Works

Takahashi, Tavares, Qian, Grassi, Hama, Kodama, Xu

correlations NEXUS strings

transverse boostSPHERIO hydro

Voloshin; Pruneau, Gavin, Voloshin;Gavin, Moschelli, McLerran; Shuryak;Mocsy & Sorenson

Blast Wave Model

Hydrodynamics

CGC Flux TubesDusling, Gelis, Lappi, & Venugopalan arXiv:0911.2720

Correlations• Partons from the same tube are correlated

• Rapidity reach: Causally disconnected

Flux Tubes and Glasma

Flux Tubes: longitudinal fields early on

• Tubesquarks+gluonsSingle flux tube phase space density of gluons

• Flux tube transverse size

• Number of flux tubes

• Gluon rapidity densityKharzeev & Nardi

Flux Tubes and Correlations

• Long range Glasma fluctuations scale the phase space density

Dumitru, Gelis, McLerran & Venugopalan;Gavin, McLerran & GM

• Correlation Strength

• Energy and centrality dependence

flux tube transverse size ~ Qs

-1 << RA

Correlation function

Soft Ridge

• Qs dependence: 200 GeV Au+Au 62 GeV, Cu+Cu

Glasma Dependence

Blast Wave

• Boltzmann Dist. f (p,x)

• Scale factor to fit 200 GeV only

• Centrality dependence on blast wave parameters (v and T) 10% uncertainty

• Blast wave only (dashed) fails

Comparison and LHC

LHC

Au+Au 200 GeV

Au+Au 62 GeV

Cu+Cu 62 GeV

Cu+Cu 200 GeV

Caution: Blast Wave parameters for LHC taken from Au+Au 200 GeV

Soft Ridge: Angular Correlations

0

0.2

0.4

0.6

0 0.5 1 1.5 2

Peak Width

Fit using Gaussian + offset

• Range:

• Error band: 20% shift in fit range

• Uncertainty due to experimental definition of peak

• A width is approximately independent of energy

• The width should decrease with increasing pt range

Most Central Width vs. pt

Soft Ridge vs. pt

• Jet-Bulk and Jet-Jet correlations should have an increasing effect with pt

• Jet contributions should force the correlation width to approach the jet correlation width

Examine bulk correlations in different pt ranges

Most Central Amplitude vs. pt

DeSilva arXiv:0910.5938

Jets + Glasma

• Correlation strength

• f(x1,p1) jet pt range f(x2,p2) bulk associated pt range

Jet-Bulk correlation function

Hard RidgeNarrow

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1

N trig

d2N

dΔφ dΔη

Hard Ridge: Jets + FlowNarrow

Wide

Jet-Bulk

Jet-Bulk width similar to E. Shuryak, Phys. Rev. C 76, 047901 (2007)

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1

N trig

d2N

dΔφ dΔη

Hard Ridge: Flow OnlyNarrow

Bulk-Bulk

Wide

Jet-Bulk

Narrow

Jet-Bulk width similar to E. Shuryak, Phys. Rev. C 76, 047901 (2007)

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1

N trig

d2N

dΔφ dΔη

Hard Ridge

dN/dpt constrains jet fraction• Bulk particles: Blast Wave• Jet particles: Total - BW• Jet scale Qs ; take 1.25 GeV

Jets + Flow Fit the Hard Ridge• Bulk-Bulk correlations ~70%.• Bulk-Bulk + Jet-Bulk better azimuthal agreement

Jorn Putschke, QM ‘06

The Ridge: From Soft to Hard

Bulk Correlations •Amplidude decreases with pt,min

• Narrow width from flow alone

Jet+Bulk Correlations• Jet contribution dominates with increasing pt,min

• r widening at large pt,min would indicate significant contribution from jet correlations out in the ridge

Summary

Ridge Azimuthal Width

• Flow induces angular correlations

• Azimuthal width vs. pt can distinguish flow from jets

Long Range Correlations

• Implications on particle production mechanism

Glasma + Blast Wave

• Blast Wave fixed by single particle spectra

• Glasma fixed by dN/dy and 200 GeV Au+Au

• Predicts the height and azimuthal width of the Soft and Hard Ridge

• Predict energy, centrality, system, and pt dependence

Bulk Correlations Dominate the Hard Ridge

Backup Slides

PHOBOS: Long Range Correlations

long range correlations

Why Long Range Correlations?

• must originate at the earliest stages of the collision

• like super-horizon fluctuations in the Universe

• information on particle production mechanism

Dumitru, Gelis, McLerran, Venugopalan, arXiv:0804.3858

Hard vs. Soft Ridge

• N. Armesto, C.A. Salgado, U.A. Wiedemann, Phys. Rev. Lett. 93, 242301 (2004)• P. Romatschke, Phys. Rev. C 75, 014901 (2007)• A. Majumder, B. Muller, S. A. Bass, Phys. Rev. Lett. 99, 042301 (2007)• C. B. Chiu, R. C. Hwa, Phys. Rev. C 72, 034903 (2005)• C. Y. Wong, arXiv:0712.3282 [hep-ph]• R. C. Hwa, C. B. Yang, arXiv:0801.2183 [nucl-th]• T. A. Trainor, arXiv:0708.0792 [hep-ph]• A. Dumitru, Y. Nara, B. Schenke, M. Strickland, arXiv:0710.1223 [hep-ph]• E. V. Shuryak, Phys. Rev. C 76, 047901 (2007)• C. Pruneau, S. Gavin, S. Voloshin, Nucl.Phys.A802:107-121,2008

• S. Gavin and M. Abdel-Aziz, Phys. Rev. Lett. 97, 162302 (2006)• S. A. Voloshin, Phys. Lett. B 632, 490 (2006)• S. Gavin and G. Moschelli, arXiv:0806.4366 [nucl-th]• A. Dumitru, F. Gelis, L. McLerran and R. Venugopalan, arXiv:0804.3858 [hep-ph]• S. Gavin, L. McLerran, G. Moschelli, arXiv:0806.4718; arXiv:0910.3590 [nucl-th] • F. Gelis, T. Lappi, R. Venugopalan, arXiv:0807.1306 [hep-ph]• J. Takahashi et. al. arXiv:0902.4870 [nucl-th]

hard ridge explanations -- jet interactions with matter

soft ridge -- similar but no jet -- collective behavior

Blast Wave Single Particle Fits

fit momentum spectra in 200 GeV Au+Au

10% systematic uncertainty in scale of v and T

Akio Kiyomichi, PHENIX

0

0.2

0.4

0.6

0.8

0 100 200 300 400

0

0.1

0.2

0.3

0 100 200 300 400

62 GeV Au+Au:

5% smaller v, 10% smaller T

temperature

velocity at r = R

Npart participants

Npart

Blast Wave and the Correlation FunctionSchnedermann, Sollfrank & Heinz

• Single Particle Spectrum

A Hubble like expansion in used in a Boltzmann Distribution

• Correlation Function

Correlation Strength

strength

N

2R ≡ c(x1,x2 )

volume∫∫ =

R=

2 − μ

μ 2

1

K+

K 2 − K2

K2

K flux tubes, assume NK=μK , N2

K− N K

2 = 2K

K varies event-by-event

N 2 − N 2 = 2 K + μ2 K 2 − K 2( )N =μ K ,

= n2 (x1, x2 ) − n1(x1)n1(x2 ){ }volume∫∫ = N(N −1) − N

2

K flux tubes

R

fluctuations per tube number of tubes

Jet Correlation Strength

Pruneau, Gavin, Voloshin Phys.Rev. C66 (2002) 044904

Soft Ridge vs. pt

Peak Amplitude Au-Au 200 GeV

STAR preliminary

Most Central Amplitude vs. pt

• Increase the lower pt limit of the soft ridge calculation toward the hard ridge range.

• As the lower pt limit is increased less particles are available for correlations.

• Correlation amplitude for the most central collision plotted vs. the lower pt limit.

Soft Ridge vs. pt

• Higher pt particles received a larger radial push narrower relative angle.

Peak Width Au-Au 200 GeV

Most Central Width vs. pt

STAR preliminary

Angular width from

Quenching + Flow

RA

r

quenched away jet

• Survival probability

• Production probability

• Jet path

• Jet Distribution

L

E. Shuryak, Phys. Rev. C 76, 047901 (2007)

• Surviving jets tend to be more radial, due to quenching.

“Jet-Bulk” correlations

“Bulk-Bulk” correlations

Two Contributions

1E-14

1E-13

1E-12

1E-11

1E-10

1E-09

1E-08

1E-07

1E-06

1E-05

0.0001

0.001

0.01

0.1

1

10

100

1000

0 2 4 6 8 10 12

Blast Wave

Invariant Spectrum

pt

Thermal Bulk

Jets

STAR PRL vol 91, number 17 (2003)

• Both the Bulk-Bulk and Jet-Bulk contributions are weighted by the fraction of bulk or jet particles to the total.

The Ridge: From Soft to Hard

Bulk Correlations •Amplidude decreases with pt,min

• Narrow width from flow alone

Jet+Bulk Correlations• Jet contribution dominates with increasing pt,min

• r widening at large pt,min would indicate significant contribution from jet correlations out in the ridge