Based on work with:

Sean Gavin&

Larry McLerran

arXiv:0806.4718 [nucl-th]

Long Range Correlations

and The Soft Ridge

George Moschelli

25th Winter Workshop on Nuclear Dynamics

Wayne State University

Outline:• Correlation Measurements

• PHOBOS• STAR

• CGC + Correlations• Flux Tubes• Glasma• Qs Dependence

• Blast Wave + Correlations• Transverse Flow• Glasma + Flow• Comparison to STAR

PHOBOS: High pt Triggered Ridge

from Edward Wenger, RHIC & AGS User’s Meeting, ‘08

PHOBOS: High pt Triggered Ridge

from Edward Wenger, RHIC & AGS User’s Meeting, ‘08

PHOBOS: High pt Triggered Ridge

from Edward Wenger, RHIC & AGS User’s Meeting, ‘08

long range correlations

PHOBOS: Untriggered Ridge

from Edward Wenger, RHIC & AGS User’s Meeting, ‘08

• soft ridge with very long range in rapidity?

• caution: v2 not yet removed

Long Range Correlations

• must originate at the earliest stages of the collision

• like super-horizon fluctuations in the Universe

• information on particle production mechanism

from Raju Venugopalan, RHIC & AGS User’s Meeting, ‘08

STAR: Soft Ridge

Medium range correlations…implications for long range?

from Lanny Ray, RHIC & AGS User’s Meeting, ‘08

Peak Amplitude Peak η Width Peak φ Width

near side peak

•v2 and experimental effects subtracted

•peak height and azimuthal width

•not the rapidity width -- structure too narrowGavin + Abdel-Aziz; Gavin + Pokharel + Moschelli

peripheral central

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 [nucl-th]• F. Gelis, T. Lappi, R. Venugopalan, arXiv:0807.1306 [hep-ph]

hard ridge explanations -- jet interactions with matter

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

Flux Tubes and Glasma

Cross sectional slices are the same

Large

• Flux Tubes: longitudinal fields early on

• Tubesquarks+gluons

• Correlated Particles come from the same tube

• Causally disconnected

Flux Tubes and Glasma

• Single flux tube: phase space density of gluons

• Flux tube transverse size

• Number of flux tubes

•Gluon rapidity density

Kharzeev & Nardi:

Flux Tubes and the Correlation Function

• Partons from the same tube are correlated

• Correlations between tubes are negligible

Assume:

flux tube transverse size ~ Qs

-1 << RA

correlation strength

pair density n2 single particle density n1

• Correlation function:

Correlation Strength

• Long range glasma fluctuations scale the phase space density

• Energy and centrality dependence of correlation strength

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

• Correlation Strength

Flow and Azimuthal Correlations

Fluid cells

STAR soft ridgeFireball cross section at freeze out

r

from Lanny Ray, RHIC & AGS User’s Meeting, ‘08

• Mean flow depends on position

• Opening angle for each fluid element depends on r

Blast Wave and Correlation Function

Schnedermann, Sollfrank & Heinz

• Single Particle Spectrum

• Cooper Frye Freeze Out Surface

• Pair Spectrum

• Boltzmann Distribution

Blast Wave and Correlation Function

• Correlation Function

Glasma + Blast Wave

0

0.2

0.4

0.6

0.8

1

1 2 3 4 5 6

Blast Wave (with correlations)

STAR 200 GeV

Peak Amplitude 200 GeV

STAR measures: We calculate:

• v and T from Blast Wave

• Scaled to fit 200 GeV

• Glasma Qs dependence

200GeV62GeV

Akio Kiyomichi, PHENIX

Glasma Energy Dependence

• v and T from Blast Wave

• Scaled to fit 200 GeV

• Glasma Qs dependence

200GeV62GeV

Akio Kiyomichi, PHENIX

Angular Correlations

0

0.2

0.4

0.6

0 0.5 1 1.5 2

computed angular width is approximately independent of energy

Peak Width

• Fit using Gaussian + offset

• Range:

• Error band: 20% shift in fit range

Summary

Long Range Correlation Measurements

• PHOBOS: may extend to large rapidity

• STAR: measurements in a smaller range

Blast Wave + Glasma

• Describes amplitude and azimuthal width

• Glasma energy and centrality dependence