long range correlations and the soft ridge
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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
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