1. 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 Q s Dependence Blast Wave + Correlations Transverse Flow Glasma + Flow Comparison to STAR

2. PHOBOS: High p t Triggered Ridge from Edward Wenger, RHIC & AGS User’s Meeting, ‘08

3. PHOBOS: High p t Triggered Ridge from Edward Wenger, RHIC & AGS User’s Meeting, ‘08

4. PHOBOS: High p t Triggered Ridge from Edward Wenger, RHIC & AGS User’s Meeting, ‘08 long range correlations

5. PHOBOS: Untriggered Ridge from Edward Wenger, RHIC & AGS User’s Meeting, ‘08 soft ridge with very long range in rapidity? caution: v 2 not yet removed

6. 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

7. STAR: Soft Ridge Medium range correlations…implications for long range? from Lanny Ray, RHIC & AGS User’s Meeting, ‘08 Peak AmplitudePeak η WidthPeak φ Width near side peak v 2 and experimental effects subtracted peak height and azimuthal width not the rapidity width -- structure too narrow Gavin + Abdel-Aziz; Gavin + Pokharel + Moschelli peripheralcentral

8. 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

9. Flux Tubes and Glasma Cross sectional slices are the same Large  Flux Tubes: longitudinal fields early on Tubes  quarks+gluons Correlated Particles come from the same tube Causally disconnected

10. 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:

11. Flux Tubes and the Correlation Function Partons from the same tube are correlated Correlations between tubes are negligible Assume: flux tube transverse size ~ Q s -1 << R A correlation strength pair density n 2 single particle density n 1 Correlation function:

12. 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

13. Flow and Azimuthal Correlations Fluid cells STAR soft ridge Fireball 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

14. Blast Wave and Correlation Function Schnedermann, Sollfrank & Heinz Single Particle Spectrum Cooper Frye Freeze Out Surface Pair Spectrum Boltzmann Distribution

15. Blast Wave and Correlation Function Correlation Function

16. Glasma + Blast Wave 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 Q s dependence 200GeV  62GeV Akio Kiyomichi, PHENIX

17. Glasma Energy Dependence v and T from Blast Wave Scaled to fit 200 GeV Glasma Q s dependence 200GeV  62GeV Akio Kiyomichi, PHENIX

18. Angular Correlations computed angular width is approximately independent of energy Peak  Width Fit using Gaussian + offset Range: Error band: 20% shift in fit range

19. 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