DENSITY FLUCTUATIONS AND TWO-PARTICLE CORRELATIONS ⎯⎯⎯⎯⎯ AND THE RISE AND FALL OF THE RIDGE

1. distributions and correlations of produced particles kinetic freeze-out hadronization lumpy initial energy density QGP phase quark and gluon degrees of freedom DENSITY FLUCTUATIONS AND TWO-PARTICLE CORRELATIONS ⎯⎯⎯⎯⎯ AND THE RISE AND FALL OF THE RIDGE Paul Sorensen Brookhaven National LabOratory P. S., B. Bolliet, A. Mocsy, Y. Pandit, N. Pruthi, arXiv:1102.1403

2. Initial Gluon Density In CGC for example, an effective field theory for QCD, this is a transverse projection of the gluon density Gluons are localized around valence charges in the nuclei x=10-5 x=10-3 H. Kowalski, T. Lappi and R. Venugopalan, Phys.Rev.Lett. 100:022303 The initial state is inhomogenous: a likely source of final-state correlations • S. Voloshin, Phys.Lett.B632:490-494,2006 • A.P. Mishra, R. K. Mohapatra, P. S. Saumia, A. M. Srivastava, Phys. Rev. C77: 064902, 2008 • C.Pruneau, S. Gavin, S. Voloshin, Nucl. Phys. A802:107-121,2008

3. Initial to Final State distributions and correlations of produced particles kinetic freeze-out hadronization lumpy initial density Do initial spatial correlations manifest as hotspots in final momentum correlations?

4. distributions and correlations of produced particles kinetic freeze-out hadronization lumpy initial energy density QGP phase quark and gluon degrees of freedom Credit: NASA Analogy with the Early Universe RHIC The Universe WMAP HIC

5. distributions and correlations of produced particles kinetic freeze-out hadronization lumpy initial energy density QGP phase quark and gluon degrees of freedom Credit: NASA Analogy with the Early Universe RHIC The Universe WMAP RHIC

6. distributions and correlations of produced particles kinetic freeze-out hadronization lumpy initial energy density QGP phase quark and gluon degrees of freedom Credit: NASA Analogy with the Early Universe RHIC The Universe WMAP WMAP RHIC

7. distributions and correlations of produced particles kinetic freeze-out hadronization lumpy initial energy density QGP phase quark and gluon degrees of freedom Credit: NASA Analogy with the Early Universe RHIC The Universe Δρ/√ρref Δφ WMAP RHIC

8. distributions and correlations of produced particles kinetic freeze-out hadronization lumpy initial energy density QGP phase quark and gluon degrees of freedom Credit: NASA Analogy with the Early Universe RHIC The Universe Δρ/√ρref Δφ WMAP RHIC

9. lmfp lmfp Relationship to Viscous Effects How much of the initial inhomogeneity is transferred to the final state? Spherical harmonic expansion of CMB sum l Higher harmonics probe smaller length-scales. Fourier expansion of HIC n=2 n=3 n=4 n=10 n=15 Efficiency of conversion depends on relation of various length scales like lmfp to the scale probed at n

10. Length Scale: Pixel Size ℓmfp Mean free path sets the resolution scale (1/n) or pixel size 10

11. Length Scale: Pixel Size 11

12. Length Scale: Pixel Size 12

13. Length Scale: Pixel Size 13

14. Length Scale: Pixel Size 14

15. Length Scale: Pixel Size Higher harmonics probe finer detail. Is there any detail there? 15

16. Characterizing the Initial Eccentricity Broniowski, Bozek, & Rybczynski: Phys. Rev. C76: 054905, 2007 PHOBOS: Phys. Rev. C77: 014906,2008 Alver and Roland: Phys. Rev. C81: 054905, 2010 • The eccentricity calculation is approximately a random walk. • Each participant represents a step • The distribution of eccentricity will end up as a 2-D gaussian. • The shift in x is the standard eccentricity • The number of steps determines the width • For odd n, the shift is zero • But participant eccentricity considers the length of the eccentricity vector which is positive definite, even for n=1,3,5,7…

17. Eccentricity and Length Scales We can introduce a length scale by smearing out the participants Monte Carlo Glauber rpart P. S., B. Bolliet, A. Mocsy, Y. Pandit, N. Pruthi, arXiv:1102.1403 Smearing out the participants washes out the higher harmonics Ideal case only retains curvature due to correlations in the Glauber Model

18. Eccentricity and Two-particle Correlations If vn2 = cn〈ε2n,part〉, a Gaussian will appear in 2-particle correlations vs Δφ Width in Δφ is inversely related to width in n and the length scale  P. S., B. Bolliet, A. Mocsy, Y. Pandit, N. Pruthi, arXiv:1102.1403 Gaussian width depends on the variation of the transfer function cn with n Shift to center of mass 〈x〉=〈y〉=0 means 〈ε1,part〉≈0. This leads to a negative cos(Δφ) term which is related to the near-side amplitude

19. Observed 2-Particle Correlations central peripheral 200 GeV Au+Au Collisions STAR Preliminary ρ12 is the density of particle pairs ρ1ρ2 is the product of single particle densities Correlations show non-trivial evolution from p+p to most central Au+Au Are these related to the initial density fluctuations? What about jets, resonance decays, cluster formation, several possible sources…

20. Centrality Dependence: Rise and Fall STAR Preliminary A1 σφΔ σηΔ AD STAR Preliminary Both collision energies show a rise and fall for A1 and AD

21. The Away-side Amplitude Shift to center of mass 〈x〉=〈y〉=0 means 〈ε1,part〉≈0. This leads to a negative cos(Δφ) term which is related to the near-side amplitude: data exhibit just this trend.

22. Estimate of the Amplitude 1) take conversion efficiency from c=(v2/ε2)2 2) take initial eccentricity from Monte-Carlo Glauber 3) convert <cos(3Δφ)> into equivalent Gaussian Amplitude prediction for “minijet” amplitude from density fluctuations

23. Are 2-particle Correlations Dominated by the Initial State Density Fluctuations? Model based on ansatz that initial density is converted into 2 particle correlations: conversion efficiency increases with density initial eccentricities Amplitude estimate agrees reasonably well with the data. Exhibits a rise and fall: where does that feature come from?

24. Rise and Fall and the Almond Shape See D. Teaney, L. Yan, arXiv:1010.1876v1 Triangular fluctuations increase in non-symmetric overlaps fluctuations for lower harmonics are highly non-statistical and depend on elliptic geometry excess from ellipse eccentricity scaled eccentricity statistical P. S., B. Bolliet, A. Mocsy, Y. Pandit, N. Pruthi, arXiv:1102.1403 • Linking the final-state correlations to initial density fluctuations • When the collision becomes spherical, the coupling subsides • This leads to the rise and fall: a feature unique to this explanation

25. Rise and Fall and the Almond Shape Triangular fluctuations are driven by edge effects: one nucleon near the edge of nucleus A can impinge on many nucleons in the center of nucleus B. Effect depends on the Woods-Saxon diffuseness parameter. a = 0.535: standard 197Au Woods-Saxon parameter a = 0: sharp edge ρ(r) r

26. Rise and Fall and the Almond Shape See D. Teaney, L. Yan, arXiv:1010.1876v1 Lowest order fluctuations couple to higher orders: In this sketch a rightward shift couples with the ellipse to produce a triangular fluctuation How I learned to stop worrying (about minijets) and love vn ellipse couples most strongly to nearby harmonics excess from ellipse eccentricity scaled eccentricity statistical P. S., B. Bolliet, A. Mocsy, Y. Pandit, N. Pruthi, arXiv:1102.1403 • Linking the final-state correlations to initial density fluctuations • When the collision becomes spherical, the coupling subsides • This leads to the rise and fall: a feature unique to this explanation

27. LHC Predictions A1 will be several times larger at the LHC: driven by increased multiplicity and flow ALICE: Phys. Rev. Lett. 105, 252302 (2010) STAR: Phys. Rev. C 72, 014904 (2005) Fit function Drescher, et. al. Phys. Rev. C 76:024905, 2007 P. S., B. Bolliet, A. Mocsy, Y. Pandit, N. Pruthi, arXiv:1102.1403 Prediction: rise and fall of the ridge will be present at all energies: it’s a feature of the overlap geometry

28. LHC Predictions A1 will be several times larger at the LHC: driven by increased multiplicity and flow A. Timmins, QM2011 Prediction confirmed by ALICE at QM 2011

29. All The Terms STAR Preliminary Rise and Fall A1 σφΔ Viscous Effects σηΔ AD STAR Preliminary

30. All The Terms STAR Preliminary Rise and Fall CM Shift A1 σφΔ Viscous Effects σηΔ AD STAR Preliminary What can we learn from the longitudinal dependence

31. Longitudinal Dependence Wide STAR Preliminary STAR Preliminary 50-60% STAR Preliminary Wide Gaussian 10-20% Narrow Gaussian STAR Preliminary σ≈2 is indistinguishable from linear within acceptance Initial state density correlations may drop with Δy: interesting physics σΔy~1/αs? Fit with a wide and a narrow peak. Wide peak amplitude first drops with 1/N but then deviates from trend near Npart=50. Above that it follows an Npartε23,part trend Dusling, Gelis, Lappi & Venugopalan, Nucl. Phys. A 836, 159 (2010) Petersen, Greiner, Bhattacharya & Bass, arXiv:1105.0340

32. Conclusions • High precision correlations data reveal information similar to CMB analysis: • Data consistent with correlations in the initial overlap geometry converted into momentum space • Fine structure is washed out and large scale structure persists • Non central collisions induce larger fluctuations explaining the centrality dependence of the ridge: • A clear demonstration of the role of density fluctuations in the development of the ridge • Heavy Ion Collisions act as a femto-scope, revealing the structure in the initial conditions! • Longitudinal dependence still needs comprehensive study

33. Density Fluctuations➙2p Correlations NexSPheRIO: J.Takahashi, B.M.Tavares, W.L.Qian, F.Grassi, Y.Hama, T.Kodama and N.X The gluon density at small x seen by a di-quark IPsat GCG • A partial reference list: • S. Voloshin, Phys.Lett.B632:490-494,2006 • A.P. Mishra, R. K. Mohapatra, P. S. Saumia, A. M. Srivastava, Phys. Rev. C77: 064902, 2008 • C.Pruneau, S. Gavin, S. Voloshin, Nucl. Phys. A802:107-121,2008 • P. Sorensen, arXiv:0808.0503 WWND Proc. • A. Dumitru, F. Gelis, L. McLerran, R. Venugopalan, T. Lappi, Nucl.Phys.A810:91-108,2008; S. Gavin, L. McLerran, G. Moschelli, Phys.Rev.C79:051902,2009 • J.Takahashi, B.M.Tavares, W.L.Qian, F.Grassi, Y.Hama, T.Kodama and N.Xu • P. Sorensen, J. Phys. G37: 094011, 2010 • B. Alver, G. Roland Phys. Rev. C81:054905, 2010 • B. Alver, C. Gombeaud, M. Luzum. J-Y. Ollitrault, Phys. Rev. C82: 034913, 2010 • H. Petersen, G-Y. Qin, S. Bass, B. Muller, Phys. Rev. C 82: 041901, 2010 • A. Mocsy, P. Sorensen, arXiv:1008.3381 [hep-ph] • G-Y. Qin, H. Petersen, S. Bass, B. Muller, arXiv:1009.1847 [nucl-ex] • D. Teaney, L. Yan, arXiv:1010.1876 [nucl-th]

34. The Widths Length scales like rpart, lmfp, cτfs, the acoustic horizon, width of thermal broadening all suppress higher harmonics and broaden the Δφ width A full dynamic model will be needed to disentagle various effects

35. Relationship of the cos(Δφ) Term to the Gaussian no C.M. shift n=1 restored -cos(Δφ) term should have the same centrality dependence as the near-side peak (as seen in data) -cos(Δφ) comes from the Gaussian shape of 〈ε2n,part〉 with the n=1 term removed (momentum conservation)

36. Calculating the -cos(Δφ) Term  For a Gaussian, we can calculate the magnitude of the n=1 term that is removed by shifting to the C.O.M. This will be the magnitude of the –cos term

37. Further Predictions: Ridge at High pT Any mechanism causing space-momentum correlations (eg. quenching, flow) will give rise to higher vn terms The jet picks up v2, v3, v4… from quenching (jet tomography) A low or intermediate pT particle picks up v2, v3, v4 from flow The ridge structure arises from where the drop of vn with n is sensitive to the length-scales relevant in the different kinematic ranges (q-hat, viscosity…) This does not require the jet to be from the same flux tube as the associated particle, only that vnquenchand vnflow are each sensitive to the geometry The width can be quite narrow