1. Roy A. Lacey, Stony Brook; 24 th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 1 Roy A. Lacey Prospects for locating the QCD Critical End Point (CEP) Source Imaging Using RHIC Data

2. Roy A. Lacey, Stony Brook; 24 th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 2 A Central Question of the Field? The location of the critical End point and the phase boundaries are fundamental to the QCD phase diagram !

3. Roy A. Lacey, Stony Brook; 24 th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 3 Theoretical Guidance ? Any search for the CEPrequires investigations Any search for the CEP requires investigations over a broad range of μ & T. Freeze out Curve Theoretical Predictions For the CEP

4. Roy A. Lacey, Stony Brook; 24 th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 4 For the first time (at last) we have access to the full range Of μ and T. (via Energy scans at RHIC, SPS & FAIR)

5. Roy A. Lacey, Stony Brook; 24 th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 5 The Crossover is a necessary requirement for locating the CEP 1)The Crossover Transition to the QGP is made clear at RHIC Space-time measurements Flow Measurements Jet Quenching Better News ! 2) Viscosity Measurements offer a new dynamical probe for the CEP Contrasts Stationary State variables

6. Roy A. Lacey, Stony Brook; 24 th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 6 Courtesy S. Bass initial state pre-equilibrium QGP and hydrodynamic expansion hadronization hadronic phase and freeze-out hadronization Are source Imaging measurements consistent with the crossover transition ? A Cross Over strongly affects the Space-time Dynamics Theory indicate a crossover transition The space-time extent (Source Image) can lend crucial insights Puzzle ? The Space-Time probe

7. Roy A. Lacey, Stony Brook; 24 th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 7 Discretize Integral Source Imaging Methodology (1D) Source function (Distribution of pair separations) Encodes FSI Correlationfunction Inversion of this integral equation  Source Function 1D Koonin Pratt Eqn. Brown & Danielewicz PRC 57(98)2474 Direct Fit Vary S(r j ) to minimize Reliable measurement of the full 1D Source Function !

8. Roy A. Lacey, Stony Brook; 24 th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 8 Source Imaging Methodology (3D) 3D Koonin Pratt Eqn. Expand R(q) and S(r) in Cartesian Harmonic basis (Danielewicz and Pratt nucl-th/0501003) Reliable measurement of the full Source Function in 3D ! Substitute (2) and (3) into (1) The 3D integral equation is reduced to a set of 1D relations for different l coefficients  moments

9. Roy A. Lacey, Stony Brook; 24 th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 9 Correlation Moments Robust Experimental Source Functions obtained from moments PHENIX Data Contributions from l > 6 is negligible

10. Roy A. Lacey, Stony Brook; 24 th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 10 Source Function Comparison to Models Give robust life time estimates  Consistent with Crossover transition Therminator: A.Kisiel et al. Comput.Phys.Commun.174, 669 (2006) Thermal model with Bjorken longitudinal expansion and transverse Flow Spectra & yields constrain thermal properties Transverse radius ρ max : controls transverse extent Breakup time in fluid element rest frame, : controls longitudinal extent Emission duration : controls tails in long and out directions a controls x-t correlations The transition is Not a Strong First order Phase Transition? The transition is Not a Strong First order Phase Transition?

11. Roy A. Lacey, Stony Brook; 24 th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 11 From E T Distributions Expect Large Pressure Gradients  Hydro Flow The Flow Probe Control Params.

12. Roy A. Lacey, Stony Brook; 24 th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 12 initial state pre-equilibrium QGP and hydrodynamic expansion hadronization hadronic phase and freeze-out Courtesy S. Bass We hold these truths to be self evident ! Scaling for identified hadrons Scaling for Heavy Quark Scaling for Phi Mesons Universal Scaling

13. Roy A. Lacey, Stony Brook; 24 th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 13 F. Karsch, hep-lat/0601013 Saturation of Elliptic flow consistent with a soft EOS associated with Crossover The expected saturation of v 2 Is observed The expected saturation of v 2 Is observed Phys.Rev.Lett.94:232302,2005

14. Roy A. Lacey, Stony Brook; 24 th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 14 The prediction for thermalization is explicit and specific Hexadecapole Flow (v 4 ) As a predictor of Thermalization Hexadecapole Flow (v 4 ) As a predictor of Thermalization v 4 /(v 2 ) 2 0.5-0.61.0

15. Roy A. Lacey, Stony Brook; 24 th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 15 The prediction for thermalization is explicit and specific Hexadecapole Flow (v 4 ) As a predictor of Thermalization Hexadecapole Flow (v 4 ) As a predictor of Thermalization v4v4 PHENIX Preliminary

16. Roy A. Lacey, Stony Brook; 24 th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 16 initial state pre-equilibrium QGP and hydrodynamic expansion hadronization hadronic phase and freeze-out Courtesy S. Bass The ratio of the harmonics for quarks is compatible with hydrodynamic prediction Scaling for Higher Harmonics

17. Roy A. Lacey, Stony Brook; 24 th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 17 ModelComparison Transport Coefficient Estimates - I 1-2 X the conjectured lower bound

18. Roy A. Lacey, Stony Brook; 24 th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 18 Transport Coefficient Thermalization facilitated by 2  3 processes C. Greiner et al

19. Roy A. Lacey, Stony Brook; 24 th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 19 x10 x20 QCD Sonic Boom Same-Side Jet High pT trigger Gives sound speed directly; Sets upper limit on viscosity. Setting an upper limit on The viscosity Setting an upper limit on The viscosity

20. Roy A. Lacey, Stony Brook; 24 th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 20 Data The data is compatible with the presence of a Mach Cone away-side jet Total 3PC jet correlations True 3PC jet correlations QCD Sonic Boom?

21. Roy A. Lacey, Stony Brook; 24 th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 21 is a potent signal for the CEP is a potent signal for the CEP CEP Search Lacey et al. arXiv:0708.3512 [nucl-ex]

22. Roy A. Lacey, Stony Brook; 24 th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 22 Nonaka et al. is a potent signal for the CEP is a potent signal for the CEP CEP Search Meyer Kharzeev-Tuchin

23. Roy A. Lacey, Stony Brook; 24 th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 23 are a potent signals for the CEP are a potent signals for the CEP How to find the CEP? First estimate T ~ 165-170 μ ~ 120-150 MeV Need two energies immediately Meyer Kharzeev-Tuchin

24. Roy A. Lacey, Stony Brook; 24 th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 24 Epilogue  Strong evidence for crossover to the QGP at RHIC. –Short emission lifetimes –Matter quenches Jets and flows as a (nearly) perfect fluid with systematic patterns consistent with quark degrees of freedom. –Matter has a soft EOS and a shear viscosity to entropy density ratio lower than any other known fluid -- a value close to the conjectured quantum bound –Corresponding bulk viscosity to entropy density is large Extracted Transport Coefficients Suggest Decay Trajectories close to the Critical End Point (CEP) Energy scans now required to do the trick !! First estimate T ~ 165 μ ~ 120 -150 MeV Need two energies immediately

25. Roy A. Lacey, Stony Brook; 24 th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 25 F. Karsch, hep-lat/0601013 v 2 /ε for ~ 0.45 GeV/cc s ~ 0.35 ± 0.05 (c s 2 ~ 0.12), so ft EOS See nucl-ex/0604011 for details The EOS is harder than that for the hadron gas but softer than for the hard QGP  no strong first order phase transition Hydro Calculations (Bhalerao et al.) The EOS of the Partonic Fluid is Soft The EOS of the Partonic Fluid is Soft

26. Roy A. Lacey, Stony Brook; 24 th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 26

27. Roy A. Lacey, Stony Brook; 24 th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 27 initial state pre-equilibrium QGP and hydrodynamic expansion hadronization hadronic phase and freeze-out Courtesy S. Bass A Crossover transition to the strongly coupled thermalized QGP occurs at RHIC We hold these truths to be self evident !