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Roy Lacey & Paul Chung Nuclear Chemistry, SUNY, Stony Brook

Evidence for a long-range pion emission source in Au+Au collisions at. Roy Lacey & Paul Chung Nuclear Chemistry, SUNY, Stony Brook. Increased System Entropy that survives hadronization. hadronic phase and freeze-out. QGP and hydrodynamic expansion. initial state. pre-equilibrium.

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Roy Lacey & Paul Chung Nuclear Chemistry, SUNY, Stony Brook

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  1. Evidence for a long-range pion emission source in Au+Au collisions at Roy Lacey & Paul Chung Nuclear Chemistry, SUNY, Stony Brook

  2. Increased System Entropy that survives hadronization hadronic phase and freeze-out QGP and hydrodynamic expansion initial state pre-equilibrium hadronization Expectation: A strong first order phase transition leads to an emitting system characterized by a much larger space-time extent thanwould be expected from a system which remained in the hadronic phase Motivation Conjecture of collisions at RHIC : Courtesy S. Bass Guiding philosophy in first few years at RHIC = Puzzle ?

  3. What do we know now ?Any Implications for HBT ?

  4. What do we know ? Extrapolation From ET Distributions Flow thermalization time (t0 ~ 0.2 – 1 fm/c) eBj~ 5 – 15 GeV/fm3

  5. v2 scales with eccentricity and across system size Strong Evidence for Thermalization and hydro scaling What do we know ? PHENIX Preliminary PHENIX Preliminary

  6. Scaling breaks Baryons scale together Mesons scale together Perfect fluid hydro Scaling holds up to ~ 1 GeV What do we know ? PHENIX preliminary data Strong hydro scaling with hint of quark degrees of freedom

  7. Scaling holds over the whole range of KET Compatible with Valence Quark degrees of freedom What do we know ? PHENIX preliminary data Scaling works

  8. What do we know ? Oh yes - It is Comprehensive !

  9. T. Renk, J. Ruppert hep-ph/0509036 What do we know ? Away-side peak consistent with mach-cone scenario nucl-th/0406018 Stoecker hep-ph/0411315 Casalderrey-Solana, et al other explanations ! nucl-ex/0507004 Strong centrality dependent modification of away-side jet in Au+Au Implication for viscosity and sound speed !

  10. A Small digression High pT particle Associated pt particles Simulated Result View associated particles in frame with high pT direction as z-axis Yes ! We have results

  11. Compatible with soft EOS What do we know ? Sound Speed Estimate cs ~ 0.35 Soft EOS F. Karsch, hep-lat/0601013 Sound speed is not zero during an extended hadronization period. Space-time evolution more subtle ?

  12. Subtle signals require a paradigm shift Extract the full source function

  13. Extraction of Source functions Imaging & Fitting Moment Expansion

  14. Emitting source Imaging Technique Technique Devised by: D. Brown, P. Danielewicz, PLB 398:252 (1997).PRC 57:2474 (1998). Inversion of Linear integral equation to obtain source function 1D Koonin Pratt Eqn. Encodes FSI Source function (Distribution of pair separations) Correlation function Inversion of this integral equation == Source Function Well established inversion procedure

  15. Correlation Fits [Theoretical correlation function] convolute source function with kernel (P. Danielewicz) Measured correlation function Minimize Chi-squared Parameters of the source function

  16. Quick Test with simulated source Input source function recovered Procedure is Robust !

  17. Experimental Results Gaussian Source functions do not provide good fits

  18. Source functions from spheroid or Gaussian + Exponential give good fit. 1D Source imaging • Source function tail is not due to: • Kinematics • Resonance contributions PHENIX Preliminary Evidence for long-range source at RHIC

  19. PHENIX Preliminary kinematics Centrality dependence also incompatible with resonance decay

  20. Pair fractions associated with long- and short-range structures Core Halo assumption T. Csorgo M. Csanad Expt  Contribution from decay insufficient to account for long-range component. Full fledge simulation indicate similar conclusion

  21. Experimental Results A hint of the shape of things to come

  22. 3D Analysis Basis of Analysis (Danielewicz and Pratt nucl-th/0501003 (v1) 2005) Expansion of R(q) and S(r) in Cartesian Harmonic basis 3D Koonin Pratt (3) Plug in (1) and (2) into (3) (1) (2)

  23. Calculation of Correlation Moments: Fitting with truncated expansion series ! 6 independent moments (a)

  24. A look at the basis L=0 L=2

  25. Strategy Get values of Such that Fit with moments as fitting parameters.

  26. Strategy With

  27. input Simulation tests of the method • Procedure • Generate moments for • source. • Carryout simultaneous • Fit of all moments output Very clear proof of principle

  28. Results - moments Very good agreement as it should

  29. Results - moments Sizeable signals observed for l = 2 Exquisite/Robust Results

  30. Results - moments l= 4 moments Exquisite/Robust Results

  31. Extensive study of two-pion source • images and moments in Au+Au collisions at RHIC • First observation of a long-range source having an • extension in the out direction for pions • Long-range source not due to • kinematics or resonances Further Studies underway to quantify A variety of other source functions! Much more to come !

  32. Comparison of Source Functions Source functions from spheroid and Gaussian + Exponential are in excellent agreement  need 3D info

  33. PHENIX Preliminary 3D Source imaging Origin of deformation Kinematics ? or Time effect • Instantaneous • Freeze-out • LCMS implies kinematics • PCMS implies time effect Deformed source in pair cm frame:

  34. PHENIX Preliminary 3D Source imaging • Isotropic emission in the • pair frame Spherically symmetric source in pair cm. frame (PCMS)

  35. Short and long-range components of the source T. Csorgo M. Csanad Short-range  Long-range 

  36. New 3D Analysis • 1D analysis  angle averaged C(q) & S(r) info only • no directional information • Need 3D analysis to access directional information Correlation and source moment fitting and imaging

  37. 3D Analysis How to calculate correlation function and Source function in any direction Source function/Correlation function obtained via moment summation

  38. Short and long-range components of the source T. Csorgo M. Csanad

  39. Extraction of Source Parameters Fit Function (Pratt et al.) Radii Pair Fractions Bessel Functions This fit function allows extraction of both the short- and long-range components of the source image

  40. Outline • Motivation • Brief Review of Apparatus & analysis technique • 1D Results • Angle averaged correlation function • Angle averaged source function • 3D analysis • Correlation moments • Source moments • Conclusion/s

  41. Imaging Inversion procedure

  42. Fitting correlation functions Kinematics “Spheroid/Blimp” Ansatz Brown & Danielewicz PRC 64, 014902 (2001)

  43. Cuts Dphi (rad) Dz (cm)

  44. Cuts Dphi (rad) Dz (cm)

  45. Two source fit function This is the single particle distribution

  46. Two source fit function This is the two particle distribution

  47. Experimental Setup PHENIX Detector Several Subsystems exploited for the analysis Excellent Pid is achieved

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