1. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 1 Azimuthally-sensitive HBT in STAR Mike Lisa Ohio State University Motivation Noncentral collision dynamics Azimuthally-sensitive interferometry & previous results STAR results Hydrodynamic predictions for RHIC and “LHC” Summary

2. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 2 Central collision dynamics @ RHIC Hydrodynamics reproduces p-space aspects of particle emission up to p T ~2GeV/c (99% of particles)  hopes of exploring the early, dense stage Heinz & Kolb, hep-th/0204061

3. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 3 Central collision dynamics @ RHIC Hydrodynamics reproduces p-space aspects of particle emission up to p T ~2GeV/c (99% of particles)  hopes of exploring the early, dense stage x-space is poorly reproduced model source lives too long and disintegrates too slowly? Correct dynamics signatures with wrong space-time dynamics? Heinz & Kolb, hep-th/0204061 Turn to richer dynamics of non-central collisions for more detailed information

4. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 4 hydro evolution Dynamical models: x-anisotropy in entrance channel  p-space anisotropy at freezeout magnitude depends on system response to pressure Noncentral collision dynamics hydro reproduces v 2 (p T,m) (details!) @ RHIC for p T < ~1.5 GeV/c system response  EoS early thermalization indicated Heinz & Kolb, hep-ph/0111075

5. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 5 hydro evolution later hadronic stage? hydro reproduces v 2 (p T,m) (details!) @ RHIC for p T < ~1.0 GeV/c system response  EoS early thermalization indicated Effect of dilute stage dilute hadronic stage (RQMD): little effect on v 2 @ RHIC Teaney, Lauret, & Shuryak, nucl-th/0110037

6. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 6 hydro evolution later hadronic stage? hydro reproduces v 2 (p T,m) (details!) @ RHIC for p T < ~1.5 GeV/c system response  EoS early thermalization indicated Effect of dilute stage dilute hadronic stage (RQMD): little effect on v 2 @ RHIC significant (bad) effect on HBT radii calculation: Soff, Bass, Dumitru, PRL 2001 STAR PHENIX hydro only hydro+hadronic rescatt

7. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 7 hydro evolution later hadronic stage? hydro reproduces v 2 (p T,m) (details!) @ RHIC for p T < ~1.5 GeV/c system response  EoS early thermalization indicated Effect of dilute stage dilute hadronic stage (RQMD): little effect on v 2 @ RHIC significant (bad) effect on HBT radii related to timescale? - need more info Teaney, Lauret, & Shuryak, nucl-th/0110037

8. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 8 hydro evolution later hadronic stage? hydro reproduces v 2 (p T,m) (details!) @ RHIC for p T < ~1.5 GeV/c system response  EoS early thermalization indicated Effect of dilute stage dilute hadronic stage (RQMD): little effect on v 2 @ RHIC significant (bad) effect on HBT radii related to timescale? - need more info qualitative change of freezeout shape!! important piece of the puzzle! in-plane- extended out-of-plane-extended Teaney, Lauret, & Shuryak, nucl-th/0110037

9. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 9 Possible to “see” via HBT relative to reaction plane?  p =0°  p =90° R side (large) R side (small) for out-of-plane-extended source, expect large R side at 0  small R side at 90  2 nd -order oscillation R s 2 [no flow expectation] pp

10. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 10 “Traditional HBT” - cylindrical sources KK R out R side Decompose q into components: q Long : in beam direction q Out : in direction of transverse momentum q Side :  q Long & q Out (beam is into board)

11. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 11 Anisotropic sources  Six HBT radii vs  Source in b-fixed system: (x,y,z) Space/time entangled in pair system (x O,x S,x L ) out pp b KK side x y ! explicit and implicit (x  x (  )) dependence on  Wiedemann, PRC57 266 (1998).

12. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 12 Symmetries of the emission function I. Mirror reflection symmetry w.r.t. reactionplane (for spherical nuclei):  with II. Point reflection symmetry w.r.t. collision center (equal nuclei):  with Heinz, Hummel, MAL, Wiedemann, nucl-th/0207003

13. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 13 Fourier expansion of HBT radii @ Y=0 Insert symmetry constraints of spatial correlation tensor into Wiedemann relations and combine with explicit  -dependence: Note: These most general forms of the Fourier expansions for the HBT radii are preserved when averaging the correlation function over a finite, symmetric window around Y=0. Relations between the Fourier coefficients reveal interplay between flow and geometry, and can help disentangle space and time Heinz, Hummel, MAL, Wiedemann, nucl-th/0207003

14. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 14 x out x side K Anisotropic HBT results @ AGS (  s~2 AGeV)  p (°) 0180 0 0 0 10 -10 20 40 R 2 (fm 2 ) outsidelong ol os sl Au+Au 2 AGeV; E895, PLB 496 1 (2000) strong oscillations observed lines: predictions for static (tilted) out-of-plane extended source  consistent with initial overlap geometry  p = 0°

15. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 15 x out x side K Meaning of R o 2 (  ) and R s 2 (  ) are clear What about R os 2 (  ) ?  p (°) 0180 0 0 0 10 -10 20 40 R 2 (fm 2 ) outsidelong ol os sl Au+Au 2 AGeV; E895, PLB 496 1 (2000) R os 2 (  ) quantifies correlation between x out and x side No correlation (tilt) b/t between x out and x side at  p =0° (or 90°) K x out x side K x out x side K x out x side K x out x side K x out x side K x out x side  p = 0°  p ~45° Strong (positive) correlation when  p =45° Phase of R os 2 (  ) oscillation reveals orientation of extended source No access to 1 st -order oscillations in STAR Y1

16. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 16 Indirect indications of x-space anisotropy @ RHIC v 2 (p T,m) globally well-fit by hydro-inspired “blast-wave” STAR, PRL 87 182301 (2001) soliddashed 0.04  0.010.09  0.02  a (c) 0.04  0.01 0.0S2S2 0.54  0.030.52  0.02  0 (c) 100  24135  20 T (MeV) temperature, radial flow consistent with fits to spectra anisotropy of flow boost spatial anisotropy (out-of-plane extended) 

17. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 17 STAR data Au+Au 130 GeV minbias preliminary significant oscillations observed blastwave with ~ same parameters as used to describe spectra & v 2 (p T,m) additional parameters: R = 11 fm  = 2 fm/c !! full blastwave consistent with R(p T ), K- 

18. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 18 preliminary full blastwave STAR data Au+Au 130 GeV minbias significant oscillations observed blastwave with ~ same parameters as used to describe spectra & v 2 (p T,m) additional parameters: R = 11 fm  = 2 fm/c !! consistent with R(p T ), K-  no spatial anisotropy no flow anisotropy both flow anisotropy and source shape contribute to oscillations, but… geometry dominates dynamics freezeout source out-of-plane extended  fast freeze-out timescale !

19. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 19 Azimuthal HBT: hydro predictions RHIC (T 0 =340 MeV @  0 =0.6 fm) Out-of-plane-extended source (but flips with hadronic afterburner) flow & geometry work together to produce HBT oscillations oscillations stable with K T Heinz & Kolb, hep-th/0204061 (note: R O /R S puzzle persists)

20. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 20 Azimuthal HBT: hydro predictions “LHC” (T 0 =2.0 GeV @  0 =0.1 fm) In-plane-extended source (!) HBT oscillations reflect competition between geometry, flow low K T : geometry high K T : flow sign flip RHIC (T 0 =340 MeV @  0 =0.6 fm) Out-of-plane-extended source (but flips with hadronic afterburner) flow & geometry work together to produce HBT oscillations oscillations stable with K T Heinz & Kolb, hep-th/0204061

21. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 21 HBT( φ ) Results – 200 GeV Oscillations similar to those measured @ 130GeV 20x more statistics  explore systematics in centrality, k T much more to come… STAR PRELIMINARY

22. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 22 Summary Quantitative understanding of bulk dynamics crucial to extracting real physics at RHIC p-space - measurements well-reproduced by models anisotropy  system response to compression (EoS) probe via v 2 (p T,m) x-space - generally not well-reproduced anisotropy  evolution, timescale information, geometry / flow interplay Azimuthally-sensitive HBT: correlating quantum correlation with bulk correlation reconstruction of full 3D source geometry Freezeout geometry out-of-plane extended early (and fast) particle emission ! consistent with blast-wave parameterization of v 2 (p T,m), spectra, R(p T ), K-  With more detailed information, “RHIC HBT puzzle” deepens what about hadronic rescattering stage? - “must” occur, or…? does hydro reproduce  t  or not?? ~right source shape via oscillations, but misses R L (m T ) Models of bulk dynamics severely (over?)constrained

23. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 23 Backup slides follow

24. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 24 Summary Freeze-out scenario f(x,t,p) crucial to understanding RHIC physics p-space - measurements well-reproduced by models anisotropy  system response to compression probe via v 2 (p T,m) x-space - generally not well-reproduced anisotropy  evolution, timescale information Azimuthally-sensitive HBT: a unique new tool to probe crucial information from a new angle  elliptic flow data suggest x-space anisotropy  HBT R(  ) confirm out-of-plane extended source for RHIC conditions, geometry dominates dynamical effects oscillations consistent with freeze-out directly from hydro stage (???) consistent description of v 2 (p T,m) and R(  ) in blastwave parameterization challenge/feedback for “real” physical models of collision dynamics

25. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 25 RHIC  AGS Current experimental access only to second-order event-plane odd-order oscillations in  p are invisible cannot (unambiguously) extract tilt (which is likely tiny anyhow) cross-terms R sl 2 and R ol 2 vanish @ y=0  concentrate on “purely transverse” radii R o 2, R s 2, R os 2 Strong pion flow  cannot ignore space-momentum correlations (unknown) implicit  -dependences in homogeneity lengths  geometrical inferences will be more model-dependent the source you view depends on the viewing angle

26. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 26 Summary of anisotropic shape @ AGS RQMD reproduces data better in “cascade” mode Exactly the opposite trend as seen in flow (p-space anisotropy) Combined measurement much more stringent test of flow dynamics!!

27. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 27 hydro: time evolution of anisotropies at RHIC and “LHC” Heinz & Kolb, hep-th/0204061

28. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 28 Blastwave Mach II - Including asymmetries R tt Flow –Space-momentum correlations – = 0.6 (average flow rapidity) – Assymetry (periph) :  a = 0.05 Temperature – T = 110 MeV System geometry – R = 13 fm (central events) –Assymetry (periph event) s 2 = 0.05 Time: emission duration –  = emission duration analytic description of freezeout distribution: exploding thermal source

29. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 29 Sensitivity to  0 within blast-wave “Reasonable” variations in radial flow magnitude (  0 )  parallel p T dependence for transverse HBT radii 00

30. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 30 Sensitivity to  within blast-wave R S insensitive to  R O increases with p T as  increases 

31. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 31 Thermal motion superimposed on radial flow Hydro-inspired “blast-wave” thermal freeze-out fits to , K, p,   R  s E.Schnedermann et al, PRC48 (1993) 2462 T th = 107 MeV  = 0.55 preliminary M. Kaneta

32. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 32 Previous Data:  - HBT(  ) @ AGS Au(4 AGeV)Au, b  4-8 fm 6 components to radius tensor: i, j = o,s,l 1D projections,  =45° 2D projections lines: projections of 3D Gaussian fit  outsidelong C(q) E895, PLB 496 1 (2000)

33. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 33 Cross-term radii R ol, R os, R sl quantify “tilts” in correlation functions in q-space   fit results to correlation functions Lines: Simultaneous fit to HBT radii to extract underlying geometry

34. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 34 First look at centrality dependence! Hot off the presses PRELIMINARY c/o Dan Magestro

35. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 35 but their freezeout source is in-plane extended? stronger in-plane (elliptic) flow “tricks” us “dynamics rules over geometry” But is that too naïve? Hydro predictions for R 2 (  ) correct phase (& ~amplitude) of oscillations (size (offset) of R O, R S, R L still wrong) Heinz & Kolb hep-ph/0111075 retracted Feb 02

36. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 36 Experimental indications of x-space anisotropy @ RHIC soliddashed 0.04  0.010.09  0.02  a (c) 0.04  0.01 0.0S2S2 0.54  0.030.52  0.02  0 (c) 100  24135  20 T (MeV) Flow boost:  b = boost direction Meaning of  a is clear  how to interpret s 2 ? hydro-inspired blast-wave model Houvinen et al (2001) soliddashed 0.04  0.010.09  0.02  a (c) 0.04  0.01 0.0S2S2 0.54  0.030.52  0.02  0 (c) 100  24135  20 T (MeV) STAR, PRL 87 182301 (2001)

37. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 37 Ambiguity in nature of the spatial anisotroy  b = direction of the boost  s 2 > 0 means more source elements emitting in plane case 1: circular source with modulating density RMS x > RMS y RMS x < RMS y case 2: elliptical source with uniform density

38. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 38 Hydro-inspired model calculations (“blast wave”)  s 2  =0.033, T=100 MeV,  0   a  R=10 fm,  =2 fm/c consider results in context of blast wave model ~same parameters describe R(  ) and v 2 (p T,m) both elliptic flow and aniostropic geometry contribute to oscillations, but… geometry rules over dynamics R(  ) measurement removes ambiguity over nature of spatial anisotropy early version of data but message the same case 1 case 2

39. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 39 To do Get “not-preliminary” plot of experimental spectra versus hydro Get Heinz/Kolb plot of epsilon and v2 versus time (from last paper)

40. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 40 Spatial anisotropy calculation Shuryak/Teaney/Lauret define which of course is just the opposite to what, e.g. Heinz/Kolb call  : I think Raimond in some paper called the Heinz/Kolb parameter s 2 also (in analogy to v 2 ). Great…. Better still, in the BlastWave, another s2 (in Lisa-B) is related to Ry/Rx via: Anyway, if we say s 2,BW = 0.04, this corresponds to  = 1.055 (5.5% extended) which gives s 2,STL = -0.05, or  HK = +0.05 This is in the range of the H/K hydro calculation, but seems a huge number for STL ?

41. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 41 Symmetries of the emission function I. Mirror reflection symmetry w.r.t. reactionplane (for spherical nuclei):  with II. Point reflection symmetry w.r.t. collision center (equal nuclei):  with

42. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 42 Fourier expansion of spatial correlation tensor S  S n = 0 for all terms containing even powers of y C n = 0 for all terms containing odd powers of y For terms with even powers of t, S n, C n are odd (even) functions of Y for odd (even) n For terms with odd powers of t, it’s the other way around The odd functions vanish at Y=0 I  II 

43. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 43 Spatial correlation tensor @ Y=0: Symmetry Implications

44. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 44 Fourier expansion of HBT radii @ Y=0 Insert symmetry constraints of spatial correlation tensor into Wiedemann relations and combine with explicit  -dependence: Note: These most general forms of the Fourier expansions for the HBT radii are preserved when averaging the correlation function over a finite, symmetric window around Y=0.

45. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 45

46. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 46 s 2 dependence dominates HBT signal error contour from elliptic flow data color:  2 levels from HBT data STAR preliminary  s 2  =0.033, T=100 MeV,  0   a  R=10 fm,  =2 fm/c

47. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 47 Joint view of  freezeout: HBT & spectra spectra (  ) HBT common model/parameterset describes different aspects of f(x,p) Increasing T has similar effect on a spectrum as increasing  But it has opposite effect on R(p T )  opposite parameter correlations in the two analyses  tighter constraint on parameters caviat: not exactly same model used here (different flow profiles) STAR preliminary

48. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 48 Typical 1-  Error contours for BP fits Primary correlation is the familiar correlation between and radii Large acceptance  no strong correlations between radii Cross-term uncorrelated with any other parameter E895 @ AGS (QM99)

49. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 49 BP analysis with 1 z bin from -75,75 mixing those events generates artifact: too many large q L pairs in denominator bad normalization, esp for transverse radii Event mixing: z vertex issue

50. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 50 2D contour plot of the pair emission angle CF….

51. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 51 Out-of-plane elliptical shape indicated in blast wave using (approximate) values of s 2 and  a from elliptical flow case 1 case 2 opposite R(  ) oscillations would lead to opposite conclusion

52. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 52 Effect of dilute stage (RQMD) on v2 SPS and RHIC: Teaney, Lauret, & Shuryak, nucl-th/0110037

53. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 53 Hydrodynamics: good description of radial and elliptical flow at RHIC data: STAR, PHENIX, QM01 model: P. Kolb, U. Heinz RHIC; p t dependence quantitatively described by Hydro Charged particles good agreement with hydrodynamic calculation

54. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 54 Hydrodynamics: problems describing HBT out side long K T dependence approximately reproduced  correct amount of collective flow R s too small, R o & R l too big  source is geometrically too small and lives too long in model Right dynamic effect / wrong space-time evolution?  the “RHIC HBT Puzzle” generic hydro

55. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 55 “Realistic” afterburner does not help… pure hydro hydro + uRQMD STAR data 1.0 0.8 Currently, no “physical” model reproduces explosive space-time scenario indicated v 2, HBT R O /R S

56. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 56 Now what? No dynamical model adequately describes freeze-out distribution Seriously threatens hope of understanding pre-freeze-out dynamics Raises several doubts –is the data “consistent with itself” ? (can any scenario describe it?) –analysis tools understood?  Attempt to use data itself to parameterize freeze-out distribution Identify dominant characteristics Examine interplay between observables “finger physics”: what (essentially) dominates observations? Isolate features generating discrepancy with “real” physics models

57. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 57 Characterizing the freezeout: An analogous situation

58. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 58 Probing f(x,p) from different angles Transverse spectra: number distribution in m T Elliptic flow: anisotropy as function of m T HBT: homogeneity lengths vs m T,  p

59. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 59 m T distribution from Hydrodynamics-inspired model E.Schnedermann et al, PRC48 (1993) 2462 R  s Infinitely long solid cylinder  b = direction of flow boost (=  s here) 2-parameter (T,  ) fit to m T distribution

60. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 60  2 contour maps for 95.5%CL T th [GeV]  s [c] -- K-K- p T th [GeV]  s [c] T th [GeV]  s [c] T th =120+40-30MeV =0.52 ±0.06[c] tanh -1 ( ) = 0.6 = 0.8  s Fits to STAR spectra;  r =  s (r/R) 0.5 -- K-K- p 1/m T dN/dm T (a.u.) m T - m [GeV/c 2 ] thanks to M. Kaneta preliminary STAR preliminary

61. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 61 Implications for HBT: radii vs p T Assuming , T obtained from spectra fits  strong x-p correlations, affecting R O, R S differently p T =0.2 p T =0.4 y (fm) x (fm) calculations using Schnedermann model with parameters from spectra fits

62. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 62 Implications for  HBT: radii vs p T STAR data model: R=13.5 fm,  =1.5 fm/c T=0.11 GeV,  0  = 0.6 Magnitude of flow and temperature from spectra can account for observed drop in HBT radii via x-p correlations, and R o <R s …but emission duration must be small p T =0.2 p T =0.4 y (fm) x (fm) Four parameters affect HBT radii

63. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 63 Space-time asymmetry from K-  correlations Evidence of a space – time asymmetry –   -  K ~ 4fm/c ± 2 fm/c, static sphere –Consistent with “default” blast wave calculation   p T  = 0.12 GeV/c K  p T  = 0.42 GeV/c

64. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 64 Non-central collisions: coordinate- and momentum-space anisotropies Equal energy density lines P. Kolb, J. Sollfrank, and U. Heinz

65. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 65 More detail: identified particle elliptic flow soliddashed 0.04  0.010.09  0.02  a (c) 0.04  0.01 0.0S2S2 0.54  0.030.52  0.02  0 (c) 100  24135  20 T (MeV) STAR, in press PRL (2001) Flow boost:  b = boost direction Meaning of  a is clear  how to interpret s 2 ? hydro-inspired blast-wave model Houvinen et al (2001)

66. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 66 Ambiguity in nature of the spatial anisotroy  b = direction of the boost  s 2 > 0 means more source elements emitting in plane case 1: circular source with modulating density RMS x > RMS y RMS x < RMS y case 2: elliptical source with uniform density

67. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 67 case 1 using (approximate) values of s 2 and  a from elliptical flow case 2 opposite R(  ) oscillations would lead to opposite conclusion Out-of-plane elliptical shape indicated

68. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 68 A consistent picture

69. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 69 Summary Combined data-driven analysis of freeze-out distribution Single parameterization simultaneously describes spectra elliptic flow HBT K-  correlations most likely cause of discrepancy is extremely rapid emission timescale suggested by data - more work needed! Spectra & HBT R(pT) Very strong radial flow field superimposed on thermal motion v2(pT,m) & HBT R  Very strong anisotropic radial flow field superimposed on thermal motion, and geometric anisotropy Dominant freezeout characteristics extracted STAR low-pT message constraints to models rapid freezeout timescale and (?) rapid evolution timescale

70. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 70 Previous Data:  - HBT(  ) @ AGS Au(4 AGeV)Au, b  4-8 fm 6 components to radius tensor: i, j = o,s,l 1D projections,  =45° 2D projections lines: projections of 3D Gaussian fit  outsidelong C(q) E895, PLB 496 1 (2000)

71. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 71 Cross-term radii R ol, R os, R sl quantify “tilts” in correlation functions   fit results to correlation functions Lines: Simultaneous fit to HBT radii to extract underlying geometry Mike Lisa: thicker lines!!! bigger symbols!! have 2 GeV handy Mike Lisa: thicker lines!!! bigger symbols!! have 2 GeV handy

72. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 72 x out x side K Meaning of R o 2 (  ) and R s 2 (  ) are clear What about R os 2 (  )  p (°) 0180 0 0 0 10 -10 20 40 R 2 (fm 2 ) outsidelong ol os sl E895 Collab., PLB 496 1 (2000) R os 2 (  ) quantifies correlation between x out and x side No correlation (tilt) b/t between x out and x side at  p =0° (or 90°) K x out x side K x out x side K x out x side K x out x side K x out x side K x out x side  p = 0°  p ~45° Strong (positive) correlation when  p =45° Phase of R os 2 (  ) oscillation reveals orientation of extended source

73. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 73

74. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 74

75. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 75

76. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 76 Hydro predictions for R 2 (  ) correct phase of oscillations ~ correct amplitude of oscillations (size (offset) of R O, R S, R L still inconsistent with data) Heinz & Kolb hep-ph/0111075

77. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 77

78. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 78 x out x side K Meaning of R o 2 (  ) and R s 2 (  ) are clear What about R os 2 (  )  p (°) 0180 0 0 0 10 -10 20 40 R 2 (fm 2 ) outsidelong ol os sl E895 Collab., PLB 496 1 (2000) R os 2 (  ) quantifies correlation between x out and x side No correlation (tilt) b/t between x out and x side at  p =0° (or 90°) K x out x side K x out x side K x out x side K x out x side K x out x side K x out x side  p = 0°  p ~45° Strong (positive) correlation when  p =45° Phase of R os 2 (  ) oscillation reveals orientation of extended source

79. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 79 Just for fun, one for the road… Let’s go to “high” p T … if different, freeze-out is earlier or later? so s 2 (~ellipticity) should be lower or higher? and  a (diff. between flow out-of-plane and in-plane) should be higher or lower? OK, to look at higher p T, what happens with higher s 2 and lower  a ? so s 2 (~ellipticity) should be lower or higher? and  a (diff. between flow out-of-plane and in-plane) should be higher or lower? if different, freeze-out is earlier or later?

80. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 80 v 2 (p T ) for “early time” parameters “saturation” of v2 @ high pT mass - dependence essentially gone

81. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 81 More detail: identified particle elliptic flow soliddashed 0.04  0.010.09  0.02  a (c) 0.04  0.01 0.0S2S2 0.54  0.030.52  0.02  0 (c) 100  24135  20 T (MeV) STAR, in press PRL (2001) Flow boost:  b = boost direction Meaning of  a is clear  how to interpret s 2 ? hydro-inspired blast-wave model Houvinen et al (2001)

82. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 82 Ambiguity in nature of the spatial anisotroy  b = direction of the boost  s 2 > 0 means more source elements emitting in plane case 1: circular source with modulating density RMS x > RMS y RMS x < RMS y case 2: elliptical source with uniform density

83. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 83 Out-of-plane elliptical shape indicated case 1 using (approximate) values of s 2 and  a from elliptical flow case 2 opposite R(  ) oscillations would lead to opposite conclusion STAR preliminary

84. STAR HBT oct 2002Mike Lisa - XXXII ISMD - Alushta, Ukraine 84 Summary (cont’) HBT radii grow with collision centrality R(mult) evidence of strong space-momentum correlations R(m T ) non-central collisions spatially extended out-of-plane R(  ) The spoiler - expected increase in radii not observed presently no dynamical model reproduces data Combined data-driven analysis of freeze-out distribution Single parameterization simultaneously describes spectra elliptic flow HBT K-  correlations most likely cause of discrepancy is extremely rapid emission timescale suggested by data - more work needed!