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Azimuthally-sensitive HBT in STAR

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. Central collision dynamics @ RHIC.

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Azimuthally-sensitive HBT in STAR

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  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 Mike Lisa - XXXII ISMD - Alushta, Ukraine

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

  3. Central collision dynamics @ RHIC • Hydrodynamics reproduces p-space aspects of particle emission up to pT~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? • Turn to richer dynamics of non-central collisions for more detailed information Mike Lisa - XXXII ISMD - Alushta, Ukraine Heinz & Kolb, hep-th/0204061

  4. Noncentral collision dynamics • hydro reproduces v2(pT,m) (details!) @ RHIC for pT < ~1.5 GeV/c • system response  EoS • early thermalization indicated Heinz & Kolb, hep-ph/0111075 hydro evolution • Dynamical models: • x-anisotropy in entrance channel  p-space anisotropy at freezeout • magnitude depends on system response to pressure Mike Lisa - XXXII ISMD - Alushta, Ukraine

  5. Effect of dilute stage later hadronic stage? hydro evolution • hydro reproduces v2(pT,m) (details!) @ RHIC for pT < ~1.0 GeV/c • system response  EoS • early thermalization indicated • dilute hadronic stage (RQMD): • little effect on v2 @ RHIC Mike Lisa - XXXII ISMD - Alushta, Ukraine Teaney, Lauret, & Shuryak, nucl-th/0110037

  6. Effect of dilute stage later hadronic stage? hydro only hydro+hadronic rescatt STAR PHENIX hydro evolution • hydro reproduces v2(pT,m) (details!) @ RHIC for pT < ~1.5 GeV/c • system response  EoS • early thermalization indicated • dilute hadronic stage (RQMD): • little effect on v2 @ RHIC • significant (bad) effect on HBT radii calculation: Soff, Bass, Dumitru, PRL 2001 Mike Lisa - XXXII ISMD - Alushta, Ukraine

  7. Effect of dilute stage later hadronic stage? hydro evolution • hydro reproduces v2(pT,m) (details!) @ RHIC for pT < ~1.5 GeV/c • system response  EoS • early thermalization indicated • dilute hadronic stage (RQMD): • little effect on v2 @ RHIC • significant (bad) effect on HBT radii • related to timescale? - need more info Mike Lisa - XXXII ISMD - Alushta, Ukraine Teaney, Lauret, & Shuryak, nucl-th/0110037

  8. Effect of dilute stage later hadronic stage? in-plane-extended out-of-plane-extended hydro evolution • hydro reproduces v2(pT,m) (details!) @ RHIC for pT < ~1.5 GeV/c • system response  EoS • early thermalization indicated • dilute hadronic stage (RQMD): • little effect on v2 @ RHIC • significant (bad) effect on HBT radii • related to timescale? - need more info • qualitative change of freezeout shape!! • important piece of the puzzle! Mike Lisa - XXXII ISMD - Alushta, Ukraine Teaney, Lauret, & Shuryak, nucl-th/0110037

  9. Possible to “see” via HBT relative to reaction plane? fp=90° Rside (small) Rside (large) fp=0° • for out-of-plane-extended source, expect • large Rside at 0 • small Rside at 90 2nd-order oscillation Rs2 [no flow expectation] fp Mike Lisa - XXXII ISMD - Alushta, Ukraine

  10. “Traditional HBT” - cylindrical sources K Rout Rside Decompose q into components: qLong: in beam direction qOut : in direction of transverse momentum qSide:  qLong & qOut (beam is into board) Mike Lisa - XXXII ISMD - Alushta, Ukraine

  11. Anisotropic sources Six HBT radii vs f side y K out • Source in b-fixed system: (x,y,z) • Space/time entangled in pair system (xO,xS,xL) fp x b ! • explicit and implicit (xmxn(f)) dependence on f Mike Lisa - XXXII ISMD - Alushta, Ukraine Wiedemann, PRC57 266 (1998).

  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 Mike 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 F-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 Mike Lisa - XXXII ISMD - Alushta, Ukraine Heinz, Hummel, MAL, Wiedemann, nucl-th/0207003

  14. Anisotropic HBT results @ AGS (s~2 AGeV) out side long 40 R2 (fm2) 20 os ol sl 10 0 -10 0 0 0 180 180 180 fp (°) Au+Au 2 AGeV; E895, PLB 496 1 (2000) xside xout K fp = 0° • strong oscillations observed • lines: predictions for static (tilted) out-of-plane extended source  consistent with initial overlap geometry Mike Lisa - XXXII ISMD - Alushta, Ukraine

  15. Meaning of Ro2(f) and Rs2(f) are clearWhat about Ros2(f) ? out side long xside 40 xside xside xside xside xside xside R2 (fm2) xout xout xout xout xout xout xout 20 K os ol sl 10 K K K K K K 0 -10 0 0 0 180 180 180 No access to 1st-order oscillations in STAR Y1 fp (°) Au+Au 2 AGeV; E895, PLB 496 1 (2000) fp = 0° fp ~45° • Ros2(f) quantifies correlation between xout and xside • No correlation (tilt) b/t between xout and xside at fp=0° (or 90°) • Strong (positive) correlation when fp=45° • Phase of Ros2(f) oscillation reveals orientation of extended source Mike Lisa - XXXII ISMD - Alushta, Ukraine

  16. Indirect indications of x-space anisotropy @ RHIC dashed solid T (MeV) 135  20 100  24 0(c) 0.52  0.02 0.54  0.03 a (c) 0.09  0.02 0.04  0.01 S2 0.0 0.04  0.01 • v2(pT,m) globally well-fit by hydro-inspired “blast-wave” temperature, radial flow consistent with fits to spectra  anisotropy of flow boost spatial anisotropy (out-of-plane extended) Mike Lisa - XXXII ISMD - Alushta, Ukraine STAR, PRL 87 182301 (2001)

  17. STAR data Au+Au 130 GeV minbias full blastwave consistent with R(pT), K-p • significant oscillations observed • blastwave with ~ same parameters as used to describe spectra & v2(pT,m) • additional parameters: • R = 11 fm •  = 2 fm/c !! preliminary Mike Lisa - XXXII ISMD - Alushta, Ukraine

  18. STAR data Au+Au 130 GeV minbias full blastwave no flow anisotropy consistent with R(pT), K-p • significant oscillations observed • blastwave with ~ same parameters as used to describe spectra & v2(pT,m) • additional parameters: • R = 11 fm •  = 2 fm/c !! no spatial anisotropy preliminary • both flow anisotropy and source shape contribute to oscillations, but… • geometry dominates dynamics • freezeout source out-of-plane extended fast freeze-out timescale ! Mike Lisa - XXXII ISMD - Alushta, Ukraine

  19. Azimuthal HBT: hydro predictions • RHIC (T0=340 MeV @ t0=0.6 fm) • Out-of-plane-extended source (but flips with hadronic afterburner) • flow & geometry work together to produce HBT oscillations • oscillations stable with KT (note: RO/RS puzzle persists) Heinz & Kolb, hep-th/0204061 Mike Lisa - XXXII ISMD - Alushta, Ukraine

  20. Azimuthal HBT: hydro predictions • RHIC (T0=340 MeV @ t0=0.6 fm) • Out-of-plane-extended source (but flips with hadronic afterburner) • flow & geometry work together to produce HBT oscillations • oscillations stable with KT • “LHC” (T0=2.0 GeV @ t0=0.1 fm) • In-plane-extended source (!) • HBT oscillations reflect competition between geometry, flow • low KT: geometry • high KT: flow sign flip Heinz & Kolb, hep-th/0204061 Mike Lisa - XXXII ISMD - Alushta, Ukraine

  21. HBT(φ) Results – 200 GeV STAR PRELIMINARY • Oscillations similar to those measured @ 130GeV • 20x more statistics explore systematics in centrality, kT • much more to come… Mike 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 v2(pT,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 v2(pT,m), spectra, R(pT), K-p • 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 RL(mT) • Models of bulk dynamics severely (over?)constrained Mike Lisa - XXXII ISMD - Alushta, Ukraine

  23. Backup slides follow Mike 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 v2(pT,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(f) 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 v2(pT,m) and R(f) in blastwave parameterization • challenge/feedback for “real” physical models of collision dynamics Mike Lisa - XXXII ISMD - Alushta, Ukraine

  25. RHIC  AGS • Current experimental access only to second-order event-plane • odd-order oscillations in fp are invisible • cannot (unambiguously) extract tilt (which is likely tiny anyhow) • cross-terms Rsl2 and Rol2 vanish @ y=0 •  concentrate on “purely transverse” radii Ro2, Rs2, Ros2 • Strong pion flow  cannot ignore space-momentum correlations • (unknown) implicit f-dependences in homogeneity lengths •  geometrical inferences will be more model-dependent • the source you view depends on the viewing angle Mike 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!! Mike Lisa - XXXII ISMD - Alushta, Ukraine

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

  28. Flow Space-momentum correlations <r> = 0.6 (average flow rapidity) Assymetry (periph) : ra = 0.05 Temperature T = 110 MeV System geometry R = 13 fm (central events) Assymetry (periph event) s2 = 0.05 Time: emission duration t = emission duration Blastwave Mach II - Including asymmetries bt R analytic description of freezeout distribution: exploding thermal source Mike Lisa - XXXII ISMD - Alushta, Ukraine

  29. Sensitivity to r0 within blast-wave “Reasonable” variations in radial flow magnitude (r0)  parallel pT dependence for transverse HBT radii r0 Mike Lisa - XXXII ISMD - Alushta, Ukraine

  30. Sensitivity to t within blast-wave RS insensitive to t RO increases with pT as t increases t Mike Lisa - XXXII ISMD - Alushta, Ukraine

  31. Thermal motion superimposed on radial flow b s s R Hydro-inspired “blast-wave” thermal freeze-out fits to p, K, p, L preliminary Tth = 107 MeV b = 0.55 M. Kaneta E.Schnedermann et al, PRC48 (1993) 2462 Mike Lisa - XXXII ISMD - Alushta, Ukraine

  32. Previous Data: p- HBT(f) @ AGSAu(4 AGeV)Au, b4-8 fm f () 2D projections 1D projections, f=45° C(q) out side long lines: projections of 3D Gaussian fit • 6 components to radius tensor: i, j = o,s,l E895, PLB 496 1 (2000) Mike Lisa - XXXII ISMD - Alushta, Ukraine

  33. Cross-term radii Rol, Ros, Rslquantify “tilts” in correlation functionsin q-space f () fit results to correlation functions Lines: Simultaneous fit to HBT radii to extract underlying geometry Mike Lisa - XXXII ISMD - Alushta, Ukraine

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

  35. But is that too naïve?Hydro predictions for R2(f) retracted Feb 02 • but their freezeout source is in-plane extended? • stronger in-plane (elliptic) flow “tricks” us • “dynamics rules over geometry” • correct phase (& ~amplitude) of oscillations • (size (offset) of RO, RS , RL still wrong) Mike Lisa - XXXII ISMD - Alushta, Ukraine Heinz & Kolb hep-ph/0111075

  36. Experimental indications of x-space anisotropy @ RHIC Flow boost: dashed dashed solid solid T (MeV) T (MeV) 135  20 135  20 100  24 100  24 0(c) 0(c) 0.52  0.02 0.52  0.02 0.54  0.03 0.54  0.03 a (c) a (c) 0.09  0.02 0.09  0.02 0.04  0.01 0.04  0.01 S2 S2 0.0 0.0 0.04  0.01 0.04  0.01 hydro-inspired blast-wave model Houvinen et al (2001) fb = boost direction STAR, PRL 87 182301 (2001) Meaning of ra is clear  how to interpret s2? Mike Lisa - XXXII ISMD - Alushta, Ukraine

  37. Ambiguity in nature of the spatial anisotroy case 1: circular source with modulating density RMSx > RMSy case 2: elliptical source with uniform density RMSx < RMSy fb = direction of the boost  s2 > 0 means more source elements emitting in plane Mike Lisa - XXXII ISMD - Alushta, Ukraine

  38. Hydro-inspired model calculations (“blast wave”) case 1 case 2 s2=0.033, T=100 MeV, r0=0.6 ra=0.033, R=10 fm, t=2 fm/c • consider results in context of blast wave model • ~same parameters describe R(f) and v2(pT,m) • both elliptic flow and aniostropic geometry contribute to oscillations, but… • geometry rules over dynamics • R(f) measurement removes ambiguity over nature of spatial anisotropy early version of data but message the same Mike 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) Mike 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 e: I think Raimond in some paper called the Heinz/Kolb parameter s2 also (in analogy to v2). Great…. Better still, in the BlastWave, another s2 (in Lisa-B) is related to Ry/Rx via: Anyway, if we say s2,BW = 0.04, this corresponds to h = 1.055 (5.5% extended) which gives s2,STL = -0.05, or eHK = +0.05 This is in the range of the H/K hydro calculation, but seems a huge number for STL ? Mike 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 Mike Lisa - XXXII ISMD - Alushta, Ukraine

  42. Fourier expansion of spatial correlation tensor Smn Sn = 0 for all terms containing even powers of y Cn = 0 for all terms containing odd powers of y I  For terms with even powers of t, Sn, Cn 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 II  Mike Lisa - XXXII ISMD - Alushta, Ukraine

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

  45. Mike Lisa - XXXII ISMD - Alushta, Ukraine

  46. s2 dependence dominates HBT signal s2=0.033, T=100 MeV, r0=0.6 ra=0.033, R=10 fm, t=2 fm/c color: c2 levels from HBT data error contour from elliptic flow data STAR preliminary Mike Lisa - XXXII ISMD - Alushta, Ukraine

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

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

  49. Event mixing: zvertex issue • mixing those events generates artifact: • too many large qL pairs in denominator • bad normalization, esp for transverse radii BP analysis with 1 z bin from -75,75 Mike Lisa - XXXII ISMD - Alushta, Ukraine

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

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