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Dan Magestro The Ohio State University for the STAR Collaboration

HBT relative to the reaction plane at RHIC. Where we stand after Year-1 Motivation for HBT( ) Centrality & k T dependence @ 200 GeV Model discussion Source geometry at freeze-out. Dan Magestro The Ohio State University for the STAR Collaboration.

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Dan Magestro The Ohio State University for the STAR Collaboration

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  1. HBT relative to the reaction plane at RHIC • Where we stand after Year-1 • Motivation for HBT() • Centrality & kT dependence @ 200 GeV • Model discussion • Source geometry at freeze-out Dan MagestroThe Ohio State Universityfor the STAR Collaboration

  2. The role of HBT at a "transverse dynamics" workshop • Bose-Einstein p correlations  disentangle STE • Goal: quantify contributions to space-time evolution (STE) of system Lifetime and duration of emission Spatial extent of system Collective flow at thermal freeze-out • Single-particle pT spectra & v2 signal also determined by STE, but... Pairs of pions experience B-E correlations Hanbury Brown–Twiss interferometry: characterize correlations Width of correlation peak as q0 reflects "length of homogeneity" static source: HBT radii ↔ true geometrical size of system dynamic source: HBT radii ↔ flow reduces observed radii  pT dependence of HBT related to collective expansion (pair relative momentum)

  3. Review of RHIC Year 1 (s=130 GeV) Heinz & Kolb, hep-ph/0111075 momentum spectra Hydrodynamics • Successfully reproduces p-space of source elliptic flow Heinz & Kolb, hep-ph/0204061

  4. Review of RHIC Year 1 (s=130 GeV) hydro only hydro+hadronic rescatt STAR PHENIX Hydrodynamics • Fails to predict spatial structure of source "HBT Puzzle" Heinz & Kolb, hep-ph/0111075 Soff, Bass, Dumitru • Including hadronic rescattering makes it worse

  5. Why study HBT()? later hadronic stage? beam into screen x b • Standard HBT provides direct access to space-time (size) information about source, "HBT radii" • Additionally, HBT() provides direct access to shape and orientation of source • Source shape+size at freeze-out evolution, expansion rateHow much of initial spatial deformation still exists at freeze-out? • Big question: What is the time scale of the collision? collective expansion of system Heinz & Kolb, Nucl.Phys. A702 (2002) 269-280

  6. HBT() predictions from hydrodynamics later hadronic stage? in-plane-extended out-of-plane-extended • Hydrodynamics: initial out-of-plane anisotropy may become in-plane kT dependence Heinz & Kolb, Nucl.Phys. A702 (2002) 269-280 Teaney, Lauret, & Shuryak, nucl-th/0110037

  7. The HBT() experimental technique beam into screen x b fp=90° Rside (small) Rside (large) • Oscillations of radii w.r.t. RP indicate if source is in-plane or out-of-plane extended fP=0° • Study (transverse) source at different angles by performing two-pion interferometry separately for bins w.r.t reaction plane reactionplane • Apply HBT formalism to extract "HBT radii" for each bin

  8. Watered-down HBT()  What we measure  What we expect to see: HBT radii as a function of emission angle 2nd-order oscillations in HBT radii analogous to v2 Rside2 reactionplane  Why we're interested  What should be remembered The size and orientation of the source at freeze-out places tight constraints on expansion/evolution At finite kT, we don't measure the entire source size. We measure "regions of homogeneity" and relating this to the full source size requires a model dependence. qlong qside qout

  9. Blast-wave applied to HBT(), 130 GeV fp=90° Rside (small) Rside (large) fP=0°  • Minimum bias data (inclusive ) • Oscillations indicate out-of-plane extended source • Blast-wave describes oscillations well Ry=11.7 fm, s2=0.037, T=100 MeV, a=0.037, 0=0.9, askin=0.001 STAR preliminary out side long out-side

  10. Consistent picture of RHIC Year-1 (s=130 GeV) "Extended" blast wave1 • Parametrization of freeze-out, works for v2, mT spectra, source geometry, and K- HBT • Consistent set of parameters describes several observables K- correlations HBT radii elliptic flow 1F. Retiere, nucl-ex/0111013

  11. Extending the HBT() systematics • 130 GeV: minimum-bias analysis • Out-of-plane extended source, consistency with blast-wave • 200 GeV: ~10x more statistics  study systematics of HBT() • Centrality dependenceStudy source deformity at freeze-out in context of initial shape - geometry • kT dependenceStudy different scenarios of pair emission – geometry/dynamics Warning: This is a very systematic analysis!

  12. Corrections applied to data Bowler/Sinyukov Coulomb correctionModifies fit function, leads to systematic increase in Rout RP resolution correction1 (Heinz et al)Applies bin-by-bin corrections to Num's and Den's of correlation functions Average lambda parameter for each centrality/kT binRemoves effects due to non-ideal behavior of fit function +, - HBT parameters averagedImproves statistics; data consistent within errors 1 Heinz, Hummel, Lisa, Wiedemann, PRC 66 (2002) 044903

  13. Effect of new Coulomb correction, "standard" HBT STAR, QM01; NPA698, 177c (2002) f CERES Coll. NPA 714 (2002) 124 • More correct CC method of Bowler (’91) & Sinyukov (’98), used by CERES (’02) • Similar effect on radii as dilution with f =  “Standard” Coulomb CC No Coulomb CC • RHIC analyses used “standard” Coulomb correction, used by previous experiments • “apples-to-apples” extension of systematics • Effects of “diluting” CC (resonances, etc) explored & reported @ QM01 • Ro affected most • Y2 data: dilution effect vs pT, centrality • RO/RS ~ 10-15% increase when f =  ≈ 0.5 In “right” direction, but does not solve RO/RS problem

  14. Centrality dependence of HBT() STAR preliminary • 12 -bin analysis (0.15 < kT < 0.65) • 15° bins, 72 CF's total12 bins × 3 centrality bins × 2 pion signs • Lines are fits to allowed oscillations • Oscillations exist in transverse radii for all bins • Amplitudes weakest for 0-10% (expected) • No higher-order oscillations observed out, side, long go as cos(2) out-side goes as sin(2)

  15. kT dependence of HBT() STAR preliminary • 4 -bin, 4 kT-bin analysis • 96 simultaneous CF's4 bins (45° wide)× 4 kT bins × 3 centrality bins × 2 pion signs • Oscillations exist in transverse radii for all kT bins To put this in perspective, the 130 GeV STAR HBT paper had 3 CF's per trend (centrality, pt) 10-30% events

  16. Data summary: Fourier coefficients HBT() summary plot • Data points are Fourier coefficients of oscillations Ri,02 =  Ri2()/Nbins Ri,22 =  Ri2()osc(2)/Nbins i=o,s,l: osc = cosi=os: osc = sin • All data consistent with out-of-plane extended sources • Weak kT dependence STAR preliminary

  17. Hydro predictions of HBT() • RHIC (T0=340 MeV @ t0=0.6 fm) • Initialize with central data, adjust geometry only • 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) Kolb & Heinz, Phys. Lett. B542 (2002) 216

  18. Hydro predictions of HBT() • 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 Kolb & Heinz, Phys. Lett. B542 (2002) 216

  19. Comparison to Hydro • 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”/IPES (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 STAR preliminary sign flip

  20. Model-independent determination of source orientation?? kT dependence • Pairs at different kT emitted from different homogeneity regions High-kT – pairs emittedfrom small H.R. As kT0, pions emitted from entire source • We observe no strong kT dependence of oscillation amplitude in transverse HBT radii finite kT measurements roughly representative of whole source... • Case (b) requires some evolution of amplitude with kT • Extrapolate toward kT=0 (risky, but...) to look at entire source... • Model-independent determination of orientation of source!? Issue: Are we being "tricked" by measurement? (Voloshin, Heinz, Kolb, ...) (b) (a) vs. reactionplane reactionplane Can we discriminate between these two scenarios in a model-independent way?(well, these drawings are already kind of a model-dependent picture...)

  21. The Blast-wave parametrization momentum space T, 0, a x-space Rx, Ry time t, t 7 parameters: • Blast-wave: Hydro-inspired parameterization of freeze-out • Use Blast-wave to relate HBT() measurements to source shape & orientation RY RX F. Retiere and M.A. Lisa, in preparation

  22. Characterizing freeze-out shape relative to initial anisotropy Ry Rx Ry Rx other BW parameters kept fixedT=100 MeV, a=0.04, 0=0.9, askin=0.01 •  increases with b, indicates source is more out-of-plane extended Glauber   of initial geometry 30-70% HBT()  of final geometry 10-30% 0-10% STAR preliminary

  23. It didn't have to be this way... Ry Rx Ry Rx What would we have expected before doing the measurement? Evolution scenarios – schematic only • Hydrodynamic source with strong flow, long lifetime • Explosive source with weak flow, very short lifetime • Rescattering/RQMD source with long lifetime

  24. Relevance to gluon saturation picture • HBT(): Relates space-momentum correlations to reconstructed RP geometry does matter: saturation dead? • Or, can minijets account for HBT() signal as well (at least qualitatively)? • What can Color Glass / gluon saturation say about HBT? Transverse plane in K&T saturation scenario reconstruted reaction planeusing v2 HBT() showssensitivity to reconstructed RP! true reaction plane • Kovchegov and Tuchin1 reproduced differential elliptic flow data using minijets in a gluon saturation model • Consequence: reconstructed RP not related to real RP  particle & v2 production is independent of geometry Kovchegov and Tuchin, NPA 708 (2002) 413 1Kovchegov and Tuchin, Nucl. Phys. A 717 (2003) 249

  25. Conclusions • "Standard" HBT: Centrality and kT dependence • No significant change in radii from 130 GeV • Now: kT dependence of centrality dependence • Coulomb correction increases Rout ~10-15% • HBT puzzle persists... • HBT() @ 200 GeV: Centrality and kT dependence • Measurements consistent with out-of-plane extended sources • Short lifetime of source  not enough time for flow to significantly affect shape • Hydrodynamics: reproduces amplitudes qualitatively with RHIC realistic source • Blast-wave: effective tool to extract source aspect ratio • Very little kT dependence of amplitudes  model-independent determination of source orientation? • Does HBT() hurt the gluon saturation picture ??

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