1. 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

2. Transverse Dynamics workshop, March 2003 Dan Magestro 2 The role of HBT at a "transverse dynamics" workshop Single-particle p T spectra & v 2 signal also determined by STE, but... 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 Pairs of pions experience B-E correlations Hanbury Brown–Twiss interferometry: characterize correlations Width of correlation peak as q  0 reflects "length of homogeneity" (pair relative momentum) Bose-Einstein p correlations  disentangle STE static source: HBT radii ↔ true geometrical size of system dynamic source: HBT radii ↔ flow reduces observed radii  p T dependence of HBT related to collective expansion

3. Transverse Dynamics workshop, March 2003 Dan Magestro 3 Review of RHIC Year 1 (  s=130 GeV) Hydrodynamics Heinz & Kolb, hep-ph/0111075 momentum spectra elliptic flow J Successfully reproduces p-space of source Heinz & Kolb, hep-ph/0204061

4. Transverse Dynamics workshop, March 2003 Dan Magestro 4 Review of RHIC Year 1 (  s=130 GeV) "HBT Puzzle" Hydrodynamics  Fails to predict spatial structure of source  Including hadronic rescattering makes it worse Heinz & Kolb, hep-ph/0111075 STAR PHENIX hydro only hydro+hadronic rescatt Soff, Bass, Dumitru

5. Transverse Dynamics workshop, March 2003 Dan Magestro 5 Why study HBT(  )? 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 rate How much of initial spatial deformation still exists at freeze-out? Big question: What is the time scale of the collision? later hadronic stage? b x beam into screen Heinz & Kolb, Nucl.Phys. A702 (2002) 269-280 collective expansion of system

6. Transverse Dynamics workshop, March 2003 Dan Magestro 6 HBT(  ) predictions from hydrodynamics Hydrodynamics: initial out-of-plane anisotropy may become in-plane later hadronic stage? in-plane- extended out-of-plane-extended Teaney, Lauret, & Shuryak, nucl-th/0110037 k T dependence Heinz & Kolb, Nucl.Phys. A702 (2002) 269-280

7. Transverse Dynamics workshop, March 2003 Dan Magestro 7 The HBT(  ) experimental technique 2.Apply HBT formalism to extract "HBT radii" for each bin reaction plane b x beam into screen 1.Study (transverse) source at different angles by performing two-pion interferometry separately for bins w.r.t reaction plane  P =0°  p =90° R side (large) R side (small) 3.Oscillations of radii w.r.t. RP indicate if source is in-plane or out-of-plane extended

8. Transverse Dynamics workshop, March 2003 Dan Magestro 8 Watered-down HBT(  ) What we measure HBT radii as a function of emission angle reaction plane  What we expect to see: 2 nd -order oscillations in HBT radii analogous to v 2 R side 2  Why we're interested The size and orientation of the source at freeze-out places tight constraints on expansion/evolution   What should be remembered At finite k T, 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. q out q side q long 

9. Transverse Dynamics workshop, March 2003 Dan Magestro 9 Blast-wave applied to HBT(  ), 130 GeV Minimum bias data (inclusive  ) Oscillations indicate out-of-plane extended source Blast-wave describes oscillations well STAR preliminary R y =11.7 fm, s 2 =0.037, T=100 MeV,  a =0.037,  0 =0.9, a skin =0.001 outside out-side long  P =0°  p =90° R side (large) R side (small)

10. Transverse Dynamics workshop, March 2003 Dan Magestro 10 Consistent picture of RHIC Year-1 (  s=130 GeV) Parametrization of freeze-out, works for v 2, m T spectra, source geometry, and K-  HBT "Extended" blast wave 1 1 F. Retiere, nucl-ex/0111013 Consistent set of parameters describes several observables elliptic flow HBT radii K-  correlations

11. Transverse Dynamics workshop, March 2003 Dan Magestro 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 dependence Study source deformity at freeze-out in context of initial shape - geometry k T dependence Study different scenarios of pair emission – geometry/dynamics Warning: This is a very systematic analysis!

12. Transverse Dynamics workshop, March 2003 Dan Magestro 12 Corrections applied to data Bowler/Sinyukov Coulomb correction Modifies fit function, leads to systematic increase in R out RP resolution correction 1 (Heinz et al) Applies bin-by-bin corrections to Num's and Den's of correlation functions Average lambda parameter for each centrality/k T bin Removes effects due to non-ideal behavior of fit function  +,  - HBT parameters averaged Improves statistics; data consistent within errors 1 Heinz, Hummel, Lisa, Wiedemann, PRC 66 (2002) 044903

13. Transverse Dynamics workshop, March 2003 Dan Magestro 13 Effect of new Coulomb correction, "standard" HBT 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 R o affected most “Standard” Coulomb CC No Coulomb CC STAR, QM01; NPA698, 177c (2002) Y2 data: dilution effect vs p T, centrality R O /R S ~ 10-15% increase when f = ≈ 0.5 f More correct CC method of Bowler (’91) & Sinyukov (’98), used by CERES (’02) Similar effect on radii as dilution with f = In “right” direction, but does not solve R O /R S problem CERES Coll. NPA 714 (2002) 124

14. Transverse Dynamics workshop, March 2003 Dan Magestro 14 Centrality dependence of HBT(  )  12  -bin analysis (0.15 < k T < 0.65) 15° bins, 72 CF's total 12  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 STAR preliminary out, side, long go as cos(2  ) out-side goes as sin(2  )

15. Transverse Dynamics workshop, March 2003 Dan Magestro 15 k T dependence of HBT(  ) 10-30% events STAR preliminary To put this in perspective, the 130 GeV STAR HBT paper had 3 CF's per trend (centrality, p t )  4  -bin, 4 k T -bin analysis 96 simultaneous CF's 4  bins (45° wide) × 4 k T bins × 3 centrality bins × 2 pion signs Oscillations exist in transverse radii for all k T bins

16. Transverse Dynamics workshop, March 2003 Dan Magestro 16 Data summary: Fourier coefficients STAR preliminary HBT(  ) summary plot Data points are Fourier coefficients of oscillations R i,0 2 =  R i 2 (  )/N bins R i,2 2 =  R i 2 (  )osc(2  )/N bins i=o,s,l: osc = cos i=os: osc = sin All data consistent with out-of-plane extended sources Weak k T dependence

17. Transverse Dynamics workshop, March 2003 Dan Magestro 17 Hydro predictions of HBT(  ) RHIC (T 0 =340 MeV @ t 0 =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 K T (note: R O /R S puzzle persists) Kolb & Heinz, Phys. Lett. B542 (2002) 216

18. Transverse Dynamics workshop, March 2003 Dan Magestro 18 Hydro predictions of HBT(  ) “LHC” (T 0 =2.0 GeV @ t 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 @ t 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 Kolb & Heinz, Phys. Lett. B542 (2002) 216

19. Transverse Dynamics workshop, March 2003 Dan Magestro 19 Comparison to Hydro STAR preliminary “LHC”/IPES (T 0 =2.0 GeV @ t 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 @ t 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

20. Transverse Dynamics workshop, March 2003 Dan Magestro 20 Model-independent determination of source orientation?? Issue: Are we being "tricked" by measurement? (Voloshin, Heinz, Kolb,...) reaction plane vs. Can we discriminate between these two scenarios in a model-independent way? (well, these drawings are already kind of a model-dependent picture...) (a) (b) High-k T – pairs emitted from small H.R. As kT  0, pions emitted from entire source k T dependence Pairs at different k T emitted from different homogeneity regions We observe no strong k T dependence of oscillation amplitude in transverse HBT radii  finite kT measurements roughly representative of whole source... Case (b) requires some evolution of amplitude with k T Extrapolate toward kT=0 (risky, but...) to look at entire source... Model-independent determination of orientation of source!?

21. Transverse Dynamics workshop, March 2003 Dan Magestro 21 The Blast-wave parametrization F. Retiere and M.A. Lisa, in preparation Blast-wave: Hydro-inspired parameterization of freeze-out momentum space T,  0,  a x-space R x, R y time t,  t 7 parameters: RYRY RXRX Use Blast-wave to relate HBT(  ) measurements to source shape & orientation

22. Transverse Dynamics workshop, March 2003 Dan Magestro 22 Characterizing freeze-out shape relative to initial anisotropy 0-10% 10-30% 30-70%  increases with b, indicates source is more out-of-plane extended Glauber   of initial geometry RxRx RyRy RxRx RyRy HBT(  )   of final geometry  RyRy 0-10%1.0212 fm 10-30%1.0511 fm 30-70%1.109.25 fm other BW parameters kept fixed T=100 MeV,  a =0.04,  0 =0.9, a skin =0.01 STAR preliminary

23. Transverse Dynamics workshop, March 2003 Dan Magestro 23 It didn't have to be this way... RxRx RyRy RxRx RyRy Evolution scenarios – schematic only 1.Hydrodynamic source with strong flow, long lifetime 2.Explosive source with weak flow, very short lifetime 3.Rescattering/RQMD source with long lifetime What would we have expected before doing the measurement?

24. Transverse Dynamics workshop, March 2003 Dan Magestro 24 Relevance to gluon saturation picture 1 Kovchegov and Tuchin, Nucl. Phys. A 717 (2003) 249 Kovchegov and Tuchin 1 reproduced differential elliptic flow data using minijets in a gluon saturation model Consequence: reconstructed  RP not related to real  RP  particle & v 2 production is independent of geometry Kovchegov and Tuchin, NPA 708 (2002) 413 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? reconstruted reaction plane using v 2 Transverse plane in K&T saturation scenario true reaction plane HBT(  ) shows sensitivity to reconstructed RP!

25. Transverse Dynamics workshop, March 2003 Dan Magestro 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 R out ~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 ??