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 200 GeV Model discussion Source geometry at freeze-out

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

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

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/ STAR PHENIX hydro only hydro+hadronic rescatt Soff, Bass, Dumitru

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) collective expansion of system

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/ k T dependence Heinz & Kolb, Nucl.Phys. A702 (2002)

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

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 

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)

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/ Consistent set of parameters describes several observables elliptic flow HBT radii K-  correlations

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!

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)

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 & 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

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  )

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

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

Transverse Dynamics workshop, March 2003 Dan Magestro 17 Hydro predictions of HBT(  ) RHIC (T 0 =340 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

Transverse Dynamics workshop, March 2003 Dan Magestro 18 Hydro predictions of HBT(  ) “LHC” (T 0 =2.0 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 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

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

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!?

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

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% fm 10-30% fm 30-70% fm other BW parameters kept fixed T=100 MeV,  a =0.04,  0 =0.9, a skin =0.01 STAR preliminary

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?

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!

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 ??