STAR HBT 30 Aug 2001Mike Lisa - ACS Nuclear Division - Chicago 1 Characterizing the freezeout at RHIC: HBT, spectra, and elliptic flow U.S. Labs: Argonne, Lawrence Berkeley National Lab, Brookhaven National Lab U.S. Universities: Arkansas, UC Berkeley, UC Davis, UCLA, Carnegie Mellon, Creighton, Indiana, Kent State, MSU, CCNY, Ohio State, Penn State, Purdue, Rice, Texas A&M, UT Austin, Washington, Wayne State, Yale Brazil: Universidade de Sao Paolo China: IHEP - Beijing, IPP - Wuhan England: University of Birmingham France: Institut de Recherches Subatomiques Strasbourg, SUBATECH - Nantes Germany: Max Planck Institute – Munich, University of Frankfurt Poland: Warsaw University, Warsaw University of Technology Russia: MEPHI – Moscow, LPP/LHE JINR–Dubna, IHEP-Protvino Mike Lisa, Ohio State University STAR Collaboration

STAR HBT 30 Aug 2001Mike Lisa - ACS Nuclear Division - Chicago 2 Schematic goal and method - soft physics Goal: EoS of dense matter - relationship b/t bulk properties (P,T,…) evidence for phase transition? Method: Full characterization of freezeout distribution f(x,p) Consistent characterization for several observables Use measurements to constrain EoS via a model (hydro?), which connects early time to freezeout This talk: Focus on transverse observables: dN/dp T, v 2 (p T,m), HBT(p T,  ) Consistent picture within “hydro-inspired” parameterization? (is the data telling a consistent story, and what does it mean?) identify features of “real” model needing attention

STAR HBT 30 Aug 2001Mike Lisa - ACS Nuclear Division - Chicago 3 An analogous situation…

STAR HBT 30 Aug 2001Mike Lisa - ACS Nuclear Division - Chicago 4 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

STAR HBT 30 Aug 2001Mike Lisa - ACS Nuclear Division - Chicago 5 m T distribution from Hydrodynamics type 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

STAR HBT 30 Aug 2001Mike Lisa - ACS Nuclear Division - Chicago 6  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 = MeV =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

STAR HBT 30 Aug 2001Mike Lisa - ACS Nuclear Division - Chicago 7 STAR HBT data for central collisions - further info? conflicting info? STAR Collab., PRL (2001) -- ++ R(p T ) probes interplay b/t space-time geometry and temperature/flow

STAR HBT 30 Aug 2001Mike Lisa - ACS Nuclear Division - Chicago 8 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)

STAR HBT 30 Aug 2001Mike Lisa - ACS Nuclear Division - Chicago 9 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

STAR HBT 30 Aug 2001Mike Lisa - ACS Nuclear Division - Chicago 10 Joint view of  freezeout: HBT & spectra spectra (  ) HBT common model/parameterset describes different aspects of f(x,p) for central collisions 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

STAR HBT 30 Aug 2001Mike Lisa - ACS Nuclear Division - Chicago 11 Non-central collisions:coordinate and momentum-space anisotropies Equal energy density lines P. Kolb, J. Sollfrank, and U. Heinz

STAR HBT 30 Aug 2001Mike Lisa - ACS Nuclear Division - Chicago 12 Elliptic flow (momentum-space anisotropy): sensitive to early pressure / thermalization in-plane enhancement P. Kolb, et al., PLB (2001) SPS: between hydro and LDL Hydro describes flow RHIC

STAR HBT 30 Aug 2001Mike Lisa - ACS Nuclear Division - Chicago 13 HBT: (transverse) spatial anisotropy Source in b-fixed system: (x,y,z) Space/time entangled in pair system (x O,x S,x L ) U. Wiedemann, PRC 57, 266 (1998) large RHIC induces space-momentum correlations  p-dependent homogeneity lengths  sensitive to more than “just” anisotropic geometry out  b KK x y side

STAR HBT 30 Aug 2001Mike Lisa - ACS Nuclear Division - Chicago 14 Reminder: observations for Au(2 AGeV)Au  p (°) R 2 (fm 2 ) outsidelong ol os sl E895 Collab., PLB (2000)  p =0°  p =90° out-of-plane extended source interesting physics, but not currenly accessible in STAR with 2 nd -order reaction plane Lines are global fit Oscillation magnitude  eccentricity Oscillation phases  orientation

STAR HBT 30 Aug 2001Mike Lisa - ACS Nuclear Division - Chicago 15 More detail: identified particle elliptic flow soliddashed 0.04   0.02  a (c) 0.04  S2S   0.02  0 (c) 100   20 T (MeV) STAR Collab, submitted to PRL Flow boost:  b = boost direction Meaning of  a is clear  how to interpret s 2 ? hydro-inspired blast-wave model Houvinen et al (2001)

STAR HBT 30 Aug 2001Mike Lisa - ACS Nuclear Division - Chicago 16 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

STAR HBT 30 Aug 2001Mike Lisa - ACS Nuclear Division - Chicago 17 STAR HBT “Out” “Side” “Long” C(Q) Q (GeV/c) Correlation function:  p =45º R O 2 (fm 2 ) R S 2 (fm 2 ) R OS 2 (fm 2 )  - from semi-peripheral events raw corrected for reactionplane resolution datafit only mix events with “same”  RP retain relative sign between q-components HBT radii oscillations similar to AGS curves are not a global fit R S almost flat STAR preliminary

STAR HBT 30 Aug 2001Mike Lisa - ACS Nuclear Division - Chicago 18 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

STAR HBT 30 Aug 2001Mike Lisa - ACS Nuclear Division - Chicago 19 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

STAR HBT 30 Aug 2001Mike Lisa - ACS Nuclear Division - Chicago 20 Time-averaged freezeout shape close to RHIC info on evolution duration? STAR preliminary (E895)

STAR HBT 30 Aug 2001Mike Lisa - ACS Nuclear Division - Chicago 21 Hydro predictions  p (º) R O 2 (fm 2 ) R OS 2 (fm 2 ) R S 2 (fm 2 ) phases and ~ magnitude of HBT radii oscillations OK  R O  too large  R S  too small

STAR HBT 30 Aug 2001Mike Lisa - ACS Nuclear Division - Chicago 22 Summary - a consistent picture main source of discrepancy?

STAR HBT 30 Aug 2001Mike Lisa - ACS Nuclear Division - Chicago 23 Summary Spectra, elliptic flow, and HBT measures consistent with a freeze-out distribution including strong space-momentum correlations In non-central collisions, v 2 measurements sensitive to existence of spatial anisotropy, while HBT measurement reveals its nature Systematics of HBT parameters: flow gradients produce pT-dependence (consistent with spectra and v 2 (p T,m)) anisotropic geometry (and anisotropic flow boost) produce  -dependence (average) out-of-plane extension indicated however, distribution almost “round,” --> more hydro-like evolution as compared to AGS  While data tell consistent story within hydro-inspired parameterization, hydro itself tells a different story - likely point of conflict is timescale

STAR HBT 30 Aug 2001Mike Lisa - ACS Nuclear Division - Chicago 24 Hydro reproduced spectra well