STAR HBT 6 Sep 2003XXXIII ISMD - Krakow Poland1 Azimuthally-sensitive HBT (asHBT) in Au+Au collisions at  s NN =200 GeV Mike Lisa, Ohio State University for the STAR Collaboration motivation – why study RHIC? BlastWave parameterization of freeze-out 130 GeV sensitivity of asHBT to F.O. shape asHBT in Au+Au collisions at  s NN =200 GeV RP/binning resolution correction radii vs centrality, k T,  physics implications Summary Zero-th – order information from ^

STAR HBT 6 Sep 2003XXXIII ISMD - Krakow Poland2 time dN/dt Already a problem with “traditional” RHIC… p-space observables well-understood within hydrodynamic framework → hope of understanding early stage x-space observables not well-reproduced correct dynamical signatures with incorrect dynamic evolution? Too-large timescales modeled? emission/freezeout duration (R O /R S ) evolution duration (R L ) Heinz & Kolb, hep-ph/

STAR HBT 6 Sep 2003XXXIII ISMD - Krakow Poland3 … so why study (more complicated) asHBT ? sensitive to interplay b/t anisotropic geometry & dynamics/evolution (Ulrich’s talk) “broken symmetry” for b  0 → more detailed, important physics information another handle on dynamical timescales – likely impt in HBT puzzle P. Kolb and U. Heinz, hep-ph/ P. Kolb, nucl-th/ “radial flow” “elliptic flow”

STAR HBT 6 Sep 2003XXXIII ISMD - Krakow Poland4 Freeze-out anisotropy as an evolution “clock” anisotropic pressure gradients → preferential in-plane flow (v 2 ) → evolution towards in-plane shape  FO sensitive to evolution duration  0 dilute (hadronic) stage little effect on p-space at RHIC significant (bad) effect on HBT radii related to timescale qualitative change in  FO  FO from asHBT? hydro evolutionlater hadronic stage? P. Kolb and U. Heinz, hep-ph/ Teaney, Lauret, Shuryak, nucl-th/ STAR PHENIX hydro only hydro+hadronic rescatt Soff, Bass, Dumitru, PRL 2001 Teaney et al, nucl-th in-plane- extended out-of-plane-extended Teaney et al, nucl-th  p =0°  p =90° R S small R S big R.P.

STAR HBT 6 Sep 2003XXXIII ISMD - Krakow Poland5 Need a model of the freezeout- BlastWave BW: hydro-inspired parameterization of freezeout longitudinal direction infinite extent geometrically boost-invariant longitudinal flow Momentum space temperature T transverse rapidity boost ~ r Teaney, Lauret & Shuryak, nucl-th/ Schnedermann et al (’93): 2-parameter (T,  max ) “hydro-inspired” functional form to fit spectra. Useful to extract thermal, collective energy R azimuthally isotropic source model – let’s generalize for finite impact parameter …

STAR HBT 6 Sep 2003XXXIII ISMD - Krakow Poland6 RYRY RXRX Need a model of the freezeout- BlastWave BW: hydro-inspired parameterization of freezeout longitudinal direction infinite extent geometrically boost-invariant longitudinal flow Momentum space temperature T transverse rapidity boost ~ r coordinate space transverse extents R X, R Y freezeout in proper time  evolution duration  0 emission duration  00 00  F. Retière & MAL, in preparation

STAR HBT 6 Sep 2003XXXIII ISMD - Krakow Poland7 RYRY RXRX Need a model of the freezeout- BlastWave BW: hydro-inspired parameterization of freezeout longitudinal direction infinite extent geometrically boost-invariant longitudinal flow Momentum space temperature T transverse rapidity boost ~ r coordinate space transverse extents R X, R Y freezeout in proper time  evolution duration  0 emission duration  7 parameters describing freezeout F. Retière & MAL, in preparation

STAR HBT 6 Sep 2003XXXIII ISMD - Krakow Poland8 BlastWave fits to published RHIC data p T spectra constrain (mostly) T,  0 central midcentral peripheral F. Retière & MAL, in preparation

STAR HBT 6 Sep 2003XXXIII ISMD - Krakow Poland9 R=9 fm R=12 fm R=18 fm BlastWave fits to published RHIC data R out R side R long R out R side R long F. Retière & MAL, in preparation p T spectra constrain (mostly) T,  0 (traditional) HBT radii constrain  R ,  0,  depend also on T,  0

STAR HBT 6 Sep 2003XXXIII ISMD - Krakow Poland10 p T spectra constrain (mostly) T,  0 (traditional) HBT radii constrain  R ,  0,  depend also on T,  0 imperfect fit (esp. PHENIX R S ) BlastWave fits to published RHIC data central midcentral peripheral F. Retière & MAL, in preparation

STAR HBT 6 Sep 2003XXXIII ISMD - Krakow Poland11 BlastWave fits to published RHIC data p T spectra constrain (mostly) T,  0 (traditional) HBT radii constrain  R ,  0,  depend also on T,  0 imperfect fit (esp. PHENIX R S ) v 2 (p T,m) constrain R Y /R X,  a ~ 2 fm/c with Bowler CC (Not this talk) reasonable centrality evolution OOP extended source in non-central collisions CentralMidcentralPeripheral T (MeV) 108  3106  395  4 0    0.02 aa 0.06    0.01 R X (fm) 12.9    0.4 R Y (fm) 12.8    0.4  0 (fm/c)8.9    0.8  (fm/c)0.0    1.9  2 / ndf 80.5 / / / 68 F. Retière & MAL, in preparation centralmidcentralperipheral

STAR HBT 6 Sep 2003XXXIII ISMD - Krakow Poland12 So far v 2 (p T,m) indicates OOP-extended FO source for non-central collisions (confirmation from minbias asHBT) Would rather “view” the geometry more directly → analyze asHBT in higher-statistics 200 GeV dataset (next…) But… HBT radii depend on “everything” (T,  0, …) can we extract FO shape from asHBT alone?  p =0°  p =90° R S small R S big R.P.

STAR HBT 6 Sep 2003XXXIII ISMD - Krakow Poland13 can we extract FO shape from asHBT alone? the BlastWave view outside out-side long non-central collisions – all HBT radii exhibit 0 th & 2 nd - order oscillations (n>2 negligible) characterize each k T bin with 7 numbers: R 2 os,0 = 0 by symmetry (Ulrich’s talk) F. Retière & MAL, in preparation

STAR HBT 6 Sep 2003XXXIII ISMD - Krakow Poland14 can we extract FO shape from asHBT alone? the BlastWave view non-central collisions – all HBT radii exhibit 0 th & 2 nd - order oscillations (n>2 negligible) characterize each k T bin with 7 numbers: for fixed (R Y 2 +R X 2 ), increasing R Y /R X R 2 ,0 unchanged |R 2 ,2 | increases (sensitivity to FO shape) both R 2 ,0 and |R 2 ,2 | fall with p T same dependence/mechanism? (flow-induced x-p correlations) examine “normalized” oscillations R 2 ,2 /R 2,0 F. Retière & MAL, in preparation

STAR HBT 6 Sep 2003XXXIII ISMD - Krakow Poland15 FO shape from “normalized” oscillations the BlastWave view no-flow scenario: independent of p T … U. Wiedemann PR C (1998) MAL, U. Heinz, U. Wiedemann PL B (2000) in BW: this remains ~true even with flow low p T ) F. Retière & MAL, in preparation  /2

STAR HBT 6 Sep 2003XXXIII ISMD - Krakow Poland16 FO shape from “normalized” oscillations the BlastWave view no-flow scenario: independent of p T … U. Wiedemann PR C (1998) MAL, U. Heinz, U. Wiedemann PL B (2000) in BW: this remains ~true even with flow low p T ) independent of R Y 2 +R X 2 independent of  (and  0 ) ~independent of T (and  0 ) → estimate  from R 2 ,2 / R 2 s,0 (  =o,s,os) fixed  F. Retière & MAL, in preparation

STAR HBT 6 Sep 2003XXXIII ISMD - Krakow Poland17 asHBT at 200 GeV in STAR – R(  ) vs centrality 12 (!)  -bins b/t  (k T -integrated) clear oscillations observed in transverse radii of symmetry-allowed (Heinz’s talk) type centrality dependence reasonable oscillation amps higher than 2 nd -order ~ 0 → extract 0 th, 2 nd Fourier coefficients vs k T with 4  -bin analysis

STAR HBT 6 Sep 2003XXXIII ISMD - Krakow Poland18 Correcting for finite  -binning &  RP -resolution Reaction-plane estimation (from event-wise p-space anisotropy) is imperfect → n th -order oscillations reduced by  cos(n(  m- -  R ))  *  m- -  R *  cos(n  m )  from flow analysis – e.g. Poskanzer & Voloshin Phys. Rev. C (1998)  m- RR

STAR HBT 6 Sep 2003XXXIII ISMD - Krakow Poland19 Correcting for finite  -binning &  RP -resolution Reaction-plane estimation (from event-wise p-space anisotropy) is imperfect → n th -order oscillations reduced by  cos(n(  m- -  R ))  *  bins have finite width  → n th -order oscillations reduced by *  cos(n  m )  from flow analysis – e.g. Poskanzer & Voloshin Phys. Rev. C (1998)

STAR HBT 6 Sep 2003XXXIII ISMD - Krakow Poland20 Correcting for finite  -binning &  RP -resolution Reaction-plane estimation (from event-wise p-space anisotropy) is imperfect → n th -order oscillations reduced by  cos(n(  m- -  R ))  *  bins have finite width  → n th -order oscillations reduced by *  cos(n  m )  from flow analysis – e.g. Poskanzer & Voloshin Phys. Rev. C (1998) oscillations of what? not the HBT radii what is measured (and averaged/smeared) are pair number distributions N(q), D(q) [ C(q) = N(q) / D(q) ]

STAR HBT 6 Sep 2003XXXIII ISMD - Krakow Poland21 Correcting for finite  -binning &  RP -resolution Heinz, Hummel, Lisa, Wiedemann, Phys. Rev. C (2002) Fourier coefficients for a given q-bin. correction factor for n th -order oscillations for the damping effects of 1)finite resolution in determining the m th - order event-plane 2)non-vanishing bin width (  ) in the emission angle with respect to the event- plane (  j ) Fourier coefficients for a given q bin “raw”corrected ~ 30% effect on 2 nd -order radius oscillations ~0% change in mean values

STAR HBT 6 Sep 2003XXXIII ISMD - Krakow Poland22 asHBT at 200 GeV in STAR – R(  ) vs k T Clear oscillations observed at all k T extract 7 radius Fourier Coefficients (shown by lines) midcentral collisions (20-30%)

STAR HBT 6 Sep 2003XXXIII ISMD - Krakow Poland23 Grand Data Summary – R 2 ,n vs k T, centrality One plot w/ relevant quantities from 2x5x3x4 3D CFs left: R 2 ,0  “traditional” radii usual kT, centrality dependence right: R 2 ,2 / R 2,0 reasonable centrality dependence BW: sensitive to FO source shape

STAR HBT 6 Sep 2003XXXIII ISMD - Krakow Poland24 Estimate of initial vs F.O. source shape estimate  INIT from Glauber from asHBT:  FO =  INIT  FO <  INIT → dynamic expansion  FO > 1 → source always OOP-extended constraint on evolution time RHIC1 [Kolb & Heinz]

STAR HBT 6 Sep 2003XXXIII ISMD - Krakow Poland25 A simple estimate –  0 from  init and  final “radial flow” P. Kolb, nucl-th/ BW →  X,  F.O. (  X >  Y ) hydro: flow velocity grows ~ t From R L (m T ):  0 ~ 9 fm/c consistent picture Longer or shorter evolution times X inconsistent toy estimate:  0 ~  0 (BW)~ 9 fm/c But need a real model comparison → asHBT valuable “evolutionary clock” constraint for models

STAR HBT 6 Sep 2003XXXIII ISMD - Krakow Poland26 Summary FO source shape a “clock” for system evolution –OOP-extended  earlier kinetic FO –further test of long-lived hadronic stage (OOP  IP-extended source) BlastWave parameterization of FO at RHIC --  s NN =130 GeV –not perfect 130 GeV, but can provide some guidance/insight –“traditional HBT” in fit  suggest short emission, evolution timescales qualitatively supported by OOP from v2, minbias asHBT –Fourier decomposition of HBT radius oscillations even with flow-induced x-p correlations, asHBT alone useful to estimate  FO (R 2 u,2 / R 2 s,0 )  s NN =200 GeV –0 th, 2 nd -order oscillation amplitudes characterize  -dependence of HBT radii of type allowed by symmetry –centrality dependence reasonable –oscillations at all k T OOP FO shape  fast evolution (~9 fm/c)

STAR HBT 6 Sep 2003XXXIII ISMD - Krakow Poland27 To do… Me –finalize analysis/systematic errors –BW fits to final 200 GeV data (spectra, v2, asHBT) – does it hang consistently together? Theorists –can satisfactory FO be reached faster (e.g. more explosive EoS)? more constraints in that direction! –modification of hadronic stage needed?? Csörgő, Akkelin, Hama, Lukács, Sinyukov PR C (2003) Heinz & Kolb, hep-ph/