1. STAR HBT 16 Oct 20032nd Warsaw Meeting on Correlations and Resonances 1 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 asHBT @ RHIC? BlastWave parameterization of freeze-out fits/predictions @ 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 ^

2. STAR HBT 16 Oct 20032nd Warsaw Meeting on Correlations and Resonances 2 time dN/dt Already a problem with “traditional” HBT @ 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/0204061 Soff, Bass, Dumitru

3. STAR HBT 16 Oct 20032nd Warsaw Meeting on Correlations and Resonances 3 time dN/dt Already a problem with “traditional” HBT @ 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 ) STAR PHENIX hydro only hydro+hadronic rescatt “Realistically” treating FO with hadronic afterburner makes it worse

4. STAR HBT 16 Oct 20032nd Warsaw Meeting on Correlations and Resonances 4 … so why study (more complicated) asHBT ? sensitive to interplay b/t anisotropic geometry & dynamics/evolution Kolb & Heinz, Phys. Lett. B542 216 (2002)

5. STAR HBT 16 Oct 20032nd Warsaw Meeting on Correlations and Resonances 5 … so why study (more complicated) asHBT ? sensitive to interplay b/t anisotropic geometry & dynamics/evolution “broken symmetry” for b  0 → more detailed, important physics information another handle on dynamical timescales – likely impt in HBT puzzle P. Kolb, nucl-th/0306081 “radial flow” “elliptic flow” P. Kolb and U. Heinz, hep-ph/0204061

6. STAR HBT 16 Oct 20032nd Warsaw Meeting on Correlations and Resonances 6 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/0204061 Teaney, Lauret, Shuryak, nucl-th/0110037 STAR PHENIX hydro only hydro+hadronic rescatt Soff, Bass, Dumitru, PRL 2001 Teaney et al, nucl-th0110037 in-plane- extended out-of-plane-extended Teaney et al, nucl-th0110037  p =0°  p =90° R S small R S big R.P.

7. STAR HBT 16 Oct 20032nd Warsaw Meeting on Correlations and Resonances 7 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/0110037 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 …

8. STAR HBT 16 Oct 20032nd Warsaw Meeting on Correlations and Resonances 8 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

9. STAR HBT 16 Oct 20032nd Warsaw Meeting on Correlations and Resonances 9 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

10. STAR HBT 16 Oct 20032nd Warsaw Meeting on Correlations and Resonances 10 BlastWave fits to published RHIC data p T spectra constrain (mostly) T,  0 central midcentral peripheral F. Retière & MAL, in preparation

11. STAR HBT 16 Oct 20032nd Warsaw Meeting on Correlations and Resonances 11 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

12. STAR HBT 16 Oct 20032nd Warsaw Meeting on Correlations and Resonances 12 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

13. STAR HBT 16 Oct 20032nd Warsaw Meeting on Correlations and Resonances 13 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 0.88  0.010.87  0.020.81  0.02 aa 0.06  0.010.05  0.010.04  0.01 R X (fm) 12.9  0.310.2  0.58.0  0.4 R Y (fm) 12.8  0.311.8  0.610.1  0.4  0 (fm/c)8.9  0.37.4  1.26.5  0.8  (fm/c)0.0  1.40.8  3.20.8  1.9  2 / ndf 80.5 / 101153.7 / 9274.3 / 68 F. Retière & MAL, in preparation centralmidcentralperipheral

14. STAR HBT 16 Oct 20032nd Warsaw Meeting on Correlations and Resonances 14 Minbias v 2, asHBT @ 130 GeV STAR, PRL 87 182301 (2001) v 2 (p T,m) globally well-fit by hydro-inspired “blast-wave”  a ~ 0.04, R Y /R X ~ 1.05 Minbias asHBT well-reproduced with same BlastWave from minbias v 2 (p T,m) R y = 11.4 fm R x = 10.8 fm  0 = 8.3 fm/c  = 0 ( → ~1.5 fm/c w/ Bowler CC)) asHBT: geometry dominates dynamics Source out-of-plane extended

15. STAR HBT 16 Oct 20032nd Warsaw Meeting on Correlations and Resonances 15 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.

16. STAR HBT 16 Oct 20032nd Warsaw Meeting on Correlations and Resonances 16 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 ( * ) F. Retière & MAL, in preparation (*) Heinz, Hummel, MAL, Wiedemann, Phys. Rev. C66 044903 (2002)

17. STAR HBT 16 Oct 20032nd Warsaw Meeting on Correlations and Resonances 17 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

18. STAR HBT 16 Oct 20032nd Warsaw Meeting on Correlations and Resonances 18 FO shape from “normalized” oscillations the BlastWave view no-flow scenario: independent of p T … U. Wiedemann PR C57 266 (1998) MAL, U. Heinz, U. Wiedemann PL B489 287 (2000) in BW: this remains ~true even with flow (esp @ low p T ) F. Retière & MAL, in preparation  /2

19. STAR HBT 16 Oct 20032nd Warsaw Meeting on Correlations and Resonances 19 FO shape from “normalized” oscillations the BlastWave view no-flow scenario: independent of p T … U. Wiedemann PR C57 266 (1998) MAL, U. Heinz, U. Wiedemann PL B489 287 (2000) in BW: this remains ~true even with flow (esp @ 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

20. STAR HBT 16 Oct 20032nd Warsaw Meeting on Correlations and Resonances 20 asHBT at 200 GeV in STAR – R(  ) vs centrality 12 (!)  -bins b/t 0-180  (k T -integrated) 72 independent CF’s clear oscillations observed in transverse radii of symmetry-allowed * type R o 2, R s 2, R l 2 ~ cos(2  ) R os 2 ~ sin(2  ) 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 (*) Heinz, Hummel, MAL, Wiedemann, Phys. Rev. C66 044903 (2002)

21. STAR HBT 16 Oct 20032nd Warsaw Meeting on Correlations and Resonances 21 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. C58 1671 (1998)  m- RR

22. STAR HBT 16 Oct 20032nd Warsaw Meeting on Correlations and Resonances 22 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. C58 1671 (1998)

23. STAR HBT 16 Oct 20032nd Warsaw Meeting on Correlations and Resonances 23 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. C58 1671 (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) ]

24. STAR HBT 16 Oct 20032nd Warsaw Meeting on Correlations and Resonances 24 Correcting for finite  -binning &  RP -resolution Heinz, Hummel, MAL, Wiedemann, Phys. Rev. C66 044903 (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

25. STAR HBT 16 Oct 20032nd Warsaw Meeting on Correlations and Resonances 25 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%)

26. STAR HBT 16 Oct 20032nd Warsaw Meeting on Correlations and Resonances 26 Grand Data Summary – R 2 ,n vs k T, centrality One plot w/ relevant quantities from 2x5x3x4=120 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 (*) first STAR HBT paper: 10 CFs

27. STAR HBT 16 Oct 20032nd Warsaw Meeting on Correlations and Resonances 27 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]

28. STAR HBT 16 Oct 20032nd Warsaw Meeting on Correlations and Resonances28 A simple estimate –  0 from  init and  final “radial flow” P. Kolb, nucl-th/0306081 BW →  X,  Y @ 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

29. STAR HBT 16 Oct 20032nd Warsaw Meeting on Correlations and Resonances29 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  inconsistent w/ data BlastWave parameterization of FO at RHIC --  s NN =130 GeV –not perfect fit @ 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 ) asHBT @  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  “consistent” story of fast evolution (~9 fm/c)

30. STAR HBT 16 Oct 20032nd Warsaw Meeting on Correlations and Resonances30 To do… Us –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)? and can it be done consistently??? 2 fm/c4 fm/c6 fm/c8 fm/c P. Kolb, Ph.D. thesis (2002) P.T.  soft spot in EOS & “stall” no P.T. in EOS  explosive

31. STAR HBT 16 Oct 20032nd Warsaw Meeting on Correlations and Resonances31 To do… Us –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)? and can it be done consistently? –modification of hadronic stage needed?? Csörgő, Akkelin, Hama, Lukács, Sinyukov PRC67 034904 (2003) Heinz & Kolb, hep-ph/0206278

32. STAR HBT 16 Oct 20032nd Warsaw Meeting on Correlations and Resonances32 To do… Us –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 PRC67 034904 (2003) Heinz & Kolb, hep-ph/0206278