1. 1 Space-time analysis of reactions at RHIC Fabrice Retière Lawrence Berkeley Lab STAR collaboration

2. 2 A sketch of a collisions: Sequence of particle freeze out (FO) 1 fm/c5 fm/c 10 fm/c 50 fm/c hadronization initial state pre-equilibrium QGP and hydrodynamic expansion hadronic phase Sketch from S.Bass Chemical: K*, dbar Kinetic: , K, K*, p,  dbar Chemical: , K, p,   Kinetic:   high mass or/and pt particles

3. 3 Many assumptions in this picture Incoming parton collisions High energy density created System expands and cools down Partonic stage Flow Hadronic stage Flow driven by hadronic x- sections Particle freeze-out sequence Early emission of high pt and high mass particles Not enough energy later on Chemical freeze-out Unique chemical freeze-out temperature Kinetic freeze-out Depends on hadronic cross sections of each particle species No sudden hadronization

4. 4 Outline Does this picture make sense? Freeze out pattern for , K, p and  Freeze out pattern of  Consistency checks Assessing the presence of transverse flow bringing in v2 and two-particle correlations Consistency of the time scales Conclusions

5. 5 , K, p,  chemical freeze-out Relative yields fit thermal models T = 176 MeV  B = 41 MeV Also fits  yields Same chemical freeze-out

6. 6 , K, p,  kinetic freeze out Blast wave parameterization R tt Rside Rout Kt = pair Pt Hydro-inspired parameterization Boost invariant longitudinal flow Transverse flow Linear rapidity profile Azymuthal oscilation in non-central Tunable system size, shape and life time Parameterization of the final state Spectra fits application described by E.Schnedermann, J. Sollfrank, and U. Heins, PRC 48 (2002) 2462

7. 7 , K, p,  kinetic-freeze out Peripheral AuAu 130 GeV SPECTRA @ 130 GeV Closed circle = Central Open circle = Mid-perif Cross = Peripheral , K, p: PHENIX Phys. Rev. Lett. 88, 242301 (2002)  : STAR Phys. Rev. Lett. 89, 092301 (2002) PeripheralCentral  2 /point74.3/6880.5/101 T (MeV)95  3108  3 Max flow rapidity 0.81  0.010.88  0.02

8. 8 , K, p,  freeze out Summary , K, p and  chemical freeze-out at T~176MeV and mB ~ 41 MeV , K, p and  kinetic freeze-out at T~110 MeV and ~ 0.6 T chemical > T kinetic Need some time to cool down to kinetic freeze-out Difference due to missing resonances? No, same results with Blast Wave + resonance (T.Peitzman) Yes, for W. Florkowski and W. Broniowski

9. 9 , kinetic freeze out Blast wave fit @ 130 GeV     K* Plain: T = 155 MeV,  max = 0.72 Dash: T = 108 MeV,  max = 0.88 , and  spectra: preliminary STAR data K* spectra: Phys. Rev. C66, 061901(R) (2002)  spectra: Phys. Rev. C 65, 041901(R) (2002)  K, p from PHENIX  From STAR  From STAR  max

10. 10 , freeze out Summary Same chemical freeze- out pattern as , K, p and   exhibit less flow than , K, p and  Only sensitive to partonic flow? Flow issue inconclusive for  and  @ 130 GeV Wait for 200 GeV Fit to , ,  T = 155 MeV  max = 0.72 Fit to , K, p,  T = 108 MeV  max = 0.88  70%66%  bar72%22%  79%28%  84%99% Confidence level Reliable point-to-point errors are mandatory to draw any conclusions

11. 11 Consistency check Issues Is the flow assumption solid? Challenging the blast wave parameterization Blast wave vs v2 Blast wave vs  HBT Blast wave vs shift between sources of , K, p Do the time-scales make sense? System life time Emission duration

12. 12 Consistency check Including v2 in blast wave fit V2 @ 130 GeV Closed circle = Central Open circle = Mid-perif Cross = Peripheral STAR Data: Phys. Rev. Lett. 87, 182301 (2001).

13. 13 Consistency check Blast wave and HBT Rside Rout RsideRout P T =160 MeV/cP T =380 MeV/c KTKT R out R side  R long Time Sketch by Scott Pratt

14. 14 PION HBT @ 130 GeV Closed circle = Central Open circle = Mid-perif Cross = Peripheral Box = PHENIX central not included in fit Consistency check Blast wave and HBT STAR data: PRL 87, 082301 (2001) PHENIX data: PRL 88, 192302 (2002)

15. 15 Consistency check Global fit to spectra, v2 and HBT Peripheralmid- peripheral Central  2 /dof 74.3/68153.7/92 80.5/101 T (MeV) 95  3106  2 108  3 Max flow rapidity 0.88  0.010.87  0.01 0.81  0.02 Flow rapidity  modulation 0.04  0.010.052  0.04 0.060  0.007 Radius in-plane (fm) 8.00  0.0910.2  0.5 12.9  0.4 Radius out-of-plane (fm) 10.0  0.211.8  0.6 12.8  0.4 Proper life time (fm/c) 6.5  0.47.4  0.7 8.9  0.3 Emission duration (fm/c) 0.8  0.90.7  1.3 0.002  1.1 Will increase with improved Coulomb correction 3D Blast wave analysis done with Mike Lisa (OSU)

16. 16 Consistency check Blast wave and non-id correlations  r* out measured by constructing non-id correlation  -K,  -p, K-p Why not one day?  ? Blast wave predict  r* out  0 Spatial shift due to transverse flow Time shift due to longitudinal flow Boost to pair Rest frame  r* out =  T (  r out –  T  t) Proton pt = 1. GeV/c  t = 0.73 Pion pt = 0.15 GeV/c  t = 0.73  r out 0  r* out

17. 17 Consistency check Blast wave and non-id correlations Blast wave in the right ballpark Points: data Plain line: Blast wave calculation Dash line: BW without time  -K  -p K-p STAR Preliminary  r* out (fm)

18. 18 Consistency check Space is OK. What about time? Data are consistently described by blast wave Very strong case in favor of flow as modeled by hydro calculations and cascade models What about time scales? Reminder of the fit results: Life time ~ 9 fm/c Hydro and cascade models cannot yield such short life time Consistent with balance function? Lets take a look at source shape Emission duration ~ 0 fm/c Emission duration should be related to the time between chemical and kinetic freeze out However, Tchem > Tkin. The system cannot cool down instantaneously!

19. 19 Consistency check Short life time and source shape In peripheral events Start out-of-plane Evolve towards in-plane source The shape of the source gives an indication of the freeze-out time scale Time Out-of-planeCircular In-plane Typical evolution in the hydro world

20. 20 Consistency check source shape _ Probe source shape with HBT with respect to reaction plane out-of-plane extended source R side (large) Reaction plane R side (small) R in-plane R out-of-plane

21. 21 Consistency check Short life time agree with source shape Initial aspect ratio From Glauber model Final aspect ratio From blast wave fit to HBT radii wrt reaction plane Take care of flow effect Centrality  initial (Glauber)  final (HBT + blast wave)  initial  final STAR preliminary R in-plane R out-of-plane  = R in-plane / R out-of-plane Do not evolve that far

22. 22 Consistency check Hints of non-zero emission duration Small yield of  (1520) and K*  (1520) and K* produced at “lower temperature” than other hadrons? Destroyed during time from chemical to thermal freeze out Thermal calculations from D.Magestro PLB 518 (2001) 41 Chemical freeze out parameters: T = 176 MeV,  B = 41 MeV STAR data K* (Haibin Zhang)  (1520) (L. Gaudichet, C. Markert)  (1520)/  K*/K STAR preliminary data

23. 23 Conclusions Data can be consistently described within a framework assuming: Transverse and longitudinal flow Short system life time Need 200 GeV data to conclude about multi- strange baryon flow One inconsistency: short emission duration from HBT doesn’t allow observed freeze-out in 2 stages, chemical  kinetic freeze-out.

24. 24 Outlook Wealth of 200 GeV data coming New HBT data. New Coulomb correction may increase emission duration HBT with respect to reaction plane, centrality, pt (high pt from PHENIX), Charged Kaon, K0s HBT “Fancy correlations” p- ,  -K  -p  K-p,  (great to probe multi-strange baryon flow) Better statistics for  (J. Ma’s talk), K* (H. Zhang’s talk),  (P. Fachini’s talk) Enough to study v2 Solid conclusions coming soon …

25. 25 Extra slides

26. 26

27. 27 Fit results R in-plane R out-of-plane Max transverse flow rapidity Flow rapidity  modulation Proper life time Emission duration

28. 28 Star preliminary CENTRAL DATA

29. 29 Example of non-identical particle correlation functions Pion slowerPion faster Pion slowerPion faster  -p  -K Star preliminary

30. 30 Multi-strange baryon flow? Non-id correlation as a probe Pion pt = 0.15 GeV/c  t = 0.73 Proton pt = 1. GeV/c  t = 0.73   pt = 1.4 GeV/c  t = 0.73   pt = 1.8 GeV/c  t = 0.73  t is kept constant to have correlated pairs r p -r  r  -r  r  -r  If  and  flow as protons: r p -r   r  -r   r  -r  Otherwise: r p -r   r  -r   r  -r 

31. 31 Flow breaks at high pt? Non-id correlation as a probe At low momentum, flow driven emission pattern At high momentum (how high?) prompt emission Say proton arrises more and more from hard processes starting at 1.5 GeV/c Points: preliminary STAR data Plain line: Blast wave calculation Dash line: BW + prompt emission of p

32. 32 , freeze out Open issues Same chemical freeze out temperature as , K, p,  What about kinetic freeze out? Expect  hadronic x-sections < , K, p and  hadronic x-sections Do flow affects  and  as , K, p and  ? Flow at partonic stage Or do they flow less? Don’t feel flow at hadronic stage

33. 33 , K, p,  kinetic freeze out Blast wave parameterization “Hydro-like” parameterization Boltzman with Flow Flow:  (r) = (  0 +  a cos(2  p )) r –Grows linearly increasing r –May vary with angle wrt event plane Parameters: T,  0 and  a System geometry Elliptical box (fuzzy edges possible) Parameters: Rx (in-plane) and Ry (out- of-plane) Time Parameters: proper life time (  ) and emission duration (  t) To calculate: - Spectra = integral over space and momentum azimuthal angle - v2(pt) = average of cos(2  p )over space at a given pt - Hbt radii (pt) = standard deviations along out, side and long directions at A given pt