1. QGP hydro + hadronic cascade model: Status report Tetsufumi Hirano Dept. of Physics The Univ. of Tokyo RCNP, Oct. 29-30, 2007 TH, U.Heinz, D.Kharzeev, R.Lacey and Y.Nara, PLB636(2006)299; in preparation TH, U.Heinz, work in progress.

2. Outline Introduction Momentum Space (elliptic flow) Mass ordering of v 2 (p T ) revisited Violation of mass ordering for  mesons Soft EOS in CGC case? Configuration Space (femtoscopy) Source functions from hydro + cascade 1D, 3D (r side, r out, r long )-directions Summary

3. Motivation To understand the QGP in H.I.C., one needs to develop a dynamical framework. One example of agreement btw. data and theory is not sufficient. (Concerning accidental reproduction) One needs to improve his/her model continuously toward establishment of the “observational QGP physics”.

4. Mechanism of Mass Ordering? STAR white paper (’05) PHENIX white paper (’05) Lines: Results from Ideal hydro

5. A Hybrid Approach: QGP hydro + hadronic cascade 0 collision axis time Au QGP fluid Initial condition: Transverse  Glauber Longitudinal  “BGK triangle” QGP fluid: 3D ideal hydrodynamics (Hirano) massless free u,d,s+g gas + bag const. T c = 170 MeV Hadron gas: Hadronic cascade, JAM1.09 (Nara) T sw = 169 MeV hadron gas TH et al.(’06) (1D) Bass, Dumitru (2D) Teaney, Lauret, Shuryak, (3D) Nonaka, Bass, Hirano et al.

6. Pseudorapidity Distribution Tune initial parameters with T th = 100MeV to reproduce dN/deta. Then, switch to hadronic cascade below T=T sw. Caveat: Rejecting in- coming particles at T sw

7. p T spectra for pi, K, and p Reasonable reproduction of yields and spectra in low p T region (p T <~1.5 GeV/c) TH et al. (in preparation).

8. v 2 (p T ) for pi, K, and p OK! Fail to reproduce data due to (absence of) fluctuation of geometry Miller&Snelling (’03), Bhalerao&Ollitrault(’06) Andrade et al (’06),Drescher&Nara (’07) Browniowski et al(’07) TH et al. (in preparation).

9. Hydro + Cascade at Work in Forward Rapidity Regions Adapted from S.J.Sanders (BRAHMS) @ QM2006

10. Origin of Mass Ordering Mass ordering behavior results from hadronic rescatterings.  Not a direct signal of “perfect fluid QGP”  Interplay btw. ideal QGP fluid and dissipative hadron gas TH and M.Gyulassy; TH et al. (in preparation). b=7.2fm

11. Why they shift oppositely? protonspions pTpT v 2 (p T ) v2v2 must decrease with proper time v 2 for protons can be negative even in positive elliptic flow TH and M.Gyulassy, NPA769,71(06) P.Huovinen et al.,PLB503,58(01); TH et al, in preparation

12.  MESON FLOW

13. What happens to strangeness sector?

14. Additive Quark Model in Transport Codes (JAM/RQMD/UrQMD) For cross sections without exp. data, Expected to be very small for phi, Omega, etc.

15. Distribution of Freeze-Out Time b=2.0fm (no decay) TH et al. (in preparation). Early kinetic freezeout for multistrange hadrons: van Hecke, Sorge, Xu(’98)

16.  -meson case in p T < 1 GeV/c Just after hadronization Final results T = T sw = 169 MeV b=7.2fm TH et al. (in preparation). Caveat: Published PHENIX data obtained in p T >~1GeV/c for  mesons This is NOT obtained within ideal hydrodynamics.

17. What happens if  -meson follows radial flow? Of course, mass ordering is seen in hydro calculations

18. CGC INITIAL CONDITIONS

19. CGC Initial Condition Unintegrated gluon distribution a.la. Kharzeev, Levin, and Nardi Gluon production via k T factorization formula Count deposited energy in dV at (  0,x,y,  s ),  0 = 0.6fm/c Transverse profile: Entropy density Longitudinal Profile: Brodsky-Gunion-Kuhn triangle Color Glass CondensateGlauber-BGK type ss x(fm) ss ene.density

20. Two Hydro Initial Conditions Which Clear the “First Hurdle” 1. CGC model Matching I.C. via e(x,y,  ) 2.Glauber model (as a reference) N part :N coll = 85%:15% Centrality dependenceRapidity dependence Kharzeev,Levin, and Nardi Implemented in hydro by TH and Nara

21. v 2 (N part ) from CGC + QGP Fluid + Hadronic Gas Model Glauber: Early thermalization Discovery of Perfect Fluid QGP CGC: No perfect fluid? Additional viscosity required in QGP Important to understand initial conditions much better for making a conclusion TH et al.(’06) Adil, Gyulassy, Hirano(’06)

22. Large Eccentricity from CGC Initial Condition x y Pocket formula (ideal hydro): v 2 ~ 0.2  @ RHIC Ollitrault(’92) Hirano and Nara(’04), Hirano et al.(’06) Kuhlman et al.(’06), Drescher et al.(’06)

23. Soft QGP EoS Soft EOS? (equilibrium) or Viscosity? (non-eq.) Soft EoS reduces v 2 as it should

24. Summary of flow part A QGP fluid with hadronic rescattering Origin of mass ordering for v 2 (p T )  Radial flow effect, not “ mass effect ”. Violation of mass ordering for  mesons Mass ordering itself is not a direct signal of perfect fluidity! Interplay btw. QGP fluids and hadron gases. CGC I.C. is “ eccentric ”. Soft EOS is needed within ideal hydrodynamics.

25. Femtoscopy from Hydro + Cascade From momentum space to configuration space

26. Source Imaging Primed in PCMS (P = 0) Source Imaging: Inverse problem from C to D with a kernel K No more Gaussian parametrization! Source Imaging: Inverse problem from C to D with a kernel K No more Gaussian parametrization! Koonin-Pratt eq.: Source function and normalized emission rate (Brown&Danielewicz (’97-))

27. Distribution of the Last Interaction Point from Hydro + Cascade Blink: Ideal Hydro, Kolb and Heinz (2003) x-t x-y p x ~ 0.5 GeV/c for pions Long tail (  decay? elastic scattering?) Positive x-t correlation

28. 1D Source Function from Hydro + Cascade 0.48 < K T <0.6 GeV/c0.2 < K T <0.36 GeV/c Angle averaged source function Broader than PHENIX data Almost no K T dependence  PHENIX data Significant effects of hadronic rescatterings K T =P T /2

29. Omega Decay or Not? Switch off omega decay by hand in hadronic cascade  Long tail still seen.  Soft elastic scattering of pions? b=5.8fm

30. 3D Source Function from Hydro + Cascade (preliminary!) side outlong Source function in PCMS 1fm-slice in each direction 0.2<K T <0.4 GeV/c, |  | < 0.35,  + -  +,  - -  - pairs Red: Without rescattering, Black: With rescattering No longer Gaussian shape (Lines: Gaussian) Broaden by hadronic rescatterings

31. Summary of Femtoscopy 1D- and 3D-source functions from a dynamical model (QGP hydro + hadronic cascade) Significant rescattering effects are seen. Source function is no longer Gaussian. Long tail in 1D source function is described within hadronic rescatterings. K T dependence?

32. Outlook Pair-angle dependence of source function in non-central collisions Other pairs (K, p, ,…)  correlation to investigate  interaction (with Ohnishi-san) Just get started. Many other things to do…