1. Sept 11- 14 WPCF-2008 Initial conditions and space-time scales in relativistic heavy ion collisions Yu. Sinyukov, BITP, Kiev Based on: Yu.S., I. Karpenko, A. Nazarenko J. Phys. G (Proc. QM-2008), in press

2. September 11-14 WPCF-2008 2 Expecting Stages of Evolution in Ultrarelativistic A+A collisions Early thermalization at 0.5 fm/c 0.2?(LHC) Elliptic flows t Relatively small space-time scales (HBT puzzle) Early thermal freeze-out: T_th Tch 150 MeV 10-15 fm/c 7-8 fm/c 1-3 fm/c

3. September 11-14 WPCF-2008 3 Basic ideas for the early stage p Hydrodynamic expansion: gradient pressure acts Free streaming: Gradient of density leads to non-zero collective velocities For nonrelativistic (massive) gas At free streaming So, even if and : Yu.S. Acta Phys.Polon. B37 (2006) 3343; Gyulassy, Yu.S., Karpenko, Nazarenko Braz.J.Phys. 37 (2007) 1031; Akkelin, Yu.S., Karpenko arXiv:0706.4066 (2007)(also in: Heavy-ion collisions at the LHC—Last call for predictions. J.Phys. G 35 054001 (2008))

4. September 11-14 WPCF-2008 4 t x F. Grassi,Y. Hama, T. Kodama Continuous emission Hydro-kinetic approach  is based on combination of Boltsmann equation and for hydro relativistic finite expanding system;  provides evaluation of escape probabili- ties and deviations (even strong) of distri- bution functions from local equilibrium;  accounts for conservation laws at the particle emission; PROVIDE earlier (as compare to CF-prescription) emission of hadrons, because escape probability accounts for whole particle trajectory in rapidly expanding surrounding (no mean-free pass criterion for freeze-out) Yu.S., Akkelin, Hama: PRL. 89, 052301 (2002); + Karpenko: PRC 78 034906 (2008). Basic ideas for the late stage

5. September 11-14 WPCF-2008 5 Boost-invariant distribution function at initial hypersurface CGC effective FT for transversally homogeneous system Transversally inhomogeneous system: of the gluon distribution proportional to the ellipsoidal Gaussian defined from the best fit to the density of number of participants in the collisions with the impact parameter b. A.Krasnitz, R.Venugopalan PRL 84 (2000) 4309; A. Krasnitz, Y. Nara, R. Venugopalan: Nucl. Phys. A 717 (2003) 268, A727 (2003) 427;T. Lappi: PRC 67 (2003) 054903, QM 2008 (J.Phys. G, 2008) If one uses the prescription of smearing of the -function as, then. As the result the initial local boost-invariant phase-space density takes the form is the variance of a Gaussian weight over the color charges of partons

6. September 11-14 WPCF-2008 6 Developing of collective velocities in partonic matter at pre-thermal stage ( Yu.S. Acta Phys. Polon. B37, 2006 ) Equation for partonic free streaming in hyperbolic coordinates between Solution where

7. September 11-14 WPCF-2008 7 Flows from non-equilibrated stage (at proper time = 1 fm/c) fm/c

8. September 11-14 WPCF-2008 8 Initial parameters even being (quasi) isotropic at becomes anisotropic at =1 fm/c. Supposing fast thermalization near this time, we use prescription: Then for fm/c the energy density profile: with the Gaussian width fm; At supposed thermalization time : is fitting parameter

9. September 11-14 WPCF-2008 9 Equation of State EoS from LattQCD (in form proposed by Laine & Schroder, Phys. Rev. D73, 2006) MeV The EoS accounts for gradual decays of the resonances during the expansion of hadron gas consistiong of 359 particle species with masses below 2.6 GeV. We evaluate the change of the compositon of the system at each space-time point x due to resonance decays in accordance with the width of each resonance and its world line in Minkowski space. MeV

10. September 11-14 WPCF-2008 10 Yu.S., Akkelin, Hama: Phys. Rev. Lett. 89, 052301 (2002); + Karpenko: to be published * Is related to local Hydro-kinetic approach MODEL is based on relaxation time approximation for relativistic finite expanding system; provides evaluation of escape probabilities and deviations (even strong) of distribution functions [DF] from local equilibrium; 3. accounts for conservation laws at the particle emission; Complete algorithm includes: solution of equations of ideal hydro [THANKS to T. Hirano for possibility to use code in 2006] ; calculation of non-equilibrium DF and emission function in first approximation; [Corresponding hydro-kinetic code: Tytarenko,Karpenko,Yu.S.(to be publ.)] Solution of equations for ideal hydro with non-zero left-hand-side that accounts for conservation laws for non-equlibrated process of the system which radiated free particles during expansion; Calculation of “exact” DF and emission function; Evaluation of spectra and correlations.

11. September 11-14 WPCF-2008 11 System's decoupling and spectra formation Emission function For pion emission is the total collision rate of the pion, carrying momentum p with all the hadrons h in the system in a vicinity of point x. is the space-time density of pion production caused by gradual decays during hydrodynamic evolution of all the suitable resonances H including cascade decays. We evaluate the compositon of the system at each space-time point x due to resonance decays in accordance with the width of each resonance and its world line in Minkowski space. The cross-sections in the hadronic gas are calculated in accordance with UrQMD.

12. September 11-14 WPCF-2008 12 Rate of collisions for pions in expanding hadron gas depending on T and p It accounts (in the way used in UrQMD) for pion cross sections with 359 hadron and resonance species with masses < 2.6 GeV. It is supposed that gas is in chemical equilibrium at Tch = 165 MeV and then is expanding. The decay of resonances into expanding liquid is taken into account.

13. September 11-14 WPCF-2008 13 Fitting parameter The maximal initial energy density: fm/c; GeV/fm 3 (the average energy density then is that bring with it the value at the thermalization time This means that the best fit corresponds to or In CGC approach at RHIC energies the value is used (T. Lappi, Talk at QM2008, J.Phys. G, in press)

14. September 11-14 WPCF-2008 14 Pion emission density for RHIC energies in HKM

15. September 11-14 WPCF-2008 15 Emission densities at different Pt

16. September 11-14 WPCF-2008 16 Transverse spectra

17. September 11-14 WPCF-2008 17 Longitudinal interferometry radius

18. September 11-14 WPCF-2008 18 Side-radius

19. September 11-14 WPCF-2008 19 Out- radius

20. September 11-14 WPCF-2008 20 Conclusions  A reasonable description of the pionic spectra and HBT (except some an overestimate for ) in cental Au+Au collisions at the RHIC energies is reached with the value of the fitting parameter or the average energy density at the initial time  The initial time fm/c and transverse width 5.3 fm (in the Gaussian approximation) of the energy density distribution are obtained from the CGC estimates.  The EoS at the temperatures corresponds to the lattice QCD calculations at  The used temperature of the chemical freeze-out MeV is taken from the latest results of particle number ratios analysis (F. Becattini,Plenary talk at QM-2008).  The anisotropy of pre-thermal transverse flows in non-central collisions, bring us a hope for a successful description of the elliptic flows with thermalization reached at a relatively late time:1-2 fm/c.