1. Jaipur February 2008 Quark Matter 2008 Initial conditions and space-time scales in relativistic heavy ion collisions Yu. Sinyukov, BITP, Kiev (with participation of Y. Karpenko, A. Nazarenko)

2. Jaipur February 5 2008 Quark Matter 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. Jaipur February 5 2008 Quark Matter 2008 3 Basic ideas for the early stage 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 (see also in “Heavy Ion Collisions at the LHC - Last Call for Predictions”). 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 :

4. Jaipur February 5 2008 Quark Matter 2008 4 Basic ideas for the late stage Yu.S., Akkelin, Hama: Phys. Rev. Lett. 89, 052301 (2002); + Karpenko: to be published; Akkelin, Yu.S., Karpenko arXiv:0706.4066 t x Y. Hama and collaborators 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)

5. Jaipur February 5 2008 Quark Matter 2008 5 Distribution function at initial hypersurface Distribution function motivated by CGC effective FT T. Lappi, R. Venugopalan, Phys. Rev. C74 (2006) 054905

6. Jaipur February 5 2008 Quark Matter 2008 6 Developing of collective velocities in partonic matter at pre-thermal stage ( Yu.S. 2006 ) Equation for partonic free streaming in hyperbolic coordinates: Solution where

7. Jaipur February 5 2008 Quark Matter 2008 7 Flows from non-equilibrated stage (at proper time = 1 fm/c) |v| in approximation for initial Gauss elliptic profile

8. Jaipur February 5 2008 Quark Matter 2008 8 Comparision of flows at free streaming and hydro evolution

9. Jaipur February 5 2008 Quark Matter 2008 9 Energy profile. even being isotropic at becomes anisotropic at =1 fm/c. Supposing fast thermalization near this time, we use prescription

10. Jaipur February 5 2008 Quark Matter 2008 10 Equation of States

11. Jaipur February 5 2008 Quark Matter 2008 11 Transverse velocities at:  =1 fm/c; Gaussian profile, R=4.3 fm 1 st order phase transition Crossover IC at  0 =0.1 (RHIC) and 0.07 (LHC) fm/c for Glasma from T. Lappy (2006) RHIC LHC

12. Jaipur February 5 2008 Quark Matter 2008 12 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] ; calculation of non-equilibrium DF and emission function in first approximation; 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; [Corresponding hydro-code (2007): Tytarenko,Karpenko,Yu.S.(to be publ.)] Calculation of “exact” DF and emission function; Evaluation of spectra and correlations.

13. Jaipur February 5 2008 Quark Matter 2008 13 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 360 hadron and resonance species with masses < 3 GeV. It is supposed that gas is in chemical equilibrium at Tch = 175 MeV and then is expanding. The decay of resonances into expanding liquid is taken into account.

14. Jaipur February 5 2008 Quark Matter 2008 14 Emission at RHIC top energy [PCE and FS initial stage] EXTRA SLIDES [Modified PCE-Hirano and FS initial stage]

15. Jaipur February 5 2008 Quark Matter 2008 15 Emission at LHC energy Sqrt(s) = 5.5 TeV [PCE and FS initial stage]

16. Jaipur February 5 2008 Quark Matter 2008 16 Transv. spectra of pions (blue line is prediction)

17. Jaipur February 5 2008 Quark Matter 2008 17 Long –radii for pions (blue line is prediction)

18. Jaipur February 5 2008 Quark Matter 2008 18 Side- radii for pions (blue line is prediction)

19. Jaipur February 5 2008 Quark Matter 2008 19 Out –radii for pions (blue line is prediction)

20. Jaipur February 5 2008 Quark Matter 2008 20 Out-to-Side ratio for pions (blue line is prediction)

21. Jaipur February 5 2008 Quark Matter 2008 21 Emission densities for fixed pt=0.3 GeV/c EoS accounts for crossover (Laine&Schroder) and CFO with resonance decays. Preliminary

22. Jaipur February 5 2008 Quark Matter 2008 22 Emission densities for fixed pt=0.6 GeV/c EoS accounts for crossover (Laine&Schroder) and CFO with resonance decays. Preliminary

23. Jaipur February 5 2008 Quark Matter 2008 23 Emission densities for fixed pt=1.2 GeV/c EoS accounts for crossover (Laine&Schroder) and CFO with resonance decays. Preliminary

24. Jaipur February 5 2008 Quark Matter 2008 24 HBT long-radius in CGC approach, with EoS accounting for crossover (Laine&Schroder) and CFO with resonance decays. Preliminary

25. Jaipur February 5 2008 Quark Matter 2008 25 Conclusions The relatively small increase of interferometry radii with energy, as compare with expectations, are caused by  increase of transverse flow due to longer expansion time;  developing of initial flows at early pre-thermal stage;  more hard transition EoS, corresponding to cross-over;  non-flat initial (energy) density distributions, similar to Gaussan;  early (as compare to CF-prescription) emission of hadrons, because escape probability account for whole particle trajectory in rapidly expanding surrounding (no mean-free pass criterion for freeze-out) The hydrokinetic approach to A+A collisions is proposed. It allows one to describe the continuous particle emission from a hot and dense finite system, expanding hydrodynamically into vacuum, in the way which is consistent with Boltzmann equations and conservation laws, and accounts also for the opacity effects.