1. CERN May 30 2007 Heavy Ion Collisions at the LHC Last Call for Predictions Initial conditions and space-time scales in relativistic heavy ion collisions Yu. Sinyukov, BITP, Kiev (with participation of Yu. Karpenko, S.Akkelin)

2. CERN May 30 2007 HIC at the LHC Last Call for Predictions 2 Expecting Stages of Evolution in Ultrarelativistic A+A collisions t

3. CERN May 30 2007 HIC at the LHC Last Call for Predictions 3 “Soft Physics” measurements x t A A ΔωKΔωK p=(p 1 + p 2 )/2 q= p 1 - p 2 (QS) Correlation function Space-time structure of the matter evolution, e.g.,

4. CERN May 30 2007 HIC at the LHC Last Call for Predictions 4 Approximately conserved observables APSD - Phase-space density averaged over some hypersurface, where all particles are already free and over momen- 0. (Bertsch) tum at fixed particle rapidity, y=0. (Bertsch) t z Chemical. f.-o. Thermal f.-o. APSD is conserved during isentropic and chemically frozen evolution (including a free streaming): n(p) is single-, n(p 1, p 2 ) is double (identical) particle spectra, correlation function is C=n(p 1, p 2 )/n(p 1 )n(p 2 ) p=(p 1 + p 2 )/2 q= p 1 - p 2 S. Akkelin, Yu.S. Phys.Rev. C 70 064901 (2004):

5. CERN May 30 2007 HIC at the LHC Last Call for Predictions 5 The averaged phase-space density. LHC prediction = 0.2-0.3 Non-hadronic DoF Limiting Hagedorn Temperature S. Akkelin, Yu.S: Phys.Rev. C 73, 034908 (2006); Nucl. Phys. A 774, 647 (2006)

6. CERN May 30 2007 HIC at the LHC Last Call for Predictions 6 Energy dependence of the interferometry radii Energy- and kt-dependence of the radii Rlong, Rside, and Rout for central Pb+Pb (Au+Au) collisions from AGS to RHIC experiments measured near midrapidity. S. Kniege et al. (The NA49 Collaboration), J. Phys. G30, S1073 (2004).

7. CERN May 30 2007 HIC at the LHC Last Call for Predictions 7 HBT PUZZLE The interferometry volume only slightly increases with collision energy (due to the long-radius growth) for the central collisions of the same nuclei. Explanation: only slightly increases and is saturated due to limiting Hagedorn temperature T H =T c (  B = 0). grows with A is fixed

8. CERN May 30 2007 HIC at the LHC Last Call for Predictions 8 HBT PUZZLE & FLOWS Possible increase of the interferometry volume with due to geometrical volume grows is mitigated by more intensive transverse flows at higher energies:,  is inverse of temperature Why does the intensity of flow grow? More more initial energy density  more (max) pressure p max BUT the initial acceleration is ≈ the same HBT puzzle Intensity of collective flows grow Time of system expansion grows: Initial flows (  < 1-2 fm/c) develop

9. CERN May 30 2007 HIC at the LHC Last Call for Predictions 9 Ro/Rs ratio and initial flows M.Borysova, Yu.S., S.Akkelin, B.Erazmus, Iu.Karpenko, Phys.Rev. C 73, 024903 (2006)

10. CERN May 30 2007 HIC at the LHC Last Call for Predictions 10 Developing of collective velocities in partonic matter at pre-thermal stage (Gyulassy, Karpenko, Yu.S., Nazarenko, BJP (2007) Distribution function at initial hypersurface  0 =1 Venagopulan, 2003, 2005; Kharzeev 2006 Equation for partonic free streaming: Solution

11. CERN May 30 2007 HIC at the LHC Last Call for Predictions 11 Transverse velocities at:  =1 fm/c; Gaussian profile, R=4.3 fm 1 st order phase transition Crossover IC at  =0.1 (RHIC) and 0.07 (LHC) fm/c for Glasma from T. Lappy (2006)

12. CERN May 30 2007 HIC at the LHC Last Call for Predictions 12 Equation of States

13. CERN May 30 2007 HIC at the LHC Last Call for Predictions 13 Freeze-out hypersurface for LHC energies

14. CERN May 30 2007 HIC at the LHC Last Call for Predictions 14 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; 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; Calculation of “exact” DF and emission function; Evaluation of spectra and correlations.

15. CERN May 30 2007 HIC at the LHC Last Call for Predictions 15 Emission at RHIC top energy EXTRA SLIDES

16. CERN May 30 2007 HIC at the LHC Last Call for Predictions 16 Emission at LHC energy Sqrt(s) = 5.5 TeV

17. CERN May 30 2007 HIC at the LHC Last Call for Predictions 17 Emission function at large p T

18. CERN May 30 2007 HIC at the LHC Last Call for Predictions 18 Transv. spectra of pions (blue line is prediction)

19. CERN May 30 2007 HIC at the LHC Last Call for Predictions 19 Long –radii for pions (blue line is prediction)

20. CERN May 30 2007 HIC at the LHC Last Call for Predictions 20 Side- radii for pions (blue line is prediction)

21. CERN May 30 2007 HIC at the LHC Last Call for Predictions 21 Out –radii for pions (blue line is prediction)

22. CERN May 30 2007 HIC at the LHC Last Call for Predictions 22 Out-to-Side ratio for pions (blue line is prediction)

23. CERN May 30 2007 HIC at the LHC Last Call for Predictions 23 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.

24. CERN May 30 2007 HIC at the LHC Last Call for Predictions 24 cccccccccccccccccccccccccccccccc c