Initial conditions and space-time scales in relativistic heavy ion collisions

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

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

3. “Soft Physics” measurements A x t ΔωK A (QS) Correlation function Space-time structure of the matter evolution, e.g., p=(p1+ p2)/2 q= p1- p2 HIC at the LHC Last Call for Predictions

4. Approximately conserved observables t Thermal f.-o. • APSD - Phase-space density averaged over some hypersurface , where all particles are already free and over momen- tum at fixed particle rapidity,y=0. (Bertsch) Chemical. f.-o. n(p) is single- , n(p1, p2 ) is double (identical) particle spectra, correlation function is C=n(p1, p2)/n(p1)n(p2) z p=(p1+ p2)/2 q= p1- p2 • APSD is conserved during isentropic and chemically frozen evolution (including a free streaming): S. Akkelin, Yu.S. Phys.Rev. C 70 064901 (2004): 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) 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 forcentral Pb+Pb(Au+Au) collisions from AGS to RHICexperiments measurednear midrapidity. S. Kniege et al. (The NA49 Collaboration), J. Phys. G30, S1073 (2004). 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 TH =Tc (B = 0). • grows with A is fixed 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 pmax 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 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) HIC at the LHC Last Call for Predictions

10. Developing of collective velocities in partonic matter at pre-thermalstage (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 HIC at the LHC Last Call for Predictions

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

12. Equation of States HIC at the LHC Last Call for Predictions

13. Freeze-out hypersurface for LHC energies HIC at the LHC Last Call for Predictions

14. Yu.S. , Akkelin, Hama: Phys. Rev. Lett. 89 , 052301 (2002); + Karpenko: to be published 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. Is related to local * HIC at the LHC Last Call for Predictions

15. Emission at RHIC top energy • EXTRA SLIDES HIC at the LHC Last Call for Predictions

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

17. Emission function at large pT HIC at the LHC Last Call for Predictions

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

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

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

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

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

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