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

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. Expecting Stages of Evolution in Ultrarelativistic A+A collisions. t.

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

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  1. 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 WPCF-2008

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

  3. Basic ideas for the early stage p 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. G35 054001 (2008)) At free streaming Hydrodynamic expansion: gradient pressure acts So, even if : and Free streaming: Gradient of density leads to non-zero collective velocities For nonrelativistic (massive) gas WPCF-2008

  4. Basic ideas for the late stage Yu.S., Akkelin, Hama: PRL. 89, 052301 (2002); + Karpenko: PRC 78 034906 (2008). Hydro-kinetic approach Continuous emission t • 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) x WPCF-2008 F. Grassi,Y. Hama, T. Kodama

  5. Boost-invariant distribution function at initial hypersurface CGC effective FT for transversally homogeneous system is the variance of a Gaussian weight over the color charges of partons A.Krasnitz, R.Venugopalan PRL84 (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) Transversally inhomogeneous system: <transverse profile> 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. 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 WPCF-2008

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

  7. Flows from non-equilibrated stage (at proper time = 1 fm/c) fm/c 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; is fitting parameter At supposed thermalization time : 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 WPCF-2008

  10. 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 [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. Is related to local * WPCF-2008

  11. System's decoupling and spectra formation • Emission function For pion emission is the total collision rate of the pion, carrying momentump with all the hadrons h in the system in a vicinityof point x. is the space-time densityof pion production caused by gradual decays during hydrodynamicevolution of all the suitable resonances H including cascadedecays. 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 inMinkowski space. The cross-sections in the hadronic gas are calculated in accordance with UrQMD . 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. WPCF-2008

  13. Fitting parameter The maximal initial energy density: fm/c;GeV/fm3 (the averageenergy density then is that bring with it the value at the thermalization time This means thatthe 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) WPCF-2008

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

  15. Emission densities at different Pt WPCF-2008

  16. Transverse spectra WPCF-2008

  17. Longitudinal interferometry radius WPCF-2008

  18. Side-radius WPCF-2008

  19. Out- radius 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. WPCF-2008

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