Jaipur February 2008 Quark Matter 2008 Initial conditions and space-time scales in relativistic heavy ion collisions Yu. Sinyukov, BITP, Kiev (with participation.

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Presentation transcript:

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)

Jaipur February Quark Matter 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 fm/c 7-8 fm/c 1-3 fm/c

Jaipur February Quark Matter 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: (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 :

Jaipur February Quark Matter Basic ideas for the late stage Yu.S., Akkelin, Hama: Phys. Rev. Lett. 89, (2002); + Karpenko: to be published; Akkelin, Yu.S., Karpenko arXiv: 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 probabilities and deviations (even strong) of distribution 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)

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

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

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

Jaipur February Quark Matter Comparision of flows at free streaming and hydro evolution

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

Jaipur February Quark Matter Equation of States

Jaipur February Quark Matter 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

Jaipur February Quark Matter Yu.S., Akkelin, Hama: Phys. Rev. Lett. 89, (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.

Jaipur February Quark Matter 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.

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

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

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

Jaipur February Quark Matter Long –radii for pions (blue line is prediction)

Jaipur February Quark Matter Side- radii for pions (blue line is prediction)

Jaipur February Quark Matter Out –radii for pions (blue line is prediction)

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

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

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

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

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

Jaipur February Quark Matter 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.