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Initial conditions and space-time scales in relativistic heavy ion collisions Yu. Sinyukov, BITP, Kiev (with participation of Y. Karpenko, A. Nazarenko) Expecting Stages of Evolution in Ultrarelativistic A+A collisions t Relatively small space-time scales (HBT puzzle) 10-15 fm/c

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

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Initial conditions and space time scales in relativistic heavy ion collisions l.jpg

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

Yu. Sinyukov, BITP, Kiev

(with participation of Y. Karpenko, A. Nazarenko)

Quark Matter 2008


Expecting stages of evolution in ultrarelativistic a a collisions l.jpg

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)

Quark Matter 2008


Slide3 l.jpg

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”).

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

Quark Matter 2008


Slide4 l.jpg

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

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

Y. Hama and collaborators

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Distribution function at initial hypersurface l.jpg

Distribution function at initial hypersurface

Distribution function motivated

by CGC effective FT

Quark Matter 2008

T. Lappi, R. Venugopalan, Phys. Rev. C74 (2006) 054905


Developing of collective velocities in partonic matter at pre thermal stage yu s 2006 l.jpg

Developing of collective velocities in partonic matter at pre-thermalstage (Yu.S. 2006)

  • Equation for partonic free streaming in hyperbolic coordinates:

  • Solution

where

Quark Matter 2008


Flows from non equilibrated stage at proper time 1 fm c l.jpg

Flows from non-equilibrated stage (at proper time = 1 fm/c)

|v| in approximation for initial Gauss elliptic profile

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Comparision of flows at free streaming and hydro evolution l.jpg

Comparision of flows at free streaming and hydro evolution

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Energy profile l.jpg

Energy profile.

even being isotropic at becomes anisotropic at =1 fm/c. Supposing fast thermalization near this time, we use prescription

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Equation of states l.jpg

Equation of States

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Transverse velocities at l.jpg

Transverse velocities at:

=1fm/c; Gaussian profile, R=4.3 fm

IC at 0=0.1 (RHIC) and 0.07(LHC) fm/c for Glasma from T. Lappy (2006)

1st order phase transition

RHIC

Crossover

LHC

Quark Matter 2008


Yu s akkelin hama phys rev lett 89 052301 2002 karpenko to be published l.jpg

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] ;

  • 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.

Is related to local

*

Quark Matter 2008


Rate of collisions for pions in expanding hadron gas depending on t and p l.jpg

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.

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Emission at rhic top energy pce and fs initial stage l.jpg

Emission at RHIC top energy [PCE and FS initial stage]

[Modified PCE-Hirano and FS initial stage]

  • EXTRA SLIDES

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Emission at lhc energy sqrt s 5 5 tev pce and fs initial stage l.jpg

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

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Transv spectra of pions blue line is prediction l.jpg

Transv. spectra of pions (blue line is prediction)

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Long radii for pions blue line is prediction l.jpg

Long –radii for pions(blue line is prediction)

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Side radii for pions blue line is prediction l.jpg

Side- radii for pions(blue line is prediction)

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Out radii for pions blue line is prediction l.jpg

Out –radii for pions(blue line is prediction)

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Out to side ratio for pions blue line is prediction l.jpg

Out-to-Side ratio for pions (blue line is prediction)

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Emission densities for fixed pt 0 3 gev c l.jpg

Emission densities for fixed pt=0.3 GeV/c

EoS accounts for crossover (Laine&Schroder) and CFO with resonance decays.

Preliminary

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Emission densities for fixed pt 0 6 gev c l.jpg

Emission densities for fixed pt=0.6 GeV/c

EoS accounts for crossover (Laine&Schroder) and CFO with resonance decays.

Preliminary

Quark Matter 2008


Emission densities for fixed pt 1 2 gev c l.jpg

Emission densities for fixed pt=1.2 GeV/c

EoS accounts for crossover (Laine&Schroder) and CFO with resonance decays.

Preliminary

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Slide24 l.jpg

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

Preliminary

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Conclusions l.jpg

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.

Quark Matter 2008


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