Sept 11- 14 WPCF-2008

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

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Expecting Stages of Evolution in Ultrarelativistic A+A collisions

Early thermalization at 0.5 fm/c

0.2?(LHC)

Elliptic flows

tRelatively small space-time

scales (HBT puzzle)

Early thermal freeze-out: T_th Tch

150 MeV

10-15 fm/c

7-8 fm/c

1-3 fm/c

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Basic ideas for the early stage p

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 an

d:

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. G 35 054001 (2008))

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t

x

outt

F. Grassi,Y. Hama, T. Kodama

Continuous emission Hydro-kinetic approach

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)

Yu.S., Akkelin, Hama: PRL. 89, 052301 (2002); + Karpenko: PRC 78 034906 (2008).

Basic ideas for the late stage

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Boost-invariant distribution function at initial hypersurface

CGC effective FT for transversally homogeneous system

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.

A.Krasnitz, R.Venugopalan PRL 84 (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)

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

is the variance of a Gaussian weight over the color charges of partons

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Developing of collective velocities in partonic matter at pre-thermal stage (Yu.S. Acta Phys. Polon. B37, 2006)

Equation for partonic free streaming in hyperbolic coordinates between

Solution

where

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

fm/c

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Initial parameters even being (quasi) isotropic atbecomes 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; At supposed thermalization time :

is fitting parameter

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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

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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 [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.

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System's decoupling and spectra formation

Emission function

For pion emission

is the total collision rate of the pion, carrying momentum p with all the hadrons h in the system in a vicinity of point x.

is the space-time density of pion production caused by gradual decays during hydrodynamic evolution of all the suitable resonances H including cascade decays. 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 in Minkowski space.

The cross-sections in the hadronic gas are calculated in accordance with UrQMD .

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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.

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Fitting parameterThe maximal initial energy density: fm/c; GeV/fm3

(the average energy density then is

that bring with it the value

at the thermalization time

This means that the 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)

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Pion emission density for RHIC energies in HKM

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Emission densities at different Pt

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Transverse spectra

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Longitudinal interferometry radius

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Side-radius

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Out- radius

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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.