# Presentation: 087957

## 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

- 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

- 10-15 fm/c

- 7-8 fm/c

- 1-3 fm/c

##               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”).

- 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

- :

##               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

***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 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)**

##                                      Distribution function at initial hypersurface 

-                                     ** **Distribution function at initial hypersurface

-   Distribution function motivated
-      by CGC effective FT

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

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

-   Equation for partonic free streaming in hyperbolic coordinates:

-   Solution

- where

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

- |v| in approximation for initial Gauss elliptic profile

## Comparision of flows at free streaming and hydro evolution 

## Energy profile. 

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

## Equation of States

## Transverse velocities at: 

****=1 fm/c; Gaussian profile, R=4.3 fm

- 1st order phase transition

**Crossover**

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

- RHIC

- LHC

##   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] ;
- 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.

## 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.

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

- EXTRA SLIDES

- [Modified PCE-Hirano and FS initial stage]

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

## Transv. spectra of pions (blue line is prediction)

## Long –radii for pions (blue line is prediction)

## Side- radii for pions (blue line is prediction)

## Out –radii for pions (blue line is prediction)

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

## Emission densities for fixed pt=0.3 GeV/c

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

- Preliminary

## Emission densities for fixed pt=0.6 GeV/c

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

- Preliminary

## Emission densities for fixed pt=1.2 GeV/c

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

- Preliminary

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

- Preliminary

## 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.**