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)
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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 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 an
d
:
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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
outt
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)
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Distribution function at initial hypersurface
Distribution function motivated
by CGC effective FT
T. Lappi, R. Venugopalan, Phys. Rev. C74 (2006) 054905
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Developing of collective velocities in partonic matter at pre-thermal stage (Yu.S. 2006)
Equation for partonic free streaming in hyperbolic coordinates:
Solution
where
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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
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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
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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
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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] ;• 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.
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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 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]
EXTRA SLIDES[Modified PCE-Hirano and FS initial stage]
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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)
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Long –radii for pions (blue line is prediction)
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Side- radii for pions (blue line is prediction)
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Out –radii for pions (blue line is prediction)
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Out-to-Side ratio for pions (blue line is prediction)
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Emission densities for fixed pt=0.3 GeV/c
EoS accounts for crossover (Laine&Schroder) and CFO with resonance decays.
Pre
limin
ary
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Emission densities for fixed pt=0.6 GeV/c
EoS accounts for crossover (Laine&Schroder) and CFO with resonance decays.
Pre
limin
ary
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Emission densities for fixed pt=1.2 GeV/c
EoS accounts for crossover (Laine&Schroder) and CFO with resonance decays.
Pre
limin
ary
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HBT long-radius in CGC approach, with EoS accounting for crossover (Laine&Schroder) and CFO with
resonance decays.Pre
limin
ary
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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.
