Transcript Signatures of new states of matter in hydrodynamic picture

Initial conditions and space-time scales in
relativistic heavy ion collisions
Yu. Sinyukov, BITP, Kiev
Based on:
Sept 11- 14
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
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
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0.5 fm/c
0.2?(LHC)
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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 (2007)(also in: Heavy-ion
collisions at the LHC—Last call for predictions. J.Phys. G 35 054001 (2008))
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
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Basic ideas for the late stage
Yu.S., Akkelin, Hama: PRL. 89, 052301 (2002);
+ Karpenko: PRC 78 034906 (2008).
Continuous emission
t
t out
x
F. Grassi,Y. Hama, T. Kodama
September 11-14
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)
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Boost-invariant distribution function at initial hypersurface
CGC effective FT for transversally
homogeneous system
is the variance of a Gaussian weight
over the color charges of partons
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)
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
-function as
parameter b. If one uses the prescription of smearing of the
, then
. As the result the initial
local boost-invariant phase-space density takes the form
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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 at
becomes 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
At supposed thermalization time
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fm;
is fitting
parameter
:
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Equation of State
MeV
MeV
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EoS from LattQCD (in form proposed by
Laine & Schroder, Phys. Rev. D73, 2006)
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.
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Hydro-kinetic approach
Yu.S. , Akkelin, Hama: Phys. Rev. Lett. 89 , 052301 (2002);
+ Karpenko: to be published
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 conserva
Is related to local
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 parameter
The 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
calculations at
corresponds to the lattice QCD
 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.
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