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

1
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

2
Expecting Stages of Evolution in
Ultrarelativistic AA 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)
3
Basic ideas for the early stage
p
Yu.S. Acta Phys.Polon. B37 (2006) 3343 Gyulassy,
Yu.S., Karpenko, Nazarenko Braz.J.Phys. 37 (2007)
1031 Akkelin, Yu.S., Karpenko arXiv0706.4066
(2007)(also in Heavy-ion collisions at the
LHCLast 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
4
Basic ideas for the late stage
Yu.S., Akkelin, Hama PRL. 89, 052301 (2002)
Karpenko PRC 78 034906 (2008).
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
F. Grassi,Y. Hama, T. Kodama
5

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) 427T. Lappi PRC
67 (2003) 054903, QM 2008 (J.Phys. G, 2008)
Transversally inhomogeneous system lttransverse
profilegt 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.
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
6
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
8
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
fm


is fitting parameter
At supposed thermalization time
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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
10
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 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.

Is related to local

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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 .


12
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 lt 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
19
Out- radius
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Conclusions

• A reasonable description of the pionic spectra
• and HBT (except some an overestimate for
  ) in cental AuAu 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
  time1-2 fm/c.