New Results on Hydrokinetic approach to A A collisions

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New Results on Hydro-kinetic approach to AA
collisions

• Yu. Karpenko
• Bogolyubov Institute for Theoretical Physics
• Kiev, Ukraine

Based on Yu. M. Sinyukov, Iu. A. Karpenko and
A. V. Nazarenko J. Phys. G Nucl. Part. Phys. 35,
104071 (QM2008 proceedings)
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The experiment RHIC collider
hexagonally shaped 3.8 km long storage
rings 1,740 superconducting magnets sqrt(s) 200
A GeV (AuAu)
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AA collisionsschematic view
time
Initial stage (hard processes)
Thermalization, 1 fm/c
Thermal freeze-out, 10-15 fm/c
Hadronization, 7-8 fm/c
QGP evolution
Before the collision
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Hydrodynamic approach

• Energy-momentum conservation
• Ideal fluid
• implies local thermodynamic equilibrium
• Needs Equation of State (EoS) to close the set of
  hydro equations.

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Kinetic stage

• The fireball has finite lifetime and spatial
  dimensions
• Connecting hydrodynamics with kinetic stage is
  hard to implement.
• Cooper-Frye prescription sudden system decay

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Hydro-kinetic approach

• The Boltzmann equation (-kinetic) is considered
  for the deviations (even strong) from the local
  equilibrium (hydro-)
• Based on relaxation time approximation and
  particle escape probability evaluation
• Accounts for conservation laws (-hydro) at the
  particle emission

Provides earlier (as compared to Cooper-Frye
prescription) but protracted emission of hadrons,
because escape probability accounts for whole
particle trajectory in rapidly expanding
surrounding (no mean-free path criterion for
freeze-out)
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Hydro-kinetic approach
Boltzmann equation
are G(ain), L(oss) terms for i-th particle species
and
Relaxation time approximation
Then
gain term
loss term
increases in time
is related to local rest system where collective
velocity
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Collision rate for pions in Hydro-kinetic

• We account 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. The decay of
  resonances into expanding hadronic matter is
  taken into account.
• The standard Breit-Wigner formula with
  energy-dependent widths is used in the same way
  as in uRQMD

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Escape probability
The probability for particle of i-th sort to be
emitted from the hot and dense medim (escape
probability)
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Emission function in Hydro-kinetic
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. The compositon of the
system is evaluated 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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Initial conditionsfor hydro-kientic evolution

• Free streaming of partons from
  (formation time for gluons with
  well-defined energy)
• Sudden thermalization of parton system at
  with the pressure, corresponding
  to LatticeQCD results
• Energy density profile at the thermalization
• (Gaussian fit)
• Initial transverse velocities(developed already
  at pre-thermal stage)

? Yu.M. Sinyukov, Acta Phys. Polon. B37, 2006
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Equation of statefor hydrodynamics
is taken from the latest results of particle
number ratios analysis (F. Becattini,Plenary talk
at QM-2008).
EoS from LattQCD (in form proposed by Laine
Schroder, Phys. Rev. D73, 2006)
QGP phase
crossover PT
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.
hadron phase
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Numerical hydrodynamics

• Finite-volume method with relativistic HLLE
  (HartenLaxvan LeerEinfeldt) solver, based on
  approximate handling of the Riemann problem by
  introduction of an intermediate state and two
  waves propagating with some signal velocities.
• Linear distributions of conservative variables in
  a cell to achieve second order of accuracy in
  space
• Predictor-corrector scheme to achieve second
  order of accuracy in time

Written (as well as the other parts of the code)
in C
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RESULTS Pion emission density for RHIC energies
in HKM
Proper time
Transverse radius
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Results Pion emission at different pT
x-p correlation is present high-pT particles
are emitted from the periphery (large x), and
vice-versa
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Pion pT spectrum vs RHIC 200 A GeV data
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The idea of interferometry measurements
Gaussian approximation of CFs (q?0)
Rout, Rside, Rlong reflect space-time
characteristics of emission process
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HBT-radii vs RHIC 200 A GeV data
The interferometry (or HBT-) radii characterize
the space-time scales of matter evolution in AA
collisions
A reasonable description of RHIC HBT data (PHENIX
STAR), except for overestimate for R_out
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Conclusions

• The hydrokinetic approach to AA 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.
• The approach is extended to account for the
  decays of the resonances during the system
  evolution
• A reasonable description of the pionic spectra
  and HBT (except some an overestimate for
  ) in cental AuAu collisions at the RHIC 200A GeV
  energy is reached