HBT results from UrQMD

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HBT results from UrQMD

• by Qingfeng Li
• (_at_ FIAS/Frankfurt Huzhou)

In cooperation with M. Bleicher and H. Stoecker
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outline

• Brief introduction to the UrQMD and potential
  updates.
• HBT results from UrQMD with cascade and with
  potentials.
• The effects of the non-Gaussian and the resonance
  decay on HBT radii.
• Other results from UrQMD with and without
  potentials stopping, elliptic flow.

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The UrQMD model

• UrQMD Ultra-relativistic Quantum Molecular
  Dynamics
• It is a non-equilibrium transport model
• It includes 55 baryon species (with mass up to
  2.25GeV) and 32 meson species (with mass up to
  1.91GeV)
• Particles interact via
• - Mean Field modification -
  Collisions (with measured and calculated cross
  sections)
• Particles produce via
• - Formation and decay of resonance
• - Excitation and fragmentation of string
• It provides full phase-space dynamics of
  heavy-ion collisions
• it can be used to study HICs at energies from
  SIS to RHIC
• The newest version 2.3 has been released.
  (http//th.physik.uni-frankfurt.de/urqmd/)

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EoS

• It is well-known that, in low-energy nuclear
  physics, the mean-field effect is essential.
• Phenomenologically, the mean field includes
• - bulk term (density dependent)
• - surface term
• - Yukawa term
• - Pauli term
• - symmetry energy term
• - momentum dependent term

And, the Coulomb potential for charged particles
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One example to solve the Flow puzzle at low
energies
At Eblt10 A GeV, the flow can be well reproduced
with a specified potential.
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Treatment of the pre-formed hadrons
before string fragmentation

• At high SPS and RHIC energies, particle
  production is dominated by the string mechanism.
• The formation time of the hadron is determined by
  the yo-yo mode. During this time, the particles
  are taken as pre-formed. The transport of the
  pre-formed particles is treated to be
  free-streaming.
• The reduced cross sections are only included for
  leading hadrons.

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Why to consider the potential for pre-formed
hadrons?

• sQGP tells us that there is a strong coupling
  between particles at early stage.
• Small elliptic flow at RHIC was predicted by
  UrQMD.
• The gg?gg interaction is believed not enough by
  Xu and Greiner (PRC71, 064901 (2005) ).
• There is no free quarks/gluons in UrQMD.
• Shorter formation time leads to increase the flow
  but also multiplicities drastically.

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How to consider the pre-formed hadronic
potential?

• To modify the interactions at early stage, more
  collisions (by considering a shorter formation
  time or larger cross sections for pre-formed
  particles) or a mean-field potential for
  pre-formed hadrons might be taken into account.
  The former idea has been checked in the AMPT and
  the HRM models. Here we would like to consider
  the latter idea.
• As the first step,
• the density dependent term used for formed
  baryons is used for pre-formed particles.
• The pre-formed mesons act like pre-formed
  baryons but with a reduction factor (2/3) due to
  the quark-number difference.
• The potential interaction between formed and
  pre-formed particles is neglected.
• The pre-formed particles also contribute to the
  hadronic density (for pre-formed mesons, the
  2/3 factor is considered).

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Meanwhile, to check Hybrid model HydroUrQMD

• Ideal (31) D hydrodynamic evolution.
• Time scales in hydro process from 6 to 12 fm/c
  at SPS energies.
• Hadron gas equation of state (EoS) (No phase
  transition))
• Hydrodynamic evolution until e lt 730 MeV/fm³ ( 5
  e0) in all cells
• After the hydro freeze-out, hadronic cascade
  follows.
• Typical times before cascade freezeout 20-25
  fm/c
• Pion production changes slightly total yields
  less momentum distribution flatter at high SPS
  energies.

Thanks Hannah Pertersen
Jan Steinhimer
Also ask them for details, ?
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Waiting for the EoS which originates from the
first principle lQCD

• Although
• The form of the potentials for the new phase is
  simple and rough (in my version)
• The EoS with the phase transition is needed (in
  JanHannahs version)
• However
• it is quite necessary to study the effect of the
  mean field on the two-particle correlation right
  now!

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The analyzing program and the Gaussian
parameterization

• CRAB analyzing program http//www.nscl.msu.edu/p
  ratt/freecodes/crab/home.html
• Three-dimensional Gaussian parameterization
• LCMS is employed in normal calculations
• Coulomb effect in FSI is considered for charged
  two-kaon correlation with a Bowler-Sinyukov
  method
• non-Gaussian effect is discussed under the
  Edgeworth expansion

The fitting work can be done by the ROOT or the
ORIGIN software (using ?-squared method)
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Non-Gaussian Effect
Non-Gaussian effect is visible in the
3D-correlation functions Its strongest in
longitudinal direction and weakest in sideward
direction.
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Effect of resonance decay on HBT radii
Treatments of resonance decay affect HBT radii at
small kT, but not the RO/RS ratio
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HBT results from UrQMD
In the pion case
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Improvement to the mT-scaling
Left Plots

• Without pre-formed hadron potential
• RL of kaons and Lambdas Large
• RO of all particles Large
• RS of Lambdas Large

Right Plots

• With pre-formed Hadron potential
• RL of Kaons and Lambda follow
• RO of all particles follow
• RS of pions and Kaons follow
• the mT-scaling

T.Csorgo etc, PRC 54, 1390(1996)
Without the consideration of the FSI in
hydro-dynamics
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To solve the HBT t-puzzle
In the pion case
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Not only for the ? source
The inclusion of pre-formed particle
interactions cures the deviations and allows for
a consistent understanding of the data.
The marked area illustrates the
uncertainties from non-Gaussian effect and
corrections on FSI
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Why so ?
Under the assumptions of thermalization and
Gaussian-source shape, the HBT radii can be
expressed analytically as
RO term can be expanded as
Due to the strong phase-correlation induced by
the potentials, the term -2lt?Txtgt might be
comparable to the term lt?t2t2gt.
An important consensus Due to the strong x-t
correlation, RO/RS?1 does not mean t?0
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Hydro EoS (Hadron-Gas) contribution
Hydro-process helps to drive down the Ro/Rs
ratio The ratio from hybrid model is still
larger than data since it is cascade after hydro
freeze-out.
In the hybrid model More EoS should be
checked More events and particle pairs Should be
analyzed.
Events4000-6000 Pairs 100M (for all kT bins)
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stopping at SPS energies
In cascade mode Gaussian-like at all energies In
potential mode Two-bump occurs for p at high SPS
energies
Results are still preliminary
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Elliptic flow at RHIC

• The v2 at pt1GeV/c is driven up
• with the pre-formed hadronic potential
• The potential effect is strong in central HICs

Of course, the collision of partons is necessary
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Conclusions

• To understand the HBT t-puzzle and the mT
  -scaling, one needs to consider more about the
  interactions of particles at the early stage of
  HICs
• The resonance decay contributes to the
  non-Gaussian phenomenon and the HBT radii but not
  the HBT t-puzzle.
• A consistently thermal dynamic description of
  high energetic HICs is still awaiting.

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Thanks
Reference list e-Print
arXiv0808.3457 nucl-th
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Phys. Lett. B 659, 525 (2008) J. Phys.
G 34, 537 (2007) J. Phys. G
34, 2037 (2007) Phys. Rev. C
74, 064908 (2006) Phys. Rev.
C 73, 064908 (2006)