1. by Qingfeng Li (@ FIAS/Frankfurt & Huzhou)
HBT results from UrQMD
by Qingfeng Li
FIAS/Frankfurt & Huzhou)
In cooperation with M. Bleicher and H. Stoecker

2. 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.
12/8/2018
QF for WPCF2008, Krakow

3. 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. (
12/8/2018
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4. 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
12/8/2018
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5. One example: to solve the Flow “puzzle” at low energies
At Eb<10 A GeV,
the flow can be well
reproduced with
a specified potential.
12/8/2018
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6. 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.
12/8/2018
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7. 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, (2005) ).
There is no free quarks/gluons in UrQMD.
Shorter formation time leads to increase the flow but also multiplicities drastically.
12/8/2018
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8. 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).
12/8/2018
QF for WPCF2008, Krakow

9. Meanwhile, to check Hybrid model: Hydro+UrQMD
Ideal (3+1) 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 < 730 MeV/fm³ (≈ 5 * e0) in all cells
After the hydro freeze-out, hadronic cascade follows.
Typical times before cascade freezeout: fm/c
Pion production changes slightly: total yields: less; momentum distribution: flatter at high SPS energies.
Thanks: Hannah Pertersen
Jan Steinhimer
12/8/2018
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Also ask them for details, 

10. 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 Jan&Hannah’s version)
However:
it is quite necessary to study the effect of the mean field on the two-particle correlation right now!
12/8/2018
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11. The analyzing program and the Gaussian parameterization
CRAB analyzing program:
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)
12/8/2018
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12. Non-Gaussian Effect
Non-Gaussian effect is visible in the 3D-correlation functions
It’s strongest in longitudinal direction and weakest in sideward direction.
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13. 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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14. HBT results from UrQMD In the pion case: kT-dep. radii: steeper
RO at large kT:
RS at small kT:
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15. 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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16. To solve the HBT t-puzzle
In the pion case:
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17. 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
12/8/2018
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18. 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 -2<Txt> might be comparable to the term <t2t2>.
An important consensus:
Due to the strong x-t correlation, RO/RS1 does not mean t0
12/8/2018
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19. 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.
Events:
Pairs: 100M (for all kT bins)
12/8/2018
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20. stopping at SPS energies
In cascade mode:
Gaussian-like at
all energies
In potential mode:
Two-bump occurs for p
at high SPS energies
12/8/2018
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Results are still preliminary

21. Elliptic flow at RHIC The v2 at pt~1GeV/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
12/8/2018
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22. 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.
12/8/2018
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23. Thanks Reference list: e-Print: arXiv:0808.3457 [nucl-th]
Phys. Lett. B 663, 395 (2008)
Phys. Lett. B 659, 525 (2008)
J. Phys. G 34, 537 (2007)
J. Phys. G 34, 2037 (2007)
Phys. Rev. C 74, (2006)
Phys. Rev. C 73, (2006)
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