HBT results from UrQMD

1. 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. QF for WPCF2008, Krakow

3. The UrQMD model • UrQMD : Ultra-relativistic Quantum Molecular Dynamics • Itis 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 • Itprovides 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/) QF for WPCF2008, Krakow

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 QF for WPCF2008, Krakow

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. QF for WPCF2008, Krakow

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. QF for WPCF2008, Krakow

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, 064901 (2005) ). • There is no free quarks/gluons in UrQMD. • Shorter formation time leads to increase the flow but also multiplicities drastically. QF for WPCF2008, Krakow

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). QF for WPCF2008, Krakow

9. Meanwhile, to check Hybrid model: Hydro+UrQMD • Ideal (3+1) Dhydrodynamic 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: 20-25 fm/c • Pion production changes slightly: total yields: less; momentum distribution: flatter at high SPS energies. Thanks: Hannah Pertersen Jan Steinhimer QF for WPCF2008, Krakow 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! QF for WPCF2008, Krakow

11. The analyzing program and the Gaussian parameterization • CRAB analyzing program: http://www.nscl.msu.edu/~pratt/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 effectis discussed under the Edgeworth expansion The fitting work can be done by the ROOT or the ORIGIN software (using -squared method) QF for WPCF2008, Krakow

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. QF for WPCF2008, Krakow

13. Effect of resonance decay on HBT radii Treatments of resonance decay affect HBT radii at small kT, but not the RO/RS ratio QF for WPCF2008, Krakow

14. kT-dep. radii: steeper RO at large kT: RS at small kT: HBT results from UrQMD In the pion case: QF for WPCF2008, Krakow

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 QF for WPCF2008, Krakow

16. To solve the HBT t-puzzle In the pion case: QF for WPCF2008, Krakow

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 QF for WPCF2008, Krakow

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 QF for WPCF2008, Krakow

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:4000-6000 Pairs: 100M (for all kT bins) QF for WPCF2008, Krakow

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 QF for WPCF2008, Krakow 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 QF for WPCF2008, Krakow

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. QF for WPCF2008, Krakow

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, 064908 (2006) Phys. Rev. C 73, 064908 (2006) QF for WPCF2008, Krakow