1. Marcus Bleicher, WPCF 08/2007 HBT results from UrQMD Marcus Bleicher & Qingfeng Li (FIAS) Institut für Theoretische Physik Goethe Universität Frankfurt Germany

2. Marcus Bleicher, WPCF 08/2007 Thanks to the UrQMD group Katharina Schmidt Manuel Reiter Sascha Vogel Xianglei Zhu Daniel Krieg Horst Stoecker Hannah Petersen Diana Schumacher Stephane Haussler Mohamed Abdel-Aziz Qingfeng Li

3. Marcus Bleicher, WPCF 08/2007 Outline HBT: How, Why, What? UrQMD model calculations HBT puzzle(s) Model explanations on the HBT puzzle Summary and outlook

4. Marcus Bleicher, WPCF 08/2007 The tool UrQMD : Ultra-Relativistic Quantum Molecular Dynamics out-of-equilibrium transport model, (rel. Boltzmann equation) Particles interact via : - measured and calculated cross sections - string excitation and fragmentation - formation and decay of resonances Provides full space-time dynamics of heavy-ion collisions

5. Marcus Bleicher, WPCF 08/2007 Why the HBT technique is important to probe the QGP? We know, the transition can only take place in a very small space-time. Correlations of two final-state particles are closely linked to the space-time of the region of homogeneity (the relevant volume for particles of a given velocity, not the entire source, which can give partly the message of the source. A non-trivial structure in the excitation function of HBT might be seen IF there is a (phase) transition.

6. Marcus Bleicher, WPCF 08/2007 Motivation At RHIC: look for signals of partonic matter. (large v2, mach cones, quenching,…) At critRHIC/SPS: look for the mixed phase and the onset of deconfinement (long life times, large fluctuations, …) E. Bratkovskaya, M.B. et al., PRC 2005

7. Marcus Bleicher, WPCF 08/2007 The promise… long life times in the mixed phase… Rischke, Gyulassy, Nucl.Phys.A608:479- 512,1996 ~ Energy density 10 fold increase in life time during the mixed phase

8. Marcus Bleicher, WPCF 08/2007 Why use the UrQMD model? Hydrodynamics failed to explain the decrease of HBT radii with kT (see, e.g. nucl-th/0305084) Might be due to the Corona effect at late stage? Transport model, considering the full rescattering process, might throw light on what other mechanisms generate the observed kT- dependence of the HBT radii

9. Marcus Bleicher, WPCF 08/2007 What’s the HBT technique? The quotient of two-particle and one-particle spectra The two-particle correlator C(q,K) is related to the emission function S(x,K), Which is the Wigner phase-space density of the particle emitting system and can be viewed as the probability that a particle with average momentum K is emitted from the space-time point x in the collision region. For identical bosons,

10. Marcus Bleicher, WPCF 08/2007 Gaussian Parameterization To better understand the three-dimensional spatio-temporal source distribution. Although the realistic source deviates from a standard Gaussian, it provides the standard description of experimental data. There exist quite a few different types of Gaussian parameterization under different coordinate system (CMS, LCMS, YKP, etc…). Nucl-ex/0505014 From one- to two- to three dimensional parameterization (e.g. nucl-th/0510049 for reviews) Yano-Koonin parametrization

11. Marcus Bleicher, WPCF 08/2007 LCMS Gaussian Parameterization Longitudinal co-moving system (out-side-long) is the incoherence or chaoticity factor, lies between 0 (complete coherence) and ±1 (complete incoherence) in the real reactions. it will be affected by many factors other than the quantum statistics (bosons: 1, fermions: -1 ), for example, misidentified particles(contamination), the (long-lived) resonance, different technical details of Coulomb corrections R L,O,S are B-P radii, R ol is the cross term and vanishes at mid-rapidity.

12. Marcus Bleicher, WPCF 08/2007 The out-side-long system sketch Long: parallel to beam, and the longitudinal components of the pair velocity vanishes.(K z =0) Side: perpendicular to beam and average pair momentum K. Out: perpendicular to Long and Side. K L O S

13. Marcus Bleicher, WPCF 08/2007 The survey of Pratt radii R L,R O, and R S R~R(K T, E b, b, (A,B), y, , (m 1,m 2 )) Next, we show the results of the source of two negatively (except otherwise stated) charged pions using UrQMD model. Quite a few model endeavors: Hydrodynamics models: matter in the collision region is taken as an ideal, locally thermalized fluid with the zero mean free path; (hydro+/PYTHIA+)UrQMD, RQMD: hadronic dynamics model with string degree of freedom. Having potentials for baryons at low beam energies. From UrQMD ver2.0, the PYTHIA (v6.1) was added in order to consider the hard process. MPC: Molnar’s Parton Cascade, (with the stiffest effective EoS) AMPT: A Multi-Phase Transport model (hadron+string+parton) HRM: Hadronic Rescattering Model (no strings/partons) etc…

14. Marcus Bleicher, WPCF 08/2007 How to calculate numerically? Standard UrQMD (v2.2) output of freeze-out particles (http://www.th.physik.uni-frankfurt/~urqmd) CRAB (v3.0) used to analyze the (three-dimensional LOS) correlation of two identical particles. (http://www.nscl.msu.edu/~pratt/freecodes/crab/home.html) Three-dimensional Gaussian fitting. Present study: pi-pi correlations

15. Marcus Bleicher, WPCF 08/2007 World HBT data 1

16. Marcus Bleicher, WPCF 08/2007 World HBT data 2 First (up to now only) systematic comparison between transport model (RQMD) and experimental data (Mike Lisa, 2005)

17. Marcus Bleicher, WPCF 08/2007 Systematic analysis is needed Hydro is known to fail for HBT radii Transport models can provide a baseline  Use UrQMD for a systematic study

18. Marcus Bleicher, WPCF 08/2007 Transverse momentum dependence of the HBT radii at various energies

19. Marcus Bleicher, WPCF 08/2007 UrQMD vs. data @ AGS <11% T <5%  T Good agreement Deviations at small k T for R L and R S

20. Marcus Bleicher, WPCF 08/2007 The mass dependence of lifetime of resonances The green lines: We consider the Mass dependence Of lifetime of Resonances. M  better agreement Time from phase shift?

21. Marcus Bleicher, WPCF 08/2007 UrQMD @ SPS-NA49 <7.2%  T Note the effect of short formation times: more early pressure

22. Marcus Bleicher, WPCF 08/2007 UrQMD @ SPS-CERES <5%  T

23. Marcus Bleicher, WPCF 08/2007 R.vs.K T @RHIC <15%  T <10%  T <5%  T Deviation for R O !

24. Marcus Bleicher, WPCF 08/2007 R.vs.b@RHIC GeV R O problems grow towards central collisions. lines shifted by 5 fm each

25. Marcus Bleicher, WPCF 08/2007  -correlations at RHIC Q. Li, M.B., H. Stoecker, nucl-th/0602032; Data: STAR Correlations are well described except for most central reactions

26. Marcus Bleicher, WPCF 08/2007 The HBT puzzle? Model calculations of R O /R S or (R O 2 -R S 2 ) 1/2 are usually larger than the experimental data Duration time (in the absence of flow): No indication of long life time in the data Li, Bleicher, Stoecker, arXiv:0706.2091. JPG in press

27. Marcus Bleicher, WPCF 08/2007 The (argued) ‘disadvantages’ in the UrQMD calculations Hadronic potentials for baryons in the above calculations. No string-string interaction although the string degree of freedom exists. Or, no deconfined quarks nor gluons and the interactions between them.

28. Marcus Bleicher, WPCF 08/2007 More collisions by setting zero formation time for strings The difference Between C(qo) and C(qs) almost disappears after considering zero formation time for string. It is very time consuming e.g. : SPS-E160:3events/h RHIC-s200:1event/d A larger early pressure especially in the sideward direction leads to larger R s

29. Marcus Bleicher, WPCF 08/2007 R o /R s at SPS(E b =160 A GeV) Zero-formation time Leads to much smaller Ro/Rs ratio mainly due to a larger Rs. Early stage, Early state!

30. Marcus Bleicher, WPCF 08/2007 At RHIC: How about other approaches? From nucl-ex/0505014 by M. Lisa AMPT:HBT is sensitive to The parton-scattering Cross sections. HRM: considering only the hadron rescattering (with sudden collisions ), No parton degree of freedom

31. Marcus Bleicher, WPCF 08/2007 How to solve the HBT puzzle reduce (or 0) string formation time for more pressure? (tremendous number of collisions make it almost impossible to calculate the HBT interferometry at RHIC)  the idea in HRM and checked for elliptic flow and HBT at SPS in UrQMD consider Partons?  the idea in AMPT Not yet in UrQMD model  with the help of another model: qMD, consider optical potential for pions (chiral symmetry) see PRL94, 102302(2005), PRC73, 024901(2006)  and, hadronic potential should be also paid attention.

32. Marcus Bleicher, WPCF 08/2007 Rapidity studies

33. Marcus Bleicher, WPCF 08/2007 R.vs.y@NA49 Weak y-dependence in all HBT radii For R S, it decreases slowly with rapidity. NA49 data For k T <100 MeV/c Weak y-dep, Why? strong x-p correlation good agreement

34. Marcus Bleicher, WPCF 08/2007 Possible reason… Different particle sources as function of rapidity: Direct production vs. decay

35. Marcus Bleicher, WPCF 08/2007 Energy dependence

36. Marcus Bleicher, WPCF 08/2007 R.vs.E b @small K T Overall reasonable agreement But, Ro/Rs too big Difference between CERES and NA49 (acceptance?)

37. Marcus Bleicher, WPCF 08/2007 Mean free path UrQMD seems to supports the finding of a (nearly) constant mfp. However, this is surprising within a microscopic analysis (here one expects mfp ~ R ~ 5 fm)

38. Marcus Bleicher, WPCF 08/2007 Droplets:  > 10-100 (Mishustin) Taken from a talk by B. Lungwitz at CPOD 2007 UrQMD data from Lungwitz& Bleicher, arXiv:0707.1788

39. Marcus Bleicher, WPCF 08/2007 Summary and outlook Good (quantitatively) agreement of the calculated HBT radii with data from AGS to RHIC. The decay of resonances affects the HBT radii (mainly at low k T ). HBT puzzle is also seen by the comparison of our calculations with data, especially at RHIC energies (flow and HBT puzzles are twin.)  It seems essential to consider the interactions between new degrees of freedom. Where are all the irregular structures expected when entering the mixed phase?