1. HBT results from a rescattering model Tom Humanic Ohio State University WPCF 2005 August 17, 2005

2. Tom Humanic OSU2 Outline Hadronic rescattering model Comparison with RHIC data Subdivision test of rescattering model Asymmetric HBT from rescattering HBT calculation for LHC Pb+Pb collisions Conclusions

3. August 17, 2005Tom Humanic OSU3 time Evolution of a heavy-ion collision Before collision (heavy nuclei) After collision: QM formation?? Hadronization Strong hadronic rescattering “Freezeout” (hadrons freely stream to detectors) In order to study QM/hadronization stage of collision from freezeout hadrons, need to understand rescattering stage first!

4. August 17, 2005Tom Humanic OSU4 Hadronic rescattering model (T. J. Humanic, Phys.Rev.C 57, 866, (1998)) 1) Assume a simple hadronization picture to set the initial geometry and momenta. 2) Put in hadrons whose multiplicities are consistent with RHIC experiments or LHC predictions. Conserve energy. 3) Let hadrons undergo strong binary collisions until the system gets so dilute (since it is expanding) that all collisions cease. 4) Record the time, mass, position, and momentum of each hadron when it no longer scatters.  freezout condition. 5) Calculate hadronic observables  p T distributions, elliptic flow, HBT, … 1/m T dN/dm T = m T exp(-m T /T) T = 300 MeV (RHIC Au+Au) 500 MeV (LHC Pb+Pb)  parameters: initial temperature (T), hadronization proper time (  ) (cylindrical) (thermal)   K, N,  ’…..   (i,j) from Prakash, etc.. r z =  sinh y ; t =  cosh y  = 1 fm/c z rapidity width (  y )

5. August 17, 2005Tom Humanic OSU5 Comparison of the Rescattering model with RHIC data for p T distributions As seen above, the qualitative shapes are the same for p T < 3 GeV/c !

6. August 17, 2005Tom Humanic OSU6 Comparison of Recattering model with RHIC data for m T distributions The slopes are seen to agree !

7. August 17, 2005Tom Humanic OSU7 Elliptic Flow vs. p T from rescattering model compared with STAR flattening at high pT as in data

8. August 17, 2005Tom Humanic OSU8 STAR  HBT vs Rescattering Model Rescattering qualitatively describes the centrality and momentum dependences of the pion HBT data.

9. August 17, 2005Tom Humanic OSU9 Time evolution of elliptic flow, HBT, and radial flow from rescattering for RHIC Au+Au with b = 8 fm, -1 < y < 1, and 125 < p T < 225 MeV/c Defining t S = stablization time t S (V 2 ) < t S (HBT) < t S (slope)

10. August 17, 2005Tom Humanic OSU10 Criticisms of rescattering calculation Criticism 1: The initial state for the calculation is too hot and too dense to be considering hadrons thus the results are meaningless…. Response: The rescattering calculation should be viewed as a limiting case study of how far one can get with such an extreme and simple model – maybe we can learn something about the true initial state from this, e.g. hadron-like objects existing in the QGP??... short QGP lifetime??.... Criticism 2: The calculation results may have reasonable agreement with data but that is only a fluke because the calculation is dominated by computational artifacts which strongly influence the results. Response: The rescattering model has been tested for Boltzmann- transport-equation-like behavior and the influence of superluminal artifacts using the Subdivision method  see next slide

11. August 17, 2005Tom Humanic OSU11 Subdivision test of rescattering calculation    and    = subdivision Expect no change in observables under this transformation for a Boltzmann Eq.  no effects from superluminal artifacts

12. August 17, 2005Tom Humanic OSU12 Asymmetric HBT for rescattering vs. STAR data Central collisions

13. August 17, 2005Tom Humanic OSU13 Asymmetric HBT for rescattering vs. STAR data Mid-central collisions

14. August 17, 2005Tom Humanic OSU14 Asymmetric HBT for rescattering vs. STAR data Semi-peripheral collisions

15. August 17, 2005Tom Humanic OSU15 Conclusion for “soft” (i.e. p T < 3 GeV/c) RHIC physics: Hadronic rescattering with a short hadronization time (  = 1 fm/c) describes dynamic features reasonably well….  Now apply the rescattering model to LHC Pb+Pb collisions

16. August 17, 2005Tom Humanic OSU16 Details the of LHC rescattering calculations Adjust the initial particle multiplicities to give a central (b=0 fm) charged particle dN/dy at y=0 of 4000. Adjust the initial hadron gas temperature and rapidity width to give the correct LHC Pb+Pb energy: use T=500 MeV. Do calculations for b = 8 fm impact parameter so elliptic flow can also be studied (and the code runs faster). Use same hadronization time as for RHIC,  = 1 fm/c Compare the LHC rescattering results with RHIC rescattering results.

17. August 17, 2005Tom Humanic OSU17 Pion freezeout time and z-position for LHC vs. RHIC Pion freezeout times are about twice as long at LHC compared to RHIC

18. August 17, 2005Tom Humanic OSU18

19. August 17, 2005Tom Humanic OSU19 m T distributions for LHC vs. RHIC Radial flow appears to be larger for LHC compared to RHIC

20. August 17, 2005Tom Humanic OSU20 Elliptic flow for LHC vs. RHIC Pion elliptic flow at LHC and RHIC are about the same

21. August 17, 2005Tom Humanic OSU21 Projected 3D two-pion C 2 for LHC Pb+Pb from rescattering for b=8 fm centrality and p T bin 0-200 MeV/c

22. August 17, 2005Tom Humanic OSU22 Transverse radius parameters for LHC vs. RHIC Transverse radius parameters are somewhat larger and show a stronger p T dependence for LHC compared with RHIC

23. August 17, 2005Tom Humanic OSU23 R Long and parameters for LHC vs. RHIC R Long for LHC is almost twice as large as for RHIC reflecting longer freezeout times; behaves about the same at LHC and RHIC

24. August 17, 2005Tom Humanic OSU24 Conclusions from Rescattering Rescattering model results in reasonable agreement with RHIC data t C (V 2 ) < t C (HBT) < t C (slope param.) Subdivision test shows no effects of artifacts in rescatt results Asymmetric HBT from rescattering in qualitative agreement with data Radial flow at the LHC appears greater than for RHIC. Pion elliptic flow at LHC and RHIC are about the same Transverse radius parameters are somewhat larger and show a stronger p T dependence for LHC compared with RHIC. R Long for LHC is almost twice as large as for RHIC reflecting longer freezeout times; behaves about the same at LHC and RHIC.