Zi-Wei Lin Department of Physics

1. Zi-Wei Lin Department of Physics 3-D Source Functions at RHIC from the AMPT Model

2. Study HBT with a transport model HBT probes phase space distribution at kinetic freeze-out → system size, space-momentum correlation →equation of state, hadronization (duration, “surface”) There is an “HBT puzzle” in that hydrodynamic models, and hydro+cascade models, have difficulties in describing HBT radius parameters, including Rout/Rside ~ 1 (in LCMS) S. Soff et al., PRL 86 (2001)

3. Study HBT with a transport model Transport models should be able to describe the dynamics of non-equilibrium processes such as freeze-out. The AMPT model has been applied to study the emission function S(x,p) and correlation function C(Q) in LCMS. There we find: ZWL, Ko & Pal, PRL 89 (2002); ZWL et al., PRC 72 (2005) • x-t correlations at freeze-out are positive & large, • tend to reduce Rout • String melting with a certain parton cross section roughly reproduces C(Q) and fitted radius parameters, • including Rout/Rside~1 A recent hydro+EventGenerator model shows agreement with data on HBT radius parameters: What are the x-t correlations at freeze-out? Kisiel et al., PRC 73 (2006); Kisiel, Braz. J. Phys.37 (2007)

4. C(Q) for mid-rapidity pions (125<Pt<225MeV/c) in AuAu at 130AGeV Q in LCMS (longitudinally comoving frame) ZWL, Ko & Pal,PRL 89 (2002)

5. Extend to Source Functions Source function analysis using moments have been proposed Data is now available from RHIC Danielewicz & Pratt, PLB 618 (2005), PRC 75 (2007) Lacey, Braz. J. Phys.37 (2007); Adler et al. PRL98 (2007); Afanasiev et al. arXiv:0712.4372v1 Here we further test the HBT results from AMPT: study moments of both S(r) and C(q)

6. Structure of A Multi-Phase Transport (AMPT) Model HIJING (parton pdfs, shadowing) energy in strings and minijet partons A+A Fragment excited strings into partons; all partons enter parton cascade In string melting: ZPC (Zhang's Parton Cascade) Partons freeze out & coalescence into hadrons ART (A Relativistic Transport model for hadrons) Hadrons freeze out (at a cut-off time); strong-decay all remaining resonances Final particle spectra Detailed descriptions of AMPT in ZWL et al., PRC 72 (2005), since thensource codes of current AMPT versions are available online at http://www-cunuke.phys.columbia.edu/OSCAR/

7. Definitions Source Function S(r): the probability of emitting a pair at a separation distance r in PCMS Moments of S(r): Angle-averaged source function S(r): Moments of C(q)≡1+R(q): Indices ai can be: out, side, long

8. For Comparisons of AMPT Results With PHENIX Data For both model and data: Au+Au at sNN=200GeV |η| < 0.35 0.2<kT<0.36 GeV/c with kT≡(PT,1+PT,2)/2 q=|p1-p2|/2 in PCMS (pair rest frame) Moments calculated up to (including) Rank-6. Data: 0-20% central events π+π+ & π-π- AMPT: at b=0 fm π+π+ Adler et al. PRL98 (2007); Afanasiev et al. arXiv:0712.4372v1 K0S decays are enabled (AMPT input file has the flag)

9. 1-D C(q)& S(r) S(r) A q-cut (q<50MeV/c) should be applied for apple-to-apple comparisons between PHENIX data and model results P. Chung, private comm.; Afanasiev et al. arXiv:0712.4372v1

10. 1-D C(q)& S(r): with q-cut (q<50MeV/c)

11. 1-D C(q)& S(r): without q-cut

12. Effects of including pions from K0S decays on S(r) Without K0S decays With K0S decays

13. S(r) moments vs C(q) moments: Long

14. S(r) moments vs C(q) moments: Side

15. S(r) moments vs C(q) moments: Out Disagree in shapes

16. Check C(Q) for 0.2<kT<2 GeV/c Q=|p1-p2| in LCMS (longitudinally comoving frame) PHENIX data from Adler et al. PRL93 (2004). 0-30% central collisions, Q-cut of 40MeV/c on orthogonal directions

17. Summary AMPT model is used to study moments of the 3-D source functions S(r)together with correlation functions C(q) For pions near mid-rapidity with kT (0.2-0.36GeV/c): • fair agreements along Side and Long directions, • disagreement in shapes along the Out direction Better agreement for a larger kT range (0.2-2GeV/c) Outlook Investigate disagreements/agreements to extract information on dynamics (x-t correlation, hadronization): • Resonance ratios after bulk hadronization? • 0-20% central vs b=0fm ? • Due to the simple quark coalescence model for hadronization?

18. Improvement needs of AMPT • Parton coalescence to hadrons: Currently, a parton can coalesce after it does not have further interactions (i.e., after kinetic freezeout). Average parton density for coalescence depends on σp Effective equation of state of AMPT depends on σp Zhang, Chen & Ko, arXiv:0705.3968 Need to ~decouple hadronization time from parton cross section

19. HBT Radii fromEmission function S(x,p)or correlation function C(q) . 2 Pratt,PRL84 2) Often use 4-parameter fit for C(q) w/o Coulomb effects: 1) Curvature at q=0: Dx,y=<x*y>-<x><y> If source is Gaussian in space-time, then: Pratt,PRL84 Wiedemann,PRC57 And

20. Fitted Radius Parameters for mid-rapidity pions (125<Pt<225MeV/c) in AuAu at 130AGeV Q in LCMS ZWL, Ko & Pal,PRL 89 (2002)

21. 3D S(r): effects of q-cut (fromAMPT with String Melting at 10mb) Effect on Side direction is the greatest

22. 3-D S(r) for Default AMPT vs String Melting

23. Hydro+EventGenerator (Therminator) model Afanasiev et al. arXiv:0712.4372v1