Why transport model? Space-time (x-t) correlation: its effect on R out/ R side Extract radii from

1. Why transport model? Space-time (x-t) correlation: its effect onRout/Rside Extract radii from 1) emission function S(x,K) 2) Gaussian fits to 3-d C(Q,K) non-Gaussian emission source Summary and Outlook Kaon HBT at RHIC from AMPT Model Zi-wei Lin The Ohio State University in collaboration with C.M. Ko

2. from S. Johnson at RWW02 • Rout/Rside ~1 • up to Kt~1GeV • Inconsistent with the hydro model. • Puzzling considering the “common” relations:

3. Why transport model? • HBT probes the space-time information of particles at freezeout • In transport models, hadrons freeze out dynamically (both chemical and kinetic freezeout), when mean-free-path is too large: Transport models may have some advantages to address HBT

4. A Multi-Phase Transport (AMPT) model with String Melting Z.W.L. &C.M.Ko,PRC65 HIJING energy in strings and minijet partons A+A Fragment excited strings into quarks and antiquarks (via Lund frag. to hadrons) ZPC (Zhang's Parton Cascade) till parton freezeout Nearest quark coalescence to hadrons ART (A Relativistic Transport model for hadrons) Strong-decay resonances for final particle spectra

5. An central Au+Au event at 130AGeV from AMPT model (no string melting here)

6. Definitions: 2 Pratt, PRD33 Pratt et al,PRC42 Bertsch et al,PRC37 in the Pratt-Bertsch out-side-long system xi(1-3)=xout, xside, xlong qi(1-3)=Qout, Qside, Qlong => Rout, Rside, Rlong => Rinv

7. . Method 1 to extract radii: Pratt,PRL84 From emission function S(x,K): curvature at q=0 Pratt,PRL84 Wiedemann,PRC57 Dx,y=<x*y>-<x><y>

8. Emission function (at freezeout): out-side out-t K: 200<pt<400 MeV -1<y<1 positive xout-t correlation

9. Mangnitude of the xout-t correlation from the emission function: K: 200<pt<400 MeV -1<y<1 (3.4fm)^2 = (35 - 2 * 22 + 20) fm^2 Spatial-size duration-time part xout-t correlation • is positive and large • reduces Rout and Rout/Rside • Complicates the extraction of the duration time from

10. Z.W.L.,C.M.Ko&S.Pal,PRL89 Similar to the pion case: out-side out-t pi: 125<pt<225 MeV -1<y<1 from the emission function: (17fm)^2 = (185 - 2*168 + 431) fm^2 also positive and large, reduces Rout/Rside

11. . Method 2 to extract radii: Pratt,PRL84 Experimentally, from 4-parameters Gaussian fits of C(q) (w/o Coulomb effects): If source is Gaussian in space-time, then: andMethod1= Method2 BUT e.g., see D.Hardtke&S.Voloshin, PRC61 Method1= Method2 if source is non-Gaussian in space-time:

12. source radii vsfitted radii Difference is up to 30% (f decays are not included in source radii) Source radii are much larger if f decays are included. Fitted radii should be used for fair comparison with data, as source radii suffer from non-Gaussian source

13. Rout/Rside from the 2 methods:

14. Summary • xout-t correlation from emission function from AMPT model: • is large & positive • tends to reduce Rout and Rout/Rside • complicates the extraction of emission duration time • same for pions • Radius parameters extracted from 2 methods: 1) from spatial correlation of the emission source 2) from Gaussian fits to 3-d C(Q) • difference is up to 30% for K (even when f decays are not included) • 2) should be used for comparison with data

15. Outlook 1) Need parton subdivision to avoid causality violation 2) Current approach in AMPT model with string melting: partons coalesce when they freezeout in parton cascade local density at hadronization controled by p (cross section) local density is directly related with collective flow (v2, ...) • investigate coalescence when local energy density < critical value 3) Resonance abundances (K*, f) from quark coalescence need further study (at least constrained by data) for quantitative statements 4) Investigate the origin of the large & positive xout-t correlation