1. SQM2003March 13Zi-wei Lin The Ohio State University ● Why transport model? ● Space-time (x-t) correlation: its effect on R out/ R side 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 Zi-wei Lin The Ohio State University in collaboration with C.M. Ko Kaon HBT at RHIC from AMPT Model

2. SQM2003March 13Zi-wei Lin The Ohio State University R out/ R side ~1 up to Kt~1GeV from S. Johnson at RWW02 ● Inconsistent with the hydro model. ● Puzzling considering the “common” relations:

3. SQM2003March 13Zi-wei Lin The Ohio State University 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. SQM2003March 13Zi-wei Lin The Ohio State University HIJING energy in strings and minijet partons ZPC (Zhang's Parton Cascade) till parton freezeout ART (A Relativistic Transport model for hadrons) A+A Strong-decay resonances for final particle spectra A Multi-Phase Transport (AMPT) model with String Melting Fragment excited strings into quarks and antiquarks (via Lund frag. to hadrons) Nearest quark coalescence to hadrons Z.W.L. &C.M.Ko,PRC65

5. SQM2003March 13Zi-wei Lin The Ohio State University An central Au+Au event at 130AGeV from AMPT model (no string melting here)

6. SQM2003March 13Zi-wei Lin The Ohio State University Definitions: in the Pratt-Bertsch out-side-long system x i (1-3)= x out, x side, x long q i (1-3)=Q out, Q side, Q long => R inv 2 => R out, R side, R long Pratt, PRD33 Pratt et al,PRC42 Bertsch et al,PRC37

7. SQM2003March 13Zi-wei Lin The Ohio State University Method 1 to extract radii: From emission function S(x,K): curvature at q=0 Pratt,PRL84 Wiedemann,PRC57 Dx,y= -.

8. SQM2003March 13Zi-wei Lin The Ohio State University out-side out-t Emission function (at freezeout): positive x out -t correlation K: 200<pt<400 MeV -1<y<1

9. SQM2003March 13Zi-wei Lin The Ohio State University (3.4fm)^2 = (35 - 2 * 22 + 20) fm^2 from the emission function: Spatial-size x out -t correlation duration-time part K: 200<pt<400 MeV -1<y<1  is positive and large  reduces R out and R out /R side  Complicates the extraction of the duration time from Mangnitude of the x out -t correlation

10. SQM2003March 13Zi-wei Lin The Ohio State University out-side out-t also positive and large, reduces R out /R side (17fm)^2 = (185 - 2*168 + 431) fm^2 pi: 125<pt<225 MeV -1<y<1 Similar to the pion case: Z.W.L.,C.M.Ko&S.Pal,PRL89 from the emission function:

11. SQM2003March 13Zi-wei Lin The Ohio State University Experimentally, from 4-parameters Gaussian fits of C(q) (w/o Coulomb effects): Pratt,PRL84. Method 2 to extract radii: If source is Gaussian in space-time, then: and Method1= Method2 BUT if source is non-Gaussian in space-time: e.g., see D.Hardtke&S.Voloshin, PRC61 Method1= Method2

12. SQM2003March 13Zi-wei Lin The Ohio State University source radii vs fitted radii Difference is up to 30%  decays are not included in source radii) Source radii are much larger if  decays are included. Fitted radii should be used for fair comparison with data, as source radii suffer from non-Gaussian source

13. SQM2003March 13Zi-wei Lin The Ohio State University R out/ R side from the 2 methods:

14. SQM2003March 13Zi-wei Lin The Ohio State University ● x out -t correlation from emission function from AMPT model:  is large & positive  tends to reduce R out and R out/ R side  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  decays are not included)  2) should be used for comparison with data Summary

15. SQM2003March 13Zi-wei Lin The Ohio State University 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*,  ) from quark coalescence need further study (at least constrained by data) for quantitative statements 4) Investigate the origin of the large & positive x out -t correlation Outlook