Zi-Wei LinCollective flow and QGP properties11/19/2003 ● Why x-t correlation may be important for HBT ● Origin of a large&positive x-t correlation: partonic?

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Zi-Wei LinCollective flow and QGP properties11/19/2003 ● Why x-t correlation may be important for HBT ● Origin of a large&positive x-t correlation: partonic? resonance decays? hadronic rescatterings? ● Can a (hydro-type) negative x-t correlation survive decays/rescatterings in a transport model? Rout/Rside: from Gaussian fit vs from emission function Strong and positive x-t correlation and its effect on Rout/Rside Zi-Wei Lin The Ohio State University

Zi-Wei LinCollective flow and QGP properties11/19/2003 HBT Radii from Emission function S(x,p) or correlation function C(q) If source is Gaussian in space-time, then: Rsource,ij=Rfit,ij 1) Curvature at q=0: 2) Often use 4-parameter fit for C(q) w/o Coulomb effects: Pratt,PRL84 Wiedemann,PRC57 Dx,y= -. 2

Zi-Wei LinCollective flow and QGP properties11/19/2003 Study HBT with a transport model Advantage: freezeout in transport is natural as the mean free path grows too big compared with system size How to relate to hydro calculations (Cooper-Frye formula at a sharp hypersurface is usually imposed)

Zi-Wei LinCollective flow and QGP properties11/19/2003 HIJING energy in strings and minijet partons ZPC (Zhang's Parton Cascade) Till Parton freezeout ART (A Relativistic Transport model for hadrons) A+A Decay all resonances; Final particle spectra Structure of AMPT model with String Melting Fragment excited strings into partons Coalescence into hadrons

Zi-Wei LinCollective flow and QGP properties11/19/2003 ZWL,Ko&Pal,PRL89 From Gaussian fits to 3-d correlation function C(q) Au+Au at 130AGeV (b=0 fm)

Zi-Wei LinCollective flow and QGP properties11/19/2003 Why x-t correlation may be important? Spatial-size x-t correlationduration-time Magnitude and sign of x-t correlation are important for Rout, Rout/Rside, & extraction of duration-time

Zi-Wei LinCollective flow and QGP properties11/19/2003 Correlations in pion emission source: out-side out-t Positive and large, tends to reduce Rout Values: (17fm)**2 = * Source Spatial-size x-t correlationDuration time ZWL,Ko&Pal,PRL89 Note:includes  decays

Zi-Wei LinCollective flow and QGP properties11/19/2003 out-side out-t K emission source (excludes  decays): ZWL&Ko,JPG29 Values: (3.4fm)**2 = 35 -2* K source also positive and large for K

Zi-Wei LinCollective flow and QGP properties11/19/2003 ● Turn off  decays to study HBT radii from the emission function ● Test hydro-like negative x-t correlation upon hadron formation in AMPT

Zi-Wei LinCollective flow and QGP properties11/19/2003 Pions at freezeout x out x side x y mostly partons ~surface emission ~volume emission >0 parton transverse flow

Zi-Wei LinCollective flow and QGP properties11/19/2003 x-t correlation for pions Au+Au at 200AGeV (b=0 fm)

Zi-Wei LinCollective flow and QGP properties11/19/2003 Already present for quarks x-t correlation for pions Au+Au at 200AGeV (b=0 fm)

Zi-Wei LinCollective flow and QGP properties11/19/2003 Effect of decays on source radii Hadronic decays produce mt-dependence in Rout & Rside

Zi-Wei LinCollective flow and QGP properties11/19/2003 Rout/Rside from emission function

Zi-Wei LinCollective flow and QGP properties11/19/2003 Can an initial negative x-t correlation survive later? Test negative x-t correlation from hydro models at RHIC energies

Zi-Wei LinCollective flow and QGP properties11/19/2003 large initial Rout/Rside ratio (source) Initial hadrons:

Zi-Wei LinCollective flow and QGP properties11/19/2003 large final Rout/Rside ratio (source) Negative x-t term becomes positive after hadronic scatterings Final hadrons:

Zi-Wei LinCollective flow and QGP properties11/19/2003 Hardtke&Voloshin, PRC61 Radii are different from source or from Gaussian fit to C(Q)

Zi-Wei LinCollective flow and QGP properties11/19/2003 from source from C(Q) fit big decrease for fitted Rout, Rout/Rside AMPT: Au+Au at 200AGeV at b=0 fm, 3mb Rout/Rside=1

Zi-Wei LinCollective flow and QGP properties11/19/2003 from source from C(Q) fit With an initial negative x-t correlation at hadron formation huge decrease for fitted Rout & Rout/Rside Rout/Rside >>1~=1 Rout/Rside=1

Zi-Wei LinCollective flow and QGP properties11/19/2003 ● Strong and positive x out -t correlation term ● tends to reduce R out and R out /R side. ● already present at parton freezeout/hadron formation ● An initial negative x-t correlation can lead to large R out /R side (when evaluated from emission function) ● R out /R side: >1 from emission function ~=1 from Gaussian fits to C(Q). ● Even with an large initial negative x-t (with Rout/Rside >>1 from the emission function) ● Further investigation is needed to find the reason. HBT summary