Kaon HBT at RHIC from AMPT Model
Zi-wei Lin
The Ohio State University
in collaboration with C.M. Ko
●
Why transport model?
●
Space-time (x-t) correlation:
its effect on Rout/Rside
•
Extract radii from
1) emission function S(x,K)
2) Gaussian fits to 3-d C(Q,K)
non-Gaussian emission source
●
SQM2003
Summary and Outlook
March 13
Zi-wei Lin
The Ohio State University
from S. Johnson at RWW02
Rout/Rside ~1
up to Kt~1GeV
Inconsistent with the hydro model.
●
●
Puzzling
considering the “common” relations:
SQM2003
March 13
Zi-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
SQM2003
March 13
Zi-wei Lin
The Ohio State University
A Multi-Phase Transport (AMPT) model
with String Melting
A+A
Z.W.L. &C.M.Ko,PRC65
HIJING
energy in strings and minijet partons
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
SQM2003
March 13
Zi-wei Lin
The Ohio State University
An central Au+Au event at 130AGeV from AMPT model
(no string melting here)
SQM2003
March 13
Zi-wei Lin
The Ohio State University
Definitions:
2
Pratt, PRD33
in the Pratt-Bertsch out-side-long system
xi(1-3)=xout, xside, xlong
qi(1-3)=Qout, Qside, Qlong
Pratt et al,PRC42
Bertsch et al,PRC37
=> Rout, Rside, Rlong
=> Rinv
SQM2003
March 13
Zi-wei Lin
The Ohio State University
.
Pratt,PRL84
Method 1 to extract radii:
From emission function S(x,K): curvature at q=0
Pratt,PRL84
Wiedemann,PRC57
Dx,y=<x*y>-<x><y>
SQM2003
March 13
Zi-wei Lin
The Ohio State University
Emission function (at freezeout):
out-side
out-t
K:
200<pt<400 MeV
-1<y<1
positive xout-t correlation
SQM2003
March 13
Zi-wei Lin
The Ohio State University
Mangnitude of the
xout-t correlation
from the emission function:
K:
200<pt<400 MeV
-1<y<1
(3.4fm)^2 = (35
- 2 * 22 +
Spatial-size
20)
fm^2
duration-time part
xout-t correlation
SQM2003

is positive and large

reduces Rout and Rout/Rside

Complicates the extraction of the duration time from
March 13
Zi-wei Lin
The Ohio State University
Similar to the pion case:
out-side
Z.W.L.,C.M.Ko&S.Pal,PRL89
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
SQM2003
March 13
Zi-wei Lin
The Ohio State University
.
Pratt,PRL84
Method 2 to extract radii:
Experimentally, from 4-parameters Gaussian fits
of C(q) (w/o Coulomb effects):
If source is Gaussian in space-time, then:
and Method1= Method2
BUT
e.g., see
if source is non-Gaussian in space-time: Method1= Method2
SQM2003
March 13
Zi-wei Lin
D.Hardtke&S.Voloshin,
PRC61
The Ohio State University
source radii vs fitted 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
SQM2003
March 13
Zi-wei Lin
The Ohio State University
Rout/Rside from the 2 methods:
SQM2003
March 13
Zi-wei Lin
The Ohio State University
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
SQM2003
March 13
Zi-wei Lin
The Ohio State University
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
SQM2003
March 13
Zi-wei Lin
The Ohio State University