Strong and positive x-t correlation
and its effect on Rout/Rside
Zi-Wei Lin
The Ohio State University
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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
Zi-Wei Lin
Collective flow and QGP properties
11/19/2003
HBT Radii from
Emission function S(x,p) or correlation function C(q)
.
2
Pratt,PRL84
1) Curvature at q=0:
Dx,y=<x*y>-<x><y>
Pratt,PRL84
Wiedemann,PRC57
2) Often use 4-parameter fit
for C(q) w/o Coulomb effects:
If source is Gaussian in space-time, then:
Rsource,ij=Rfit,ij
Zi-Wei Lin
Collective flow and QGP properties
11/19/2003
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 Lin
Collective flow and QGP properties
11/19/2003
Structure of AMPT model
with String Melting
A+A
HIJING
energy in strings and minijet partons
Fragment excited strings
into partons
ZPC (Zhang's Parton Cascade)
Till Parton freezeout
Coalescence into hadrons
ART (A Relativistic Transport model for hadrons)
Decay all resonances;
Final particle spectra
Zi-Wei Lin
Collective flow and QGP properties
11/19/2003
From Gaussian fits to 3-d correlation function C(q)
Au+Au at
130AGeV
(b=0 fm)
ZWL,Ko&Pal,PRL89
Zi-Wei Lin
Collective flow and QGP properties
11/19/2003
Why x-t correlation may be important?
Spatial-size x-t correlation duration-time
Magnitude and sign of x-t correlation
are important for Rout, Rout/Rside,
& extraction of duration-time
Zi-Wei Lin
Collective flow and QGP properties
11/19/2003
Correlations in pion emission source:
out-side
out-t
ZWL,Ko&Pal,PRL89
<Xout (t)>
Spatial-size x-t correlation Duration time
Source
Values: (17fm)**2 = 185 -2*168 + 431
Positive and large, tends to reduce Rout
Zi-Wei Lin
Collective flow and QGP properties
Note:includes  decays
11/19/2003
K emission source (excludes  decays):
out-side
out-t
ZWL&Ko,JPG29
<Xout (t)>
K source
Values: (3.4fm)**2 = 35 -2*22
+ 20
also positive and large for K
Zi-Wei Lin
Collective flow and QGP properties
11/19/2003
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Zi-Wei Lin
Turn off  decays to study HBT radii
from the emission function
Test hydro-like negative x-t correlation
upon hadron formation in AMPT
Collective flow and QGP properties
11/19/2003
Pions at freezeout
mostly partons
~volume emission
~surface emission
x
<xout> >0
parton transverse flow
Zi-Wei Lin
xout
Collective flow and QGP properties
11/19/2003
x-t correlation for pions
Au+Au at 200AGeV (b=0 fm)
Zi-Wei Lin
Collective flow and QGP properties
11/19/2003
x-t correlation for pions
Already present for quarks
Au+Au at 200AGeV (b=0 fm)
Zi-Wei Lin
Collective flow and QGP properties
11/19/2003
Effect of decays on source radii
Hadronic decays produce
mt-dependence in Rout & Rside
Zi-Wei Lin
Collective flow and QGP properties
11/19/2003
Rout/Rside from emission function
Zi-Wei Lin
Collective flow and QGP properties
11/19/2003
Can an initial negative x-t correlation survive later?
Test negative x-t correlation
from hydro models
at RHIC energies
Zi-Wei Lin
Collective flow and QGP properties
11/19/2003
Initial hadrons:
large initial Rout/Rside ratio (source)
Zi-Wei Lin
Collective flow and QGP properties
11/19/2003
Final hadrons:
large final Rout/Rside ratio (source)
Negative x-t term becomes positive
after hadronic scatterings
Zi-Wei Lin
Collective flow and QGP properties
11/19/2003
Radii are different from source or from Gaussian fit to C(Q)
Hardtke&Voloshin, PRC61
Zi-Wei Lin
Collective flow and QGP properties
11/19/2003
AMPT: Au+Au at 200AGeV at b=0 fm, 3mb
from source
from C(Q) fit
Rout/Rside=1
big decrease for fitted Rout, Rout/Rside
Zi-Wei Lin
Collective flow and QGP properties
11/19/2003
With an initial negative x-t correlation
at hadron formation
from source
from C(Q) fit
Rout/Rside=1
Rout/Rside >>1
Zi-Wei Lin
huge decrease for fitted Rout & Rout/Rside
~=1
Collective flow and QGP properties
11/19/2003
HBT summary
●Strong
and positive xout-t correlation term
●tends to reduce Rout and Rout/Rside.
already present at parton freezeout/hadron formation
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An initial negative x-t correlation can lead to
●
large Rout/Rside (when evaluated from emission function)
●Rout/Rside:
>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
Zi-Wei Lin
investigation is needed to find the reason.
Collective flow and QGP properties
11/19/2003