Why x-t correlation may be important for HBT

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Strong and positive x-t correlation and its
effect on Rout/Rside
Zi-Wei Lin The Ohio State University

• Why x-t correlation may be important for HBT
• Origin of a largepositive 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

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HBT Radii fromEmission function S(x,p) or
correlation function C(q)
.
2
Pratt,PRL84
2) Often use 4-parameter fit for C(q) w/o Coulomb
effects
1) Curvature at q0
Dx,yltxygt-ltxgtltygt
If source is Gaussian in space-time, then
Pratt,PRL84 Wiedemann,PRC57
Rsource,ijRfit,ij
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Study HBT with a transport model Advantage free
zeout 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)
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Structure of AMPT model with String Melting
HIJING energy in strings and minijet partons
AA
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
5
From Gaussian fits to 3-d correlation function
C(q)
AuAu at 130AGeV (b0 fm)
ZWL,KoPal,PRL89
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Why x-t correlation may be important?
x-t correlation
duration-time
Spatial-size
Magnitude and sign of x-t correlation are
important for Rout, Rout/Rside, extraction of
duration-time
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Correlations in pion emission source
out-side out-t
ZWL,KoPal,PRL89
ltXout (t)gt
x-t correlation
Duration time
Spatial-size
Source
Values (17fm)2 185 -2168 431
Positive and large, tends to reduce Rout
Noteincludes ? decays
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K emission source (excludes ? decays)
out-side out-t
ZWLKo,JPG29
ltXout (t)gt
K source
Values (3.4fm)2 35 -222 20
also positive and large for K
9

• Turn off ? decays to study HBT radii
• from the emission function
• Test hydro-like negative x-t correlation
• upon hadron formation in AMPT

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Pions at freezeout
mostly partons
volume emission
surface emission
y
x
xside
xout
ltxoutgt gt0 parton transverse flow
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x-t correlation for pions
AuAu at 200AGeV (b0 fm)
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Already present for quarks
x-t correlation for pions
AuAu at 200AGeV (b0 fm)
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Effect of decays on source radii
Hadronic decays produce mt-dependence in Rout
Rside
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Rout/Rside from emission function
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Can an initial negative x-t correlation survive
later?
Test negative x-t correlation from hydro models
at RHIC energies
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Initial hadrons
large initial Rout/Rside ratio (source)
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Final hadrons
large final Rout/Rside ratio (source)
Negative x-t term becomes positive after
hadronic scatterings
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Radii are different from source or from Gaussian
fit to C(Q)
HardtkeVoloshin, PRC61
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AMPT AuAu at 200AGeV at b0 fm, 3mb
from source
from C(Q) fit
Rout/Rside1
big decrease for fitted Rout, Rout/Rside
20
With an initial negative x-t correlation at
hadron formation
from source
from C(Q) fit
Rout/Rside1
huge decrease for fitted Rout Rout/Rside
Rout/Rside gtgt1 1
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HBT summary

• Strong and positive xout-t correlation term
• tends to reduce Rout and Rout/Rside.
• already present at parton freezeout/hadron
  formation
• An initial negative x-t correlation can lead to
• large Rout/Rside (when evaluated from emission
  function)
• Rout/Rside gt1 from emission function
• 1 from Gaussian fits to C(Q).
• Even with an large initial negative x-t
• (with Rout/Rside gtgt1 from the emission function)
• Further investigation is needed to find the
  reason.

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v2(pt) for AuAu at 130A GeV eta (-0.3, 0.3),
minimum bias (b0-13 fm in AMPT)
ZWLKo,PRC65
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1) From emission function (10mb) for
midrapidity charged pions, central 130AGeV
25
?- correlation function (w/o Coulomb
effects) data corrected for Coulomb effects
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Fitted radius parameters vs parton cross sections
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Ratio from source gt1 gt ratio from fit (1)
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10 mb results
Kaon source radiifitted radii
MT-scaling for fitted R?
ZWLKo,JPG29
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Zi-Wei Lin The Ohio State University
Summary We study two-pion interferometry at
RHIC energies using a multi-phase transport
(AMPT) transport model. Strong and positive x-t
correlation at kinetic freezeout is present
already at the end of the partonic stage, and it
remains after hadronic decays and after hadronic
interactions. This positive x-t term tends to
reduce Rout/Rside when they are evaluated from
the space-time widths of the emission
source. Moreover, when they are evaluated from
Gaussian fits to the 3-d correlation function
C(Q), values of Rout/Rside are found to decrease
in general and become consistent with one.
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x-y distributions at freezeout
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Xout-Xside distributions at freezeout
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Can an initial negative x-t correlation survive
later?
Negative x-t term expected at RHIC energies
from Cooper-Frye used in hydro models
Toy model hadron formation at surface
rtrttt(10fm)2
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Negative x-t term becomes positive after
hadronic scatterings
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With an initial negative x-t correlation at
rtrttt(10fm)2
from source
from C(q) fit
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With an initial negative x-t correlation but at a
larger surface rtrttt(20fm)2
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due to larger initial surface of hadron
formation rtrttt(20fm)2