ZiWei Lin

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3-D Source Functions at RHIC from the AMPT Model

• Zi-Wei Lin
• Department of Physics

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Study HBT with a transport model
HBT probes phase space distribution at kinetic
freeze-out ? system size, space-momentum
correlation
? equation of state, hadronization (duration,
surface)
There is an HBT puzzle in that hydrodynamic
models, and hydrocascade models, have
difficulties in describing HBT radius parameters,
including Rout/Rside 1 (in LCMS)
S. Soff et al., PRL 86 (2001)
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Study HBT with a transport model
Transport models should be able to describe the
dynamics of non-equilibrium processes such as
freeze-out.
The AMPT model has been applied to study the
emission function S(x,p) and correlation
function C(Q) in LCMS. There we find
ZWL, Ko Pal, PRL 89 (2002) ZWL et al., PRC 72
(2005)

• x-t correlations at freeze-out are positive
  large,
• tend to reduce Rout
• String melting with a certain parton cross
  section roughly reproduces C(Q) and fitted radius
  parameters,
• including Rout/Rside1

A recent hydroEventGenerator model shows
agreement with data on HBT radius
parameters What are the x-t correlations at
freeze-out?
Kisiel et al., PRC 73 (2006) Kisiel, Braz. J.
Phys.37 (2007)
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C(Q) for mid-rapidity pions (125ltPtlt225MeV/c) in
AuAu at 130AGeV Q in LCMS (longitudinally
comoving frame) ZWL, Ko Pal,PRL 89 (2002)
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Extend to Source Functions
Source function analysis using moments have been
proposed Data is now available from RHIC
Danielewicz Pratt, PLB 618 (2005), PRC 75
(2007)
Lacey, Braz. J. Phys.37 (2007) Adler et al.
PRL98 (2007) Afanasiev et al. arXiv0712.4372v1
Here we further test the HBT results from
AMPT study moments of both S(r) and C(q)
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Structure of A Multi-Phase Transport (AMPT) Model

• HIJING (parton pdfs, shadowing)
• energy in strings and minijet partons

AA
Fragment excited strings into partons all
partons enter parton cascade
In string melting
ZPC (Zhang's Parton Cascade)
Partons freeze out coalescence into hadrons
ART (A Relativistic Transport model for hadrons)
Hadrons freeze out (at a cut-off
time) strong-decay all remaining resonances
Final particle spectra
Detailed descriptions of AMPT in ZWL et al., PRC
72 (2005), since then source codes of current
AMPT versions are available online at
http//www-cunuke.phys.columbia.edu/OSCAR/
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Definitions
Source Function S(r) the probability of emitting
a pair at a separation distance r in
PCMS Moments of S(r) Angle-averaged source
function S(r) Moments of C(q)1R(q)
Indices ai can be out, side, long
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For Comparisons of AMPT Results With PHENIX Data
For both model and data AuAu at
?sNN200GeV ? lt 0.35 0.2ltkTlt0.36 GeV/c with
kT(PT,1PT,2)/2 qp1-p2/2 in PCMS (pair rest
frame) Moments calculated up to (including)
Rank-6.
Data 0-20 central events pp p-p- AMPT
at b0 fm pp
Adler et al. PRL98 (2007) Afanasiev et al.
arXiv0712.4372v1
K0S decays are enabled (AMPT input file has the
flag)
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1-D C(q) S(r)
S(r) A q-cut (qlt50MeV/c) should be applied for
apple-to-apple comparisons between PHENIX data
and model results
P. Chung, private comm. Afanasiev et al.
arXiv0712.4372v1
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1-D C(q) S(r) with q-cut (qlt50MeV/c)
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1-D C(q) S(r) without q-cut
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Effects of including pions from K0S decays on S(r)
With K0S decays
Without K0S decays
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S(r) moments vs C(q) moments Long
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S(r) moments vs C(q) moments Side
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S(r) moments vs C(q) moments Out
Disagree in shapes
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Check C(Q) for 0.2ltkTlt2 GeV/c Qp1-p2 in LCMS
(longitudinally comoving frame)
PHENIX data from Adler et al. PRL93 (2004). 0-30
central collisions, Q-cut of 40MeV/c on
orthogonal directions
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Summary

• AMPT model is used to study moments of the 3-D
  source functions S(r) together with correlation
  functions C(q)
• For pions near mid-rapidity with kT
  (0.2-0.36GeV/c)
• fair agreements along Side and Long directions,
• disagreement in shapes along the Out direction
• Better agreement for a larger kT range
  (0.2-2GeV/c)

Outlook

• Investigate disagreements/agreements
• to extract information on dynamics (x-t
  correlation, hadronization)
• Resonance ratios after bulk hadronization?
• 0-20 central vs b0fm ?
• Due to the simple quark coalescence model for
  hadronization?

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Improvement needs of AMPT

• Parton coalescence to hadrons
• Currently, a parton can coalesce after it does
  not have
• further interactions (i.e., after kinetic
  freezeout).

Average parton density for coalescence depends
on sp
Effective equation of state of AMPT depends on
sp Zhang, Chen Ko, arXiv0705.3968
Need to decouple hadronization time from parton
cross section
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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
And
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• Fitted Radius Parameters
• for mid-rapidity pions
• (125ltPtlt225MeV/c)
• in AuAu at 130AGeV
• Q in LCMS
• ZWL, Ko Pal,PRL 89 (2002)

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3D S(r) effects of q-cut (from AMPT with String
Melting at 10mb)
Effect on Side direction is the greatest
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3-D S(r) for Default AMPT vs String Melting
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HydroEventGenerator (Therminator) model
Afanasiev et al. arXiv0712.4372v1