Zi-Wei Lin Department of Physics
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Transcript of Zi-Wei Lin Department of Physics
Feb. 9, 2008 Zi-Wei Lin
3-D Source Functions at RHIC from the AMPT Model
Zi-Wei LinDepartment of Physics
Feb. 9, 2008 Zi-Wei Lin
Study HBT with a transport model
There is an “HBT puzzle” in that hydrodynamic models, and hydro+cascade models, have difficulties in describing HBT radius parameters, including Rout/Rside ~ 1 (in LCMS)
S. Soff et al., PRL 86 (2001)
HBT probes phase space distribution at kinetic freeze-out→ system size, space-momentum correlation
→ equation of state, hadronization (duration, “surface”)
Feb. 9, 2008 Zi-Wei Lin
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)
Study HBT with a transport model
Transport models should be able to describe the dynamics of non-equilibrium processes such as freeze-out.
• 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/Rside~1
A recent hydro+EventGenerator 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)
Feb. 9, 2008 Zi-Wei Lin
C(Q) for mid-rapidity pions (125<Pt<225MeV/c)in AuAu at 130AGeVQ in LCMS (longitudinally comoving frame)ZWL, Ko & Pal,PRL 89 (2002)
Feb. 9, 2008 Zi-Wei Lin
Source function analysis using momentshave been proposed
Data is now available from RHIC
Extend to Source Functions
Lacey, Braz. J. Phys.37 (2007); Adler et al. PRL98 (2007); Afanasiev et al. arXiv:0712.4372v1
Danielewicz & Pratt, PLB 618 (2005), PRC 75 (2007)
Here we further test the HBT results from AMPT:study moments of both S(r) and C(q)
Feb. 9, 2008 Zi-Wei Lin
HIJING (parton pdfs, shadowing)energy in strings and minijet partons
ZPC (Zhang's Parton Cascade)
ART (A Relativistic Transport model for hadrons)
A+A
Final particle spectra
Structure of A Multi-Phase Transport (AMPT) Model
Fragment excited strings into partons;all partons enter parton cascade
Partons freeze out & coalescence into hadrons
Hadrons freeze out (at a cut-off time);strong-decay all remaining resonances
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/
In string melting:
Feb. 9, 2008 Zi-Wei Lin
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)≡1+R(q):
1)( 3 rdrS
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Definitions
Indices ai can be:
out, side, long
Feb. 9, 2008 Zi-Wei Lin
For both model and data: Au+Au at sNN=200GeV|η| < 0.350.2<kT<0.36 GeV/c with kT≡(PT,1+PT,2)/2q=|p1-p2|/2 in PCMS (pair rest frame)Moments calculated up to (including) Rank-6.
Data: 0-20% central events π+π+ & π-π-
AMPT: at b=0 fm π+π+
For Comparisons of AMPT ResultsWith PHENIX Data
Adler et al. PRL98 (2007); Afanasiev et al. arXiv:0712.4372v1
K0S decays are enabled (AMPT input file has the flag)
Feb. 9, 2008 Zi-Wei Lin
1-D C(q) & S(r)
S(r)A q-cut (q<50MeV/c) should be applied for apple-to-apple comparisons between PHENIX data and model results
P. Chung, private comm.;Afanasiev et al. arXiv:0712.4372v1
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1-D C(q) & S(r): with q-cut (q<50MeV/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 decaysWithout K0
S decays
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S(r) moments vs C(q) moments: Long
here S(r)for same qqqq CCCCqC zzzzzz(4)zzzzzz ,)()()()( )6()2()0()(
Feb. 9, 2008 Zi-Wei Lin
S(r) moments vs C(q) moments: Side
here S(r)for same qqqq CCCCqC yyyyyy(4)yyyyyy ,)()()()( )6()2()0()(
Feb. 9, 2008 Zi-Wei Lin
S(r) moments vs C(q) moments: Out
here S(r)for same qqqq CCCCqC xxxxxx(4)xxxxxx ,)()()()( )6()2()0()(
Disagree in shapes
Feb. 9, 2008 Zi-Wei Lin
Check C(Q) for 0.2<kT<2 GeV/cQ=|p1-p2| in LCMS (longitudinally comoving frame)
PHENIX data fromAdler et al. PRL93 (2004).0-30% central collisions,Q-cut of 40MeV/c on orthogonal directions
Feb. 9, 2008 Zi-Wei Lin
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)
Summary
Investigate disagreements/agreementsto extract information on dynamics (x-t correlation, hadronization):
Resonance ratios after bulk hadronization?0-20% central vs b=0fm ?Due to the simple quark coalescence model for hadronization?
Outlook
Feb. 9, 2008 Zi-Wei Lin
Parton coalescence to hadrons: Currently, a parton can coalesce after it does not have further interactions (i.e., after kinetic freezeout).
Effective equation of state of AMPT depends on σp
Zhang, Chen & Ko, arXiv:0705.3968
Need to ~decouple hadronization time from parton cross section
Average parton density for coalescence depends on σp
Improvement needs of AMPT
Feb. 9, 2008 Zi-Wei Lin
HBT Radii fromEmission function S(x,p) or correlation function C(q)
If source is Gaussian in space-time, then:
And
1) Curvature at q=0: 2) Often use 4-parameter fitfor C(q) w/o Coulomb effects:
Pratt,PRL84
Pratt,PRL84Wiedemann,PRC57
Dx,y=<x*y>-<x><y>
. 2
Feb. 9, 2008 Zi-Wei Lin
Fitted Radius Parameters for mid-rapidity pions (125<Pt<225MeV/c)in AuAu at 130AGeV
Q in LCMSZWL, Ko & Pal,PRL 89 (2002)
Feb. 9, 2008 Zi-Wei Lin
3D S(r): effects of q-cut(from AMPT with String Melting at 10mb)
Effect on Side directionis the greatest
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3-D S(r) for Default AMPT vs String Melting
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Afanasiev et al. arXiv:0712.4372v1
Hydro+EventGenerator (Therminator) model