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


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”)


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)


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)


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)


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:


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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aal aa

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aa

laa

rl

aa

rr rrS or

;ArSd

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S

S r

...)()(

)(4!

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)(2

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qAqRd

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aaql

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Definitions

Indices ai can be:

out, side, long


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)


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


1-D C(q) & S(r): with q-cut (q<50MeV/c)


1-D C(q) & S(r): without q-cut


Effects of including pions from K0S decays on S(r)

With K0S decaysWithout K0

S decays


S(r) moments vs C(q) moments: Long

here S(r)for same qqqq CCCCqC zzzzzz(4)zzzzzz ,)()()()( )6()2()0()(


S(r) moments vs C(q) moments: Side

here S(r)for same qqqq CCCCqC yyyyyy(4)yyyyyy ,)()()()( )6()2()0()(


S(r) moments vs C(q) moments: Out

here S(r)for same qqqq CCCCqC xxxxxx(4)xxxxxx ,)()()()( )6()2()0()(

Disagree in shapes


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


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


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


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


Fitted Radius Parameters for mid-rapidity pions (125<Pt<225MeV/c)in AuAu at 130AGeV

Q in LCMSZWL, Ko & Pal,PRL 89 (2002)


3D S(r): effects of q-cut(from AMPT with String Melting at 10mb)

Effect on Side directionis the greatest


3-D S(r) for Default AMPT vs String Melting


Afanasiev et al. arXiv:0712.4372v1

Hydro+EventGenerator (Therminator) model

zi-wei lin department of physics

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