why transport model? space-time (x-t) correlation: its effect on r out/ r side extract radii from

SQM2003 March 13 Zi-wei Lin The Ohio State University

● Why transport model?

● Space-time (x-t) correlation:its effect on Rout/Rside

• Extract radii from1) emission function S(x,K) 2) Gaussian fits to 3-d C(Q,K)

non-Gaussian emission source

● Summary and Outlook

Zi-wei Lin The Ohio State Universityin collaboration with C.M. Ko

Kaon HBT at RHIC from AMPT Model


Rout/Rside ~1up to Kt~1GeV

from S. Johnson at RWW02

●Inconsistent with the hydro model.

● Puzzling considering the “common” relations:


Why transport model?

● HBT probes the space-time information of particles at freezeout

● In transport models, hadrons freeze out dynamically (both chemical and kinetic freezeout),

when mean-free-path is too large:

Transport models may have some advantages to address HBT


HIJINGenergy in strings and minijet partons

ZPC (Zhang's Parton Cascade)

till parton freezeout

ART (A Relativistic Transport model for hadrons)

A+A

Strong-decay resonances for final particle spectra

A Multi-Phase Transport (AMPT) model with String Melting

Fragment excited strings into quarks and antiquarks (via Lund frag. to hadrons)

Nearest quark coalescence to hadrons

Z.W.L. &C.M.Ko,PRC65


An central Au+Au event at 130AGeV from AMPT model(no string melting here)


Definitions:

in the Pratt-Bertsch out-side-long system

xi(1-3)=xout, xside, xlong

qi(1-3)=Qout, Qside, Qlong

=> Rinv

2

=> Rout, Rside, Rlong

Pratt, PRD33

Pratt et al,PRC42

Bertsch et al,PRC37


Method 1 to extract radii:From emission function S(x,K): curvature at q=0

Pratt,PRL84

Pratt,PRL84

Wiedemann,PRC57

Dx,y=<x*y>-<x><y>

.


out-side out-t

Emission function (at freezeout):

positive xout-t correlation

K:200<pt<400 MeV -1<y<1


(3.4fm)^2 = (35 - 2 * 22 + 20) fm^2

from the emission function:

Spatial-size

xout-t correlation

duration-time part

K:200<pt<400 MeV -1<y<1

is positive and large

reduces Rout and Rout/Rside

Complicates the extraction of the duration time from

Mangnitude of the xout-t correlation


out-side out-t

also positive and large, reduces Rout/Rside

(17fm)^2 = (185 - 2*168 + 431) fm^2

pi:125<pt<225 MeV -1<y<1

Similar to the pion case: Z.W.L.,C.M.Ko&S.Pal,PRL89

from the emission function:


Experimentally, from 4-parameters Gaussian fits of C(q) (w/o Coulomb effects):

Pratt,PRL84

.

Method 2 to extract radii:

If source is Gaussian in space-time, then:

and Method1= Method2

BUT

if source is non-Gaussian in space-time:e.g., see

D.Hardtke&S.Voloshin,

PRC61Method1= Method2


source radii vs fitted radii

Difference is up to 30%

decays are not included in

source radii)

Source radii are much larger

if decays are included.

Fitted radii should be used for fair comparison with data, as source radii suffer from non-Gaussian source


Rout/Rside from the 2 methods:


● xout-t correlation from emission function from AMPT model:

is large & positive tends to reduce Rout and Rout/Rside

complicates the extraction of emission duration time same for pions

●Radius parameters extracted from 2 methods:

1) from spatial correlation of the emission source

2) from Gaussian fits to 3-d C(Q) difference is up to 30% for K (even when decays are not included) 2) should be used for comparison with data

Summary


1) Need parton subdivision to avoid causality violation

2) Current approach in AMPT model with string melting:

partons coalesce when they freezeout in parton cascade

local density at hadronization controled by p (cross

section)local density is directly related with collective flow

(v2, ...)investigate coalescence when local energy density < critical value

3) Resonance abundances (K*, ) from quark coalescence need

further study (at least constrained by data) for quantitative

statements

4) Investigate the origin of the large & positive xout-t correlation

Outlook

why transport model? space-time (x-t) correlation: its effect on r out/ r side extract radii from

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