Why x-t correlation may be important for HBT

Zi-Wei LinZi-Wei Lin Collective flow and QGP propertiesCollective flow and QGP properties 11/19/200311/19/2003

● Why x-t correlation may be important for HBT● Origin of a large&positive 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

Strong and positive x-t correlation and its effect on Rout/Rside

Zi-Wei LinThe Ohio State University


HBT Radii fromEmission function S(x,p) or correlation function C(q)

If source is Gaussian in space-time, then:

Rsource,ij=Rfit,ij

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


Study HBT with a transport model

Advantage:freezeout 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)


HIJINGenergy in strings and minijet partons

ZPC (Zhang's Parton Cascade)

Till Parton freezeout

ART (A Relativistic Transport model for hadrons)

A+A

Decay all resonances;Final particle spectra

Structure of AMPT modelwith String Melting

Fragment excited strings into partons

Coalescence into hadrons


ZWL,Ko&Pal,PRL89

From Gaussian fits to 3-d correlation function C(q)

Au+Au at 130AGeV(b=0 fm)


Why x-t correlation may be important?

Spatial-size x-t correlation duration-time

Magnitude and sign of x-t correlationare important for Rout, Rout/Rside, & extraction of duration-time


Correlations in pion emission source: out-side out-t

<Xout (t)>

Positive and large, tends to reduce Rout Values: (17fm)**2 = 185 -2*168 + 431

SourceSpatial-size x-t correlation Duration time

ZWL,Ko&Pal,PRL89

Note:includes decays


out-side out-t

K emission source (excludes decays):

ZWL&Ko,JPG29

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

K source

<Xout (t)>

also positive and large for K


●Turn off decays to study HBT radiifrom the emission function

●Test hydro-like negative x-t correlationupon hadron formation in AMPT


Pions at freezeout

xout

xsid

e

x

y

mostly partons

~surface emission ~volume emission

<xout> >0parton transverse flow


x-t correlation for pions

Au+Au at 200AGeV (b=0 fm)


Already present for quarksx-t correlation for pions

Au+Au at 200AGeV (b=0 fm)


Effect of decays on source radii

Hadronic decays produce mt-dependence in Rout & Rside


Rout/Rside from emission function


Can an initial negative x-t correlation survive later?

Test negative x-t correlation from hydro models at RHIC energies


large initial Rout/Rside ratio (source)

Initial hadrons:


large final Rout/Rside ratio (source)

Negative x-t term becomes positive after hadronic scatterings

Final hadrons:


Hardtke&Voloshin, PRC61

Radii are different from source or from Gaussian fit to C(Q)


from source from C(Q) fit

big decrease for fitted Rout, Rout/Rside

AMPT: Au+Au at 200AGeV at b=0 fm, 3mb

Rout/Rside=1


from source from C(Q) fit

With an initial negative x-t correlationat hadron formation

huge decrease for fitted Rout & Rout/Rside Rout/Rside >>1 ~=1

Rout/Rside=1


●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: >1 from emission function

~=1 from Gaussian fits to C(Q).

●Even with an large initial negative x-t

(with Rout/Rside >>1 from the emission function)

●Further investigation is needed to find the reason.

HBT summary



v2(pt) for AuAu at 130A GeV: eta (-0.3, 0.3), minimum bias (b=0-13 fm in AMPT)

ZWL&Ko,PRC65


1) From emission function (10mb) for midrapidity charged pions, central 130AGeV:


data corrected for Coulomb effects


Fitted radius parameters vs parton cross sections


Ratio from source >1

> ratio from fit (~=1)


MT-scaling for fitted R?

Kaon:source radii~fitted radii

10 mb results

ZWL&Ko,JPG29


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.


x-y distributions at freezeout


Xout-Xside distributions at freezeout


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 rt*rt+t*t=(10fm)^2



Negative x-t term becomes positive after hadronic scatterings


from source from C(q) fit

With an initial negative x-t correlationat: rt*rt+t*t=(10fm)^2


With an initial negative x-t correlationbut at a larger surface: rt*rt+t*t=(20fm)^2


due to larger initial surfaceof hadron formation: rt*rt+t*t=(20fm)^2

Why x-t correlation may be important for HBT

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