# Presentation: 380707

## Zi-Wei Lin
Department of Physics

- Zi-Wei Lin
- Department 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”)

## Study HBT with a transport model

- 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) 

**C(Q) **
- for mid-rapidity pions
- (125<Pt<225MeV/c)
- in AuAu at 130AGeV
*Q in **LCMS (longitudinally *
*comoving frame)*
- ZWL, Ko & Pal,PRL 89 (2002)

## Extend to Source Functions

- have 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**)

## A+A

*energy in *strings* and *minijet partons* *

- ZPC (Zhang's Parton Cascade)

- ART (A Relativistic Transport model for hadrons)

- 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:***

## Definitions

- 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**):

**Definitions**

- Indices *a**i* can be:
**out, side, long**

## For Comparisons of AMPT Results

**For both model and data: **
- Au+Au at sNN=200GeV
- |η| < 0.35
- 0.2<kT<0.36 GeV/c with kT≡(PT,1+PT,2)/2
- q=|**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 Results**
**With PHENIX Data**

- Adler et al. PRL98 (2007);
- Afanasiev et al. arXiv:0712.4372v1

*K**0**S**  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

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

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

- With K0S decays

- Without K0S decays

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

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

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

*Disagree in shapes*

## Check C(Q) for 0.2<kT<2 GeV/c

*Q=|****p1-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*

## Summary

- 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/agreements
- to 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 fromEmission function S(x,p)     or   correlation function C(q)

*HBT Radii from**Emission 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 fit
- for C(q) w/o Coulomb effects:

- Pratt,PRL84

- Pratt,PRL84
- Wiedemann,PRC57

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

- .

- 2

## Fitted Radius Parameters 

**Fitted Radius Parameters **
- for mid-rapidity pions
- (125<Pt<225MeV/c)
- in AuAu at 130AGeV
*Q in LCMS*
- ZWL, Ko & Pal,PRL 89 (2002)

## 3D S(r): effects of q-cut

*(from* *AMPT with String Melting at 10mb)*

- Effect on Side direction
- is the greatest

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

## Hydro+EventGenerator 

- Afanasiev et al. arXiv:0712.4372v1

- Hydro+EventGenerator
- (Therminator) model