# Presentation: 183765

## Transport description of viscous effects

-        Che-Ming Ko
- Texas A&M University

-  Introduction
-  A multi-phase transport (AMPT) model
-  Anisotropic flow
-    - Elliptic flow
-    - Higher-order anisotropic flow
-    - Rapidity dependence
-    - System size dependence
-    - Flavor dependence
-  Summary

- Collaborators: Lie-wen Chen (SJTU), Zie-wei Lin (Univ. Alabama),
-                         Bin Zhang (Arkansas State Univ.)

## Elliptic flow from parton cascade

- Zhang, Gyulassy & Ko, PLB 455, 45 (1999)

**Elliptic flow from parton cascade**

- Based on Zhang’s parton cascade (ZPC) (CPC 109, 193 (1998))
- using minijet partons from HIJING for Au+Au @ 200 AGeV and b=7.5fm

- v2 of partons is sensitive to their scattering cross section

## Zhang’s parton cascade (ZPC)

-  Using αs=0.5 and screening mass μ=gT≈0.6 GeV at T≈0.25 GeV,
-    then 
1/2≈4.2T≈1 GeV, and pQCD gives σ≈2.5 mb and a
-    transport cross section
-  σ=6 mb → μ≈0.44 GeV, σt≈2.7 mb
-  σ=10 mb → μ≈0.35 GeV, σt≈3.6 mb

**Zhang’s parton cascade (ZPC)**

- Bin Zhang, Comp. Phys. Comm. 109, 193 (1998)

## A multiphase transport (AMPT) model

- Default: Lin, Pal, Zhang, Li &Ko, PRC 61, 067901 (00); 64, 041901 (01);
-    72, 064901 (05); http://www-cunuke.phys.columbia.edu/OSCAR

-  Initial conditions: HIJING (soft strings and hard minijets)
-  Parton evolution: ZPC
-  Hadronization: Lund string model for default AMPT
-  Hadronic scattering: ART

-  Convert hadrons from string fragmentation into quarks and antiquarks
-  Evolve quarks and antiquarks in ZPC
-  When partons stop interacting, combine nearest quark and antiquark
-    to meson, and nearest three quarks to baryon (coordinate-space
-    coalescence)
-  Hadron flavors are determined by quarks’ invariant mass

- String melting:  PRC 65, 034904 (02); PRL 89, 152301 (02)

## Elliptic flow from AMPT

-  Need string melting and large parton scattering cross section
-  Mass ordering of v2 at low pT as in ideal hydrodynamic model

- Lin & Ko, PRC 65, 034904 (2002)

**Elliptic flow from AMPT**

- σp= 6 mb

## Coalescence model

- Quark distribution function

- Spin-color statistical factor

- e.g.

- Coalescence
- probability
- function

- PRL 90, 202102 (2003); PRC 68, 034904 (2003)

- Number of hadrons with n quarks and/or antiquarks

- For baryons, Jacobi coordinates for three-body system are used.

## Momentum-space coalescence model

- Including 4th order quark flow

- Meson flow

- Baryon flow

- Kolb, Chen, Greco, & Ko, PRC 69 (2004) 051901

## Higher-order anisotropic flow 

- Data can be described by
- a multiphase transport
- (AMPT) model

- Data

- Parton cascade

**Higher-order anisotropic flow**** **

- Momentum-space coalescence

- Chen, Ko, & Lin, PRC 69, 031901 (04)

## Strange quarks from AMPT

**Strange quarks from AMPT**

- Chen & Ko, PRC 73, 044903 (2006)

## Phi & Omega flows

**Phi & Omega flows**

- same for phi & Omega
- but different from quark

- instead of 1.1 and 0.7 from dynamical
- coalescence model

- Chen & Ko, PRC 73, 044903 (2006)

## Flows of phi & Omega with 

- satisfied for large phi and Omega
- sizes of 4.5 fm

**Flows of phi & Omega with **
**large sizes**

## Pseudorapidity dependence of v1 and v2

-  String melting describes data near mid-rapidity (||<1.5)
-  At large rapidity (||>3), hadronic picture works better

- Chen, Greco, Ko & Koch, PLB 605, 95 (2005)

## System size dependence of elliptic flow

**System size dependence of elliptic flow**

- Chen & Ko, nucl-th/0505044

- v2 is proportional to size of colliding system

## Elliptic flow in collisions of asymmetric systems

**Elliptic flow in collisions of asymmetric systems**

- Compared to symmetric collisions
-  Directed flow v1 is stronger
-  Elliptic flow v2 is more sensitive to parton cross section
-  Both directed and elliptic flows are asymmetric in forward
-    and backward rapidities

## Quark elliptic flow from AMPT

**Quark elliptic flow from AMPT**

-  PT dependence of charm quark v2 is different from that of light quarks.
-  At high pT, charm quark has similar v2 as light quarks.
-  Charm elliptic flow is also sensitive to parton cross sections

## Charm elliptic flow from AMPT

**Charm elliptic flow from AMPT**

- Zhang, Chen & Ko, PRC 72, 024906 (05)

-  Current light quark masses are used in AMPT. Charmed meson
-    elliptic flow will be larger if constituent quark masses are used.
-  To increase v2 at low pt requires going beyond parton cascade.

- 15

- 10

- 5

- 0

- -5

## Summary

-  Elliptic flow is sensitive to parton scattering cross section
-  The AMPT model with string melting can reproduce observed
-    large elliptic flow and mass ordering at low pT with large parton
-    cross section (quasi bound states in QGP and/or multiparton dynamics
-    gg↔ggg?)
-   Observed hadron v4≈1.2v22 is reproduced with parton v4≈v22
-   v1 and v2 at midrapidity requires formation of partonic matter, while
-    those at large rapidity is consistent with a hadronic matter
-  AMPT predicts:
-    - v2 scales with the size of colliding system
-    - Stronger v1 and more sensitivity of v2 to parton cross section in asymmetric
-        than symmetric collisions, and both show forward-backward asymmetry in
-        rapidity
-  Observed large charmed meson flow requires large charm quark
-    scattering cross section (resonance effect?)