# Presentation: 529369

## Heavy Flavor Flow

-          Che-Ming Ko
- Texas A&M University

-  Light hadron flows at RHIC
-  Charm flow at RHIC
-  Charm and beauty flow at LHC
-  Summary

- Collaborator: Lie-Wen Chen (Shanghai),
-                       Vincenzo Greco, Ralf Rapp,
-                       Bin Zhang (Arkansas)

## Elliptic flow from hydrodynamic model

- _Elliptic flow from hydrodynamic model_

- With an initial energy density of
- ~25 GeV/fm3, hydro describes very
- well data at low pT (mass effect)
- but fails at intermediate pT.

- e: energy density
- p: pressure
- uμ: four velocity

- Heinz & Kolb; Teaney & Shuryak; Hirano

## Elliptic flow from AMPT

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

- Need string melting and large parton
- scattering cross section.

-  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

## Elliptic flow from quark coalescence/recombination

- _Elliptic flow from quark coalescence/recombination_

- Greco, Levai & Ko, PRC 68, 034904 (2003)
- Fries, Meuller, Nonaka & Bass, PRC 68, 044902 (2003)

- With Δp=0.24 GeV for mesons
- and 0.36 GeV for baryons

## Naïve quark coalescence model and constituent quark numer 

- _scaling of hadron elliptic flows_

- Quark transverse momentum distribution

- Meson elliptic flow

- Baryon elliptic flow

- Quark number scaling
- of hadron v2 (except pions):

- Only quarks of same momentum
- can coalescence, i.e., Δp=0

- same for mesons and baryons

## Effects due to momentum dispersion and resonance decays

- _Effects due to momentum dispersion and resonance decays_

- Momentum dispersion effect

- Effect of resonance decays

- Mom. Disp + res. decays

## Higher-order anisotropic flows 

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

- Data

- Parton cascade

- _Higher-order anisotropic flows_

## Charm elliptic flow at RHIC 

- _Charm elliptic flow at RHIC _

- V2 of electrons

- Data consistent with thermalized
- charm quark with same v2 as light
- quarks.

- Smaller charm v2 than light quark
- V2 at low pT due to mass effect

## Quark elliptic flows from AMPT

- _Quark elliptic flows from AMPT_

-  Compared to v2 of light quarks, charm quark v2 is smaller at low
-   pT due to its large mass but becomes comparable at high pT.
-  Charm quark v2 is also sensitive to it scattering cross section.

## Charm transverse momentum spectra from AMPT

- _Charm transverse momentum spectra from AMPT_

## Charmed meson elliptic flow from AMPT

- _Charmed meson elliptic flow from AMPT_

- Zhang, Chen & Ko, nucl-th/0502056

- Current light quark masses are used in AMPT. Charmed meson elliptic flow will be larger if constituent quark masses are used.

## Elliptic flow from Molnar’s Parton Cascade

- _Elliptic flow from Molnar’s Parton Cascade_

- Molnar, JPG 31, S421 (2005)

- Results were obtained with constituent quark masses and
- σgg→gg≈(9/4)σqg→qg≈(9/4)2σqq→qq=10 mb, which is about 4 times
- those from pQCD.

## Charm elliptic flow from the Langevin model

- _Charm elliptic flow from the Langevin model_

- Moore & Teaney, hep-ph/0412346

- pQCD gives D≈a/(2πT) in QGP
- with a=6

- Light hadron v2 from STAR

- Spatial diffusion coefficient

- a=1.5

- a=3

- a=6

- a=12

- a=24

- Momentum drag coefficient

- mean squared momentum transfer
- per unit time, proportional to σ

## Charm flow from HSD (Hadron-String-Dynamics) 

- _Charm flow from HSD (Hadron-String-Dynamics) _
- _transport model_

- Bratkovskaya, Cassing, Stoecker & Xu, PRC 71, 044901 (2005)

- Hadronic scattering in HSD gives a smaller elliptic flow than that
- from partonic scattering in AMPT and MPC.

## Hadron rapidity distributions at LHC from AMPT

- _Hadron rapidity distributions at LHC from AMPT_

- Pb+Pb @ 5.5 TeV

- Charged particle multiplicity is about a factor of two larger than at RHIC.

## Hadron transverse momentum spectra at LHC

- Larger inverse slope parameters due to larger radial flow at LHC.

## Quark elliptic flow at LHC 

- _Quark elliptic flow at LHC_

- Quark elliptic flow is about twice that at RHIC.

## Heavy flavor 4th-order anisotropic flow

- _Heavy flavor 4th-order anisotropic flow_

## Summary

-  Heavy flavor flow is sensitive to its scattering cross
-    section or diffusion coefficient in QGP.
-  Existing data at RHIC are consistent with a large
-    scattering cross section.
-  Heavy flavor flows are expected to be even larger
-    at LHC than at RHIC.
-  Heavy flavor v4 non-negligible and v4~1.1(v2)2.
-  What is the origin of large charm scattering cross
-    section?
-  How does charm elliptic flow depend on system size?

## Resonance effect on charm scattering in QGP

- Van Hees & Rapp, PRC 71, 034907 (2005)

- With mc≈1.5 GeV, mq≈5-10 MeV, mD≈2 GeV, ΓD≈0.3-0.5 GeV, and
- including scalar, pseudoscalar, vector, and axial vector D mesons gives

- σcq→cq(s1/2=mD)≈6 mb

- Since the cross section is isotropic, the transport cross section
- is 6 mb, which is about 4 times larger than that due to pQCD
- t-channel diagrams.

## System size dependence of elliptic flow

- _System size dependence of elliptic flow_