1

Heavy Flavor Flow

Che-Ming KoTexas 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)

2

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.

@¹ T¹ º = 0@¹ n¹

i = 0

T ¹ º = (e+p)u¹ uº ¡ pg¹ º

e: energy densityp: pressureuμ: four velocity

Heinz & Kolb; Teaney & Shuryak; Hirano

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Elliptic flow from AMPT

Lin & Ko, PRC 65, 034904 (2002)

)f'-ff')(fΩ/dd(×

|v-v|Ωddp∝t)p,(x,f∂p

2121

2121 ∫σ

μμ

Need string melting and large parton scattering cross section.

sμμ

πασ

μ

πασ ss

/+1

1

2

9=,

)-t(2

9≈

dt

d22

2

22

2

• Using αs=0.5 and screening mass μ=gT≈0.6 GeV at T≈0.25 GeV, then <s>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

1.5mb≈)cos-(1Ωd

dΩd≡ ∫t θσ

σ

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Elliptic flow from quark coalescence/recombination

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

)p,...,p;x,...,(xf)p,x(f ×

E)(2

pddpg=N

n1n1niiq,i

n

1=i i3

i3

iin ∫∏π

σ

}]/2Δ)m-(m-)p-exp{[(p×

]/2Δ)x-exp[(x= )p,p;x,(xf

functionWigner Meson

2p

221

221

2x

2212121M

px

With Δp=0.24 GeV for mesons

and 0.36 GeV for baryons

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Naïve quark coalescence model and constituent quark numer scaling of hadron elliptic flows

Quark transverse momentum distribution

)cos(2)p(v2+1∝)(pf Tq,2Tq φ

Meson elliptic flow

Baryon elliptic flow

)2/p(v2)2/p(v21

)2/p(2v)p(v T2,q

T22,q

T2,qTM2,

)3/p(v3)3/p(v61

)3/p(3v)p(v T2,q

T22,q

T2,qTB2,

Quark number scaling of hadron v2 (except pions):

n)/p(vn

1T2

Only quarks of same momentumcan coalescence, i.e., Δp=0

same for mesons and baryons

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Effects due to momentum dispersion and resonance decays

Momentum dispersion effect Effect of resonance decays

Mom. Disp + res. decays

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22,q4,q2

2

4 2v v 1.2 v

v

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

22,q4,q v v

Data

Parton cascade

Higher-order anisotropic flows

8Greco, Rapp & Ko, PLB595, 202 (04)

S. Kelly,QM04

Charm elliptic flow at RHIC

V2 of electrons

Data consistent with thermalizedcharm quark with same v2 as lightquarks.

Smaller charm v2 than light quarkV2 at low pT due to mass effect

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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.

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Charm transverse momentum spectra from AMPT

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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.

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Elliptic flow from Molnar’s Parton Cascade

Molnar, JPG 31, S421 (2005)

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

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Charm elliptic flow from the Langevin model

Moore & Teaney, hep-ph/0412346

pQCD gives D≈a/(2πT) in QGPwith a=6

Light hadron v2 from STAR

t)p,f(x,mTp∂

∂p

p∂

∂

x∂

f∂

m

p

t∂

f∂

2

2

ii

ii

ηM

T=DSpatial diffusion coefficient

a=1.5

a=3

a=6

a=12

a=24

Momentum drag coefficientmT2

=κ

η

:κ mean squared momentum transferper unit time, proportional to σ

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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.

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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.

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Hadron transverse momentum spectra at LHC

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

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Quark elliptic flow at LHC

Quark elliptic flow is about twice that at RHIC.

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Heavy flavor 4th-order anisotropic flow

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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?

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Resonance effect on charm scattering in QGP

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

4/m-k4

1J2

9

12D

2

D2/1

2D

2qc→qc

s

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.

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System size dependence of elliptic flow