J/ψ Production and Elliptic Flow in Relativistic Heavy Ion Collisions

Che-Ming Ko Texas A&M University

  Introduction   J/ψ production mechanisms   The two-component model   Nuclear modification factor for J/ψ   Elliptic flow of J/ψ   Summary

Collaborators: Taesoo Song (TAMU), Su Houng Lee (Yonsei Univ.), Jun Xu (TAMU)

Support in part by US National Science Foundation and Welch Foundation

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  Dilepton enhancement (Shuryak, 1978)   Strangeness enhancement (Meuller & Rafelski, 1982)   J/ψ suppression (Matsui & Satz, 1986)   Pion interferometry (Pratt; Bertsch, 1986)   Elliptic flow (Ollitrault, 1992)   Jet quenching (Gyulassy & Wang, 1992)   Net baryon and charge fluctuations (Jeon & Koch; Asakawa, Heinz

& Muller, 2000)   Quark number scaling of hadron elliptic flows (Voloshin 2002)   ……………

Introduc*on:  Signatures  of  quark-­‐gluon  plasma  

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J/ψ properties in QGP    Perturbative QCD screening mass

€

λD =Nc

3+Nf

6⎛

⎝ ⎜

⎞

⎠ ⎟ −12gT( )−1 ≈ 2

3gT( )−1

J/ψ suppression in HIC (Matsui & Satz)

  Lattice QCD (Asakawa & Hatuda, Karsch et al.)

J/ψ survives below 1.62~1.70Tc

rTc

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Pd : Color screening (critical density nc~ 5/fm3)

Pcg : gluons (σ=3 mb)

Pch : hadrons (σ=3 mb)

Pf : formation

Ps : survival

J/ψ absorption probability at RHIC

Zhang et al., PRC 62, 054905 (2000)

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  Charm  quark  mass  mc=1.35  GeV                                      

  Au+Au  @  200A  GeV  

  Ini=al    

  Final  

J/ψ evolution in partonic matter

Zhang et al., PRC 65, 054909 (2002)

with  screening  

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Statistical hadronization model for J/ψ production Andronic, Braun-Munzinger, Redlich & Stachel, NPA 789, 334 (2007)

N

N

μ  

μ  

€

NJ/ψ =g2p2

γ c2 p2dpe m2 +p2 /T +10

∞

∫

  Results are sensitive to the number of charm quark pairs produced in the collisions.

N μ  

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Two component model for J/ψ production

Zhao  &  Rapp,  EPJ  62,  109  (2009)  

  Regeneration from coalescence of charm and anticharm quark is non- negligible at RHIC as first pointed out by Thews et al.

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The two-component model: directly produced J/ψ

   Number  of  ini=ally  produced  

€

NJ /ψAA =σJ /ψ

NN A2TAA ( b )

€

Snucl ( b , s ) =

1TAB

dzd ʹ′ z ρA ( s ,z)ρB (

b − s ,z)∫

× exp −(A −1) dzAρA ( s ,zA )σ nuc

z

∞

∫⎧ ⎨ ⎩

⎫ ⎬ ⎭

× exp −(B −1) dzBρB ( s ,zB )σ nuc

z

∞

∫⎧ ⎨ ⎩

⎫ ⎬ ⎭

€

TAA ( b ) = d2 s TA (

s )TA ( b − s )∫

•  : J/ψ production cross section in NN collision; ~ 0.774 µb at s1/2= 200 GeV

€

σJ /ψNN

€

TA ( s ) = dz

−∞

∞

∫ ρA ( s ,z)

•  Overlap function

•   Thickness function

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ρ r( ) =ρ0

1+ e r−r0( ) / c

•  Normalized density distribution

  Nuclear absorption

r0=  6.38  fm,  c=0.535  fm  for  Au  

- Survival probability

Song, Park & Lee, PRC 81, 034914 (10)

Thermal dissociation of directly produced J/ψ

€

M 2 =43

g4mc2mJ /ψ

∂ψ(p)∂p

2

−12

+(k1

0)2 + (k20)2

2k1⋅ k2

⎧ ⎨ ⎩

⎫ ⎬ ⎭

  Dissociation by partons

  Dissociation by hadrons  

€

σ(s) = dxni(x,Q2)σi(xs,Q

2)∫i∑

  Thermal dissociation width

€

Γ(T) =d3k(2π)3

vrel (k)ni(k,T)σ idiss(k,T)∫

i∑

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  Thermal dissociate probability

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Sth ( b , s ) = exp − Γ ʹ′ τ ( )

τ0

τcf

∫ d ʹ′ τ ⎧ ⎨ ⎪

⎩ ⎪

⎫ ⎬ ⎪

⎭ ⎪

Sth ( b , s ) = 0.67Sth

J /ψ ( b , s ) + 0.25Sth

χ c ( b , s )

+ 0.08Sthʹ′ ψ ( b , s )

J/ψ Ψ’ χc

Song, Park & Lee, PRC 81, 034914 (10)

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€

Nreg−J /ψAA = γ 2 nJ /ψSth−H

J /ψ + Br(χc →J /ψ)nχ cSth−Hχ c + Br( ʹ′ ψ →J /ψ)n ʹ′ ψ Sth−Hʹ′

ψ { }VR

As in statistical model

The two-component model: regenerated J/ψ

€

Ncc AA =

12γno

I1(γn0V )I0(γn0V )

+γ 2nh

⎡

⎣ ⎢

⎤

⎦ ⎥ V =σ cc

NN A2TAA ( b )

  Charm fugacity is determined by

€

R =1− exp − dτΓc (T(τ ))τ 0

τQGP

∫⎧ ⎨ ⎪

⎩ ⎪

⎫ ⎬ ⎪

⎭ ⎪

Γ(T) =d3k(2π )3

vrel (k)ni(k,T)σ idiss(k,T)∫

i∑

  Charm relaxation factor  

•  : charm production cross section in NN collision; ~ 63.7 µb at s1/2= 200 GeV

€

σcc NN

as J/ψ is more likely to be formed if charm quarks are in thermal equilibrium

Song, Park & Lee, PRC 81, 034914 (10)

Quasiparticle model for QGP

€

p(T) =gi

6π 2dkfi(T)

k 4

Ei0

∞

∫ − B(T)i=g,q,q ∑

e(T) =gi

2π 2dkk 2 f i(T)Ei0

∞

∫ + B(T)i=g,q,q ∑

mg2 =

Nc

3+

N f

6⎛

⎝ ⎜

⎞

⎠ ⎟

g2(T)T 2

2

mq2 =

g2(T)T 2

3

g2(T) =48π 2

(11Nc − 2N f )lnF 2(T,Tc,Λ)

F(T,Tc,Λ) =18

18.4e(T /Tc )2 / 2 +1

TTc

Tc

Λ

P. Levai and U. Heinz, PRC , 1879 (1998)

  The model reproduces reasonably the QGP equation of state from LQCD 11  

Fire-cylinder model for relativistic heavy ion collisions

€

ax = aT (1+ zε), ay = aT (1− zε)

aT =(p − pf )A

M, ε =

Ry − Rx

Ry + Rx

  The acceleration aT and asymmetry ε can in principle be determined self-consistently from the EOS but are taken as parameters. 12  

Light hadrons mean transverse momentum and elliptic flow

€

Δv = (vx − vy )exp[−C(pT /n)]

Introduced viscous effect at freeze out T=125 MeV

with n= number of quarks in a hadron

  Good description of experimental data 13  

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J/ψ average squared transverse momentum

€

dNdydpT

2 =1

2(2π)3dϕ dσ⋅ pe−p⋅u /T∫

0

2π

∫

×τmT

(2π)2dAT∫ I0

pT sinhρT

⎛

⎝ ⎜

⎞

⎠ ⎟ K1

mT coshρT

⎛

⎝ ⎜

⎞

⎠ ⎟

pT2 =

dpT2 pT

2 (dN /dydpT2 )∫

dpT2 (dN /dydpT

2 )∫

  Large value for large Npart is due to overestimate of charm quark diffusion

  J/ψ freeze out temperature T=175 MeV

Centrality and transverse momentum dependence of J/ψ nuclear modification factor

  Most J/ψ are survivors from initially produced.   The kink in RAA is due to different survival probabilities of initially produced J/ψ in high and low regions of the fire-cylinder

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J/ψ elliptic flow

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v2 =dϕcos(2ϕ)(dN /dyd2pT )∫

dϕ(dN /dyd2pT )∫

=dAT cos(2ϕ)I2(pT sinhρ /T)K1(mT coshρ /T)∫

dAT I0(pT sinhρ /T)K1(mT coshρ /T)∫

  Initially produced J/ψ have essentially vanishing v2   Regenerated J/ψ have large v2   Final J/ψ v2 is small as most are initially produced

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Effects of higher-order corrections

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ʹ′ σ (J /ψ + q(g)→c + c + X) = Aσ(J /ψ + q(g)→c + c + X)ʹ′ σ (c + q(g)→c + q(g)) = Bσ(c + q(g)→c + q(g))

  Higher-order effects are small on J/ψ average squared transverse momentum

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Higher-order effects on J/ψ nuclear modification factor

  Higher-order effects are small on J/ψ nuclear modification factor

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Higher-order effects on J/ψ elliptic flow

  Higher-order effects on v2 of J/ψ are large   v2 of J/ψ provides information on J/ψ production mechanism in HIC

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

S. Kelly,QM04

Charmed meson elliptic flow

v2  of  electrons  

   Data  consistent  with  thermalized        charm  quarks  with  similar  v2  as  light        quarks      

Smaller  charm  v2  than  light  quark  v2  at  low  pT  due  to  mass  effect  Quark  coalescence  

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J/ψ elliptic flow in the coalescence model

D. Krieg & M. Bleicher, EPJA 39, 1 (2009)

  Negative charm quark v2 is required to obtain negative J/ψ v2.   Resulting non-photonic electron v2 does not agree with data.

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Charm 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

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Charmonium spectra and elliptic flow Zhang, PLB 647, 249 (2007)

  AMPT shows that charmonium elliptic flow is appreciable and increases with increasing parton cross sections

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Zhang, PLB 647, 249 (2007)

  In AMPT, large (small) charm quark scattering cross section leads to suppressed (enhanced) yield but larger (smaller) average squared pt.

J/ψ production from charm quark coalescence

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Summary

  Both the statistical model, in which all J/ψ are due to regeneration from QGP, and the two-component model, which includes both J/ψ from initial hard scattering and regeneration from QGP, can describe measured <pT

2> and

RAA at RHIC.

  v2 of regenerated J/ψ is large, while that of directly produced ones is essentially zero.

  Studying v2 of J/ψ is useful for distinguishing the mechanism for J/ψ production in HIC.