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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
1
2
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
3
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
4
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)
5
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
6
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
7
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.
8
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
€
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∑
9
Thermal dissociate probability
€
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)
10
€
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
14
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
15
16
J/ψ elliptic flow
€
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
17
Effects of higher-order corrections
€
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
18
Higher-order effects on J/ψ nuclear modification factor
Higher-order effects are small on J/ψ nuclear modification factor
19
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
20
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
21
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.
22
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
23
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
24
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
25
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.