Heavy quark free energies and screening in lattice QCD Olaf Kaczmarek Universität Bielefeld June 10, 2008 RBC-Bielefeld collaboration O. Kaczmarek, PoS CPOD07 (2007) 043 RBC-Bielefeld, Phys.Rev.D77 (2008) 014511 O. Kaczmarek, F. Zantow, Phys.Rev.D71 (2005) 114510 O. Kaczmarek, F. Zantow, hep-lat/0506019 Heavy quark free energies and screening in lattice QCD Hard Probes 2008, Illa da Toxa, June 10, 2008 – p.1/15
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Heavy quark free energies and screening in latticeQCD
Olaf Kaczmarek
Universität Bielefeld
June 10, 2008
RBC-Bielefeld collaboration
O. Kaczmarek, PoS CPOD07 (2007) 043
RBC-Bielefeld, Phys.Rev.D77 (2008) 014511
O. Kaczmarek, F. Zantow, Phys.Rev.D71 (2005) 114510
O. Kaczmarek, F. Zantow, hep-lat/0506019
Heavy quark free energies and screening in lattice QCD Hard Probes 2008, Illa da Toxa, June 10, 2008 – p.1/15
Net quark number induced by a single staticquark source,
NQ(T) =⟨
Nq⟩
Q =
⟨
NqTr P(~0)⟩
⟨
Tr P(~0)⟩ .
Heavy quark free energies and screening in lattice QCD Hard Probes 2008, Illa da Toxa, June 10, 2008 – p.11/15
Diquark free energies - Screening and string breaking[M.Doring et al., Phys.Rev.D75 (2007) 054504]
-1
-0.5
0
0.5
0 0.5 1 1.5 2
rT
NQQ T/Tc = 0.87 T/Tc = 0.90 T/Tc = 0.96
-2
-1.5
-1
-0.5
0
0.5
1
0 0.5 1 1.5 2
T/Tc
NQQ(r0)
NQQ(∞)
Net quark number induced by a qq-pair:
N(c)QQ(r,T) =
⟨
Nq⟩
QQ =
⟨
NqL(c)QQ(r,T)
⟩
⟨
L(c)QQ(r,T)
⟩ ,
where Nq is the quark number operator,
Nq =12
Tr
[
D−1(m̂,0)
(
∂D(m̂,µ)
∂µ
)
µ=0
]
.
Net quark number induced by a single staticquark source,
NQ(T) =⟨
Nq⟩
Q =
⟨
NqTr P(~0)⟩
⟨
Tr P(~0)⟩ .
Diquark is neutralized by quarks or antiquarks
from the vacuum to be color neutral overall
limT→0
NQQ(r,T) =
1 , r < rc
−2 , r > rc
,
Heavy quark free energies and screening in lattice QCD Hard Probes 2008, Illa da Toxa, June 10, 2008 – p.11/15
Diquark free energies - Screening and string breaking[M.Doring et al., Phys.Rev.D75 (2007) 054504]
-1
-0.5
0
0.5
0 0.5 1 1.5 2
rT
NQQ T/Tc = 0.87 T/Tc = 0.90 T/Tc = 0.96
-2
-1.5
-1
-0.5
0
0.5
1
0 0.5 1 1.5 2
T/Tc
NQQ(r0)
NQQ(∞)
Net quark number induced by a qq-pair:
N(c)QQ(r,T) =
⟨
Nq⟩
QQ =
⟨
NqL(c)QQ(r,T)
⟩
⟨
L(c)QQ(r,T)
⟩ ,
where Nq is the quark number operator,
Nq =12
Tr
[
D−1(m̂,0)
(
∂D(m̂,µ)
∂µ
)
µ=0
]
.
Net quark number induced by a single staticquark source,
NQ(T) =⟨
Nq⟩
Q =
⟨
NqTr P(~0)⟩
⟨
Tr P(~0)⟩ .
Diquark is neutralized by quarks or antiquarks
from the vacuum to be color neutral overall
limT→0
NQQ(r,T) =
1 , r < rc
−2 , r > rc
,
Heavy quark free energies and screening in lattice QCD Hard Probes 2008, Illa da Toxa, June 10, 2008 – p.11/15
Free energy vs. Entropy at large separations
-400
-200
0
200
400
600
800
1000
1200
0 1 2 3 4 5
F∞ [MeV]
T/Tc
SU(3): Nτ=4SU(3): Nτ=8
2F-QCD: Nτ=42+1F-QCD: Nτ=42+1F-QCD: Nτ=6
Free energies not only determinedby potential energy
F∞ = U∞ −TS∞
Entropy contributions play a role at finite T
S∞ = − ∂F∞∂T
Heavy quark free energies and screening in lattice QCD Hard Probes 2008, Illa da Toxa, June 10, 2008 – p.12/15
Free energy vs. Entropy at large separations
-500
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
0 0.5 1 1.5 2 2.5 3
T/Tc
U∞[MeV] F∞[MeV]
-500
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
0 0.5 1 1.5 2 2.5 3
T/Tc
U∞[MeV] F∞[MeV]
S∞ = −∂F∞
∂T
U∞ = −T2 ∂F∞/T∂T
-500
0
500
1000
1500
2000
2500
3000
3500
4000
0 0.5 1 1.5 2 2.5 3
T/Tc
TS∞[MeV] F∞[MeV]
High temperatures:
F∞(T) ≃ −43
mD(T)α(T) ≃ −O (g3T)
TS∞(T) ≃ +43
mD(T)α(T)
U∞(T) ≃ −4mD(T)α(T)β(g)
g
≃ −O (g5T)
(a) (c)(b)
cloud2r r
The large distance behavior of the finitetemperature energiesis rather related toscreeningthan to t he temperature depen-dence of masses of corresponding heavy-light mesons!
Heavy quark free energies and screening in lattice QCD Hard Probes 2008, Illa da Toxa, June 10, 2008 – p.12/15
Free energy vs. Entropy at large separations
-500
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
0 0.5 1 1.5 2 2.5 3
T/Tc
U∞[MeV] F∞[MeV]
-500
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
0 0.5 1 1.5 2 2.5 3
T/Tc
U∞[MeV] F∞[MeV]
S∞ = −∂F∞
∂T
U∞ = −T2 ∂F∞/T∂T
0
1000
2000
3000
4000
0 1 2 3
TS∞ [MeV]
T/Tc
Nf=0 Nf=2 Nf=3 Nf=2+1
High temperatures:
F∞(T) ≃ −43
mD(T)α(T) ≃ −O (g3T)
TS∞(T) ≃ +43
mD(T)α(T)
U∞(T) ≃ −4mD(T)α(T)β(g)
g
≃ −O (g5T)
(a) (c)(b)
cloud2r r
The large distance behavior of the finitetemperature energiesis rather related toscreeningthan to t he temperature depen-dence of masses of corresponding heavy-light mesons!
Heavy quark free energies and screening in lattice QCD Hard Probes 2008, Illa da Toxa, June 10, 2008 – p.12/15
r-dependence of internal energies (Nf = 2+1)
-1000
-500
0
500
1000
1500
2000
0 0.2 0.4 0.6 0.8 1 1.2
TS(r,T) [MeV]
r[fm]
T[MeV] 0
191
-100
0
100
200
300
400
500
600
700
800
900
0 0.2 0.4 0.6 0.8 1
TS(r,T) [MeV]
r[fm]
T[MeV] 0
233249345394
F1(r,T) = U1(r,T)−TS1(r,T)
S1(r,T) =∂F1(r,T)
∂T
U1(r,T) = −T2 ∂F1(r,T)/T∂T
Entropy contributions vanish in the limit r → 0
F1(r ≪ 1,T) = U1(r ≪ 1,T) ≡V1(r)
important at intermediate/large distances
Heavy quark free energies and screening in lattice QCD Hard Probes 2008, Illa da Toxa, June 10, 2008 – p.13/15
r-dependence of internal energies (Nf = 2+1)
-2000
-1000
0
1000
2000
3000
4000
5000
6000
7000
8000
0 0.2 0.4 0.6 0.8 1 1.2
U(r,T) [MeV]
r[fm]
T[MeV] 0
166191199
F1(r,T) = U1(r,T)−TS1(r,T)
S1(r,T) =∂F1(r,T)
∂T
U1(r,T) = −T2 ∂F1(r,T)/T∂T
Entropy contributions vanish in the limit r → 0
F1(r ≪ 1,T) = U1(r ≪ 1,T) ≡V1(r)
important at intermediate/large distances
-2000
-1500
-1000
-500
0
500
1000
1500
0 0.2 0.4 0.6 0.8 1
U(r,T) [MeV]
r[fm]
T[MeV] 0
233249345394
=⇒ Implications on heavy quark bound states?
=⇒ What is the correct Ve f f(r,T)?
Heavy quark free energies and screening in lattice QCD Hard Probes 2008, Illa da Toxa, June 10, 2008 – p.13/15
Heavy quark bound states from potential models
0
500
1000
0 0.5 1 1.5
Veff(r,T) [MeV]
r [fm]
V(∞)
∆EJ/ψ(T=0)
steeper slope of Ve f f(r,T) = U1(r,T)
=⇒ J/ψ stronger bound using Ve f f = U1(r,T)
=⇒ dissociation at higher temperatures compared to Ve f f(r,T) = F1(r,T)
Heavy quark free energies and screening in lattice QCD Hard Probes 2008, Illa da Toxa, June 10, 2008 – p.14/15
Conclusions
- Heavy quark free energies, internal energies and entropy
Results for almost physical quark masses, nf = 2+1
Complex r and T dependence
Running coupling shows remnants of confinenement above Tc
Entropy contributions play a role at finite T
Non-perturbative effects in mD up to high T
Non-perturbative effects dominated by gluonic sector
- Bound states in the quark gluon plasma
Estimates from potential models?
What is the correct potential for such models?
Higher dissociation temperature using V1
(directly produced) J/ψ may exist well above Tc
Full QCD calculations of correlation/spectral functions needed
What are relevant processes for charmonium?
Heavy quark free energies and screening in lattice QCD Hard Probes 2008, Illa da Toxa, June 10, 2008 – p.15/15