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
Heavy quark bound states above deconfinement
Strong interactions in the deconfined phase T>∼Tc
Possibility of heavy quark bound states?
Suppression patterns of charmonium/bottomonium
Charmonium (χc,J/ψ) as thermometer above Tc
=⇒ Potential models
→ heavy quark potential (T=0)
V1(r) = −43
α(r)r
+σ r
→ heavy quark free energies (T > Tc)
F1(r,T) ≃−43
α(r,T)
re−m(T)r
→ heavy quark internal energies (T 6=0)
F1(r,T) = U1(r,T)−T S1(r,T)
=⇒ Charmonium correlation functions/spectral functions
Heavy quark free energies and screening in lattice QCD Hard Probes 2008, Illa da Toxa, June 10, 2008 – p.2/15
Zero temperature potential -nf =2+1
-2
0
2
4
6
8
0 0.5 1 1.5 2 2.5 3
r/r0
r0 Vqq(r)-
3.3823.43 3.51 3.57 3.63 3.69 3.76 3.82 3.92
Vstring
1.0
1.1
1.2
1.3
1.4
1.5
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0 0.05 0.1 0.15 0.2 0.25 0.3
a/r0
a [fm]
r0/r1r0σ1/2
1.30
1.35
1.40
1.45
1.50
1.55
1.60
3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1
β
Zren(β)
renormalization: VT=0(r) = − log(
(Zren(β))2 W(r,τ)W(r,τ+1)
)
cut-off effects are small
r2 dVq̄q(r)
dr
∣
∣
∣
∣
r=r0
= 1.65
r2 dVq̄q(r)
dr
∣
∣
∣
∣
r=r1
= 1.0
(r0 = 0.469(7) fm)
2+1 flavor QCD
highly improved p4-staggered
almost realistic quark masses
mπ ≃ 220 MeV, physical ms
Large distance behaviourconsistent with string model prediction:
V(r) = − π12r +σ r , for large r
−→ used for renormalization
Heavy quark free energies and screening in lattice QCD Hard Probes 2008, Illa da Toxa, June 10, 2008 – p.3/15
Zero temperature potential -nf =2+1
-2
0
2
4
6
8
0 0.5 1 1.5 2 2.5 3
r/r0
r0 Vqq(r)-
3.3823.43 3.51 3.57 3.63 3.69 3.76 3.82 3.92
Vstring
2+1 flavor QCD
highly improved p4-staggered
almost realistic quark masses
mπ ≃ 220 MeV, physical ms
Large distance behaviourconsistent with string model prediction:
V(r) = − π12r +σ r , for large r
−→ used for renormalization
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
r0V(r)
r/r0
VstringCornell
Cornell+1/r2
Short distance behaviourdeviations at small r
enhancement of the running coupling
fit: V(r) = −0.392(6)/r +σ r
r-dependent running coupling α(r)
Heavy quark free energies and screening in lattice QCD Hard Probes 2008, Illa da Toxa, June 10, 2008 – p.3/15
The lattice set-up
log() =⇒ −FQQ̄(r ,T)
TQQ̄ = 1, 8, av
Polyakov loop correlation function and free energy:L. McLerran, B. Svetitsky (1981)
ZQQ̄
Z (T)≃ 1Z (T)
Z
D A... L(x) L†(y) exp
(
−Z 1/T
0dt
Z
d3xL [A, ...]
)
Lattice data used in our analysis:
Nf = 0:323×4,8,16-lattices( Symanzik )HB-OR
O. Kaczmarek,F. Karsch,P. Petreczky,F. Zantow (2002, 2004)
Nf = 2:163×4-lattices( Symanzik, p4-stagg. )hybrid-R
mπ/mρ ≃ 0.7 (m/T = 0.4)
O. Kaczmarek, F. Zantow (2005),O. Kaczmarek et al. (2003)
Nf = 3:163×4-lattices( stagg., Asqtad )hybrid-R
mπ/mρ ≃ 0.4
P. Petreczky,K. Petrov (2004)
Nf = 2+1:244×6-lattices( Symanzik, p4fat3 )RHMC
mπ ≃ 220MeV, phys.ms
O. Kaczmarek (2007),RBC-Bielefeld (2008)
Heavy quark free energies and screening in lattice QCD Hard Probes 2008, Illa da Toxa, June 10, 2008 – p.4/15
The lattice set-up
log() =⇒ −FQQ̄(r ,T)
TQQ̄ = 1, 8, av
Polyakov loop correlation function and free energy:L. McLerran, B. Svetitsky (1981)
ZQQ̄
Z (T)≃ 1Z (T)
Z
D A... L(x) L†(y) exp
(
−Z 1/T
0dt
Z
d3xL [A, ...]
)
O. Philipsen (2002)O. Jahn, O. Philipsen (2004)
− ln(
〈T̃rL(x)T̃rL†(y)〉)
=Fq̄q(r,T)
T
− ln(
〈T̃rL(x)L†(y)〉)
∣
∣
∣
∣
∣
GF
=F1(r,T)
T
− ln
(
98〈T̃rL(x)T̃rL†(y)〉− 1
8〈T̃rL(x)L†(y)〉
∣
∣
∣
∣
∣
GF
)
=F8(r,T)
T
1/T =Nτ
1/3σV =N
a
a
a
Heavy quark free energies and screening in lattice QCD Hard Probes 2008, Illa da Toxa, June 10, 2008 – p.4/15
Heavy quark free energy - 2+1-flavors
-1000
-500
0
500
1000
0 0.5 1 1.5 2 2.5
F(r,T) [MeV]
r [fm]
T[MeV] 175186197200203215226240259281326365424459548
Renormalization of F(r,T)
using Zren(g2) obtained at T=0
e−F1(r,T)/T =(
Zr (g2))2Nτ 〈Tr (LxL
†y)〉
alternative renormalization proceduresall equivalent!(O. Kaczmarek et al.,PLB543(2002)41,
S. Gupta et al., Phys.Rev.D77 (2008) 034503)
Heavy quark free energies and screening in lattice QCD Hard Probes 2008, Illa da Toxa, June 10, 2008 – p.5/15
Heavy quark free energy - 2+1-flavors
-1000
-500
0
500
1000
0 0.5 1 1.5 2 2.5
F(r,T) [MeV]
r [fm]
T[MeV] 175186197200203215226240259281326365424459548
xxxxxxxxx
-1200
-1000
-800
-600
-400
-200
0
200
400
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
F(r,T) [MeV]
r [fm]
T-independentr ≪ 1/
√σ
F(r,T) ∼ g2(r)/r
Renormalization of F(r,T)
using Zren(g2) obtained at T=0
e−F1(r,T)/T =(
Zr (g2))2Nτ 〈Tr (LxL
†y)〉
alternative renormalization proceduresall equivalent!(O. Kaczmarek et al.,PLB543(2002)41,
S. Gupta et al., Phys.Rev.D77 (2008) 034503)
Heavy quark free energies and screening in lattice QCD Hard Probes 2008, Illa da Toxa, June 10, 2008 – p.5/15
Heavy quark free energy - 2+1-flavors
-1000
-500
0
500
1000
0 0.5 1 1.5 2 2.5
F(r,T) [MeV]
r [fm]
T[MeV] 175186197200203215226240259281326365424459548
xxxxxxxxx
-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
T-independentr ≪ 1/
√σ
F(r,T) ∼ g2(r)/r
String breakingT < Tc
F(r√
σ ≫ 1,T) < ∞
high-T physics
rT ≫ 1 ; screeningµ(T) ∼ g(T)T
F(∞,T) ∼−T
Heavy quark free energies and screening in lattice QCD Hard Probes 2008, Illa da Toxa, June 10, 2008 – p.5/15
Renormalized Polyakov loop
-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
-1000
-500
0
500
1000
0 0.5 1 1.5 2 2.5
F(r,T) [MeV]
r [fm]
T[MeV] 175186197200203215226240259281326365424459548
Lren = exp
(
−F(r = ∞,T)
2T
)
Using short distance behaviour of free energies
Renormalization of F(r,T) at short distances
e−F1(r,T)/T =(
Zr (g2))2Nτ 〈Tr (LxL
†y)〉
Renormalization of the Polyakov loop
Lren =(
ZR(g2))Nt Llattice
Lren defined by long distance behaviour of F(r,T)
Heavy quark free energies and screening in lattice QCD Hard Probes 2008, Illa da Toxa, June 10, 2008 – p.6/15
Renormalized Polyakov loop
0.0
0.2
0.4
0.6
0.8
1.0
100 150 200 250 300 350 400 450
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
T [MeV]
Tr0 Lren
Nτ=468
-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
0
0.5
1
0.5 1 1.5 2 2.5 3 3.5 4
Lren
T/Tc
SU(3): Nτ=4SU(3): Nτ=8
2F-QCD: Nτ=42+1F-QCD: Nτ=42+1F-QCD: Nτ=6
Lren = exp
(
−F(r = ∞,T)
2T
)
Heavy quark free energies and screening in lattice QCD Hard Probes 2008, Illa da Toxa, June 10, 2008 – p.6/15
Renormalized Polyakov loop
0
0.5
1
1.5
0 5 10 15 20 25
Lren
T/Tc
Nτ=4Nτ=8
SU(3) pure gauge results
Lren = exp
(
−F(r = ∞,T)
2T
)
High temperature limit, Lren = 1,reached from above as expected from PT
Clearly non-perturbative effects below 5Tc
Heavy quark free energies and screening in lattice QCD Hard Probes 2008, Illa da Toxa, June 10, 2008 – p.6/15
Temperature depending running coupling
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0.70.60.50.40.30.20.1
αeff(r,T)
r[fm]
T[MeV] 156186197200203215226240259281326365424459548
non-perturbative confining part for r>∼0.4 fm
αqq(r) ≃ 3/4r2σ
present below and just above Tc
remnants of confinement at T>∼Tc
temperature effects set in at smaller r with increasing T
maximum due to screening
=⇒ At which distance do T-effects set in ?
=⇒ definition of the screening radius/mass
=⇒ definition of the T-dependent coupling
Free energy in perturbation theory:
F1(r,T) ≡V(r) ≃−43
α(r)r
for rΛQCD ≪ 1
F1(r,T) ≃−43
α(T)
re−mD(T)r for rT ≫ 1
QCD running coupling in the qq-scheme
αqq(r,T) =34
r2 dF1(r,T)
dr
Heavy quark free energies and screening in lattice QCD Hard Probes 2008, Illa da Toxa, June 10, 2008 – p.7/15
Temperature depending running coupling
0
0.2
0.4
0.6
0.8
1
1.2
1 1.5 2 2.5 3
αmax(T)
T/Tc
nf=0nf=2
nf=2+1 Nt=6nf=2+1 Nt=4
define α̃qq(T) by maximum of αqq(r,T):
α̃qq(T) ≡ αqq(rmax,T)
perturbative behaviour at high T:
g−22-loop(T) = 2β0 ln
(
µTΛMS
)
+β1
β0ln
(
2ln
(
µTΛMS
))
,
non-perturbative large values near Tc
not a large Coulombic coupling
remnants of confinement at T>∼Tc
string breaking and screening difficult to separate
slope at high T well described by perturbation theory
=⇒ At which distance do T-effects set in ?
=⇒ calculation of the screening mass/radius
Heavy quark free energies and screening in lattice QCD Hard Probes 2008, Illa da Toxa, June 10, 2008 – p.8/15
Screening mass - perturbative vs. non-perturbative effects
0
1
2
3
4
5
1 1.5 2 2.5 3 3.5 4
T/Tc
mD/T Nf=2Nf=0
Screening masses obtained from fits to:
F1(r,T)−F1(r = ∞,T) = −4α(T)
3re−mD(T)r
at large distances rT >∼ 1
leading order perturbation theory:
mD(T)
T= A
(
1+Nf
6
)1/2
g(T)
Heavy quark free energies and screening in lattice QCD Hard Probes 2008, Illa da Toxa, June 10, 2008 – p.9/15
Screening mass - perturbative vs. non-perturbative effects
0
1
2
3
4
1 2 3 4T/Tc
Nf=0 Nf=2 Nf=2+1
ααmax
0
1
2
3
4
5
1 1.5 2 2.5 3 3.5 4
T/Tc
mD/T Nf=2+1
Nf=2Nf=0
ANf =2+1 = 1.66(2)
ANf =2 = 1.42(2)
ANf =0 = 1.52(2)
Screening masses obtained from fits to:
F1(r,T)−F1(r = ∞,T) = −4α(T)
3re−mD(T)r
at large distances rT >∼ 1
leading order perturbation theory:
mD(T)
T= A
(
1+Nf
6
)1/2
g(T)
perturbative limit reached very slowly
Heavy quark free energies and screening in lattice QCD Hard Probes 2008, Illa da Toxa, June 10, 2008 – p.9/15
Screening mass - perturbative vs. non-perturbative effects
0
1
2
3
4
5
1 1.5 2 2.5 3 3.5 4
T/Tc
mD/T Nf=2+1
Nf=2Nf=0
0
1
2
3
0 5 10 15 20 25
T/Tc
mD/T
ANf =2+1 = 1.66(2)
ANf =2 = 1.42(2)
ANf =0 = 1.52(2)
ANf =0 = 1.39(2)
Screening masses obtained from fits to:
F1(r,T)−F1(r = ∞,T) = −4α(T)
3re−mD(T)r
at large distances rT >∼ 1
leading order perturbation theory:
mD(T)
T= A
(
1+Nf
6
)1/2
g(T)
perturbative limit reached very slowly
T depencence qualitativelydescribed by perturbation theory
But A≈ 1.4 - 1.5 =⇒ non-perturbative effects
A→ 1 in the (very) high temperature limit
Heavy quark free energies and screening in lattice QCD Hard Probes 2008, Illa da Toxa, June 10, 2008 – p.9/15
Screening mass - density dependence (Nf = 2) [M.Doring et al., Eur.Phys.J. C46 (2006) 179]
0
0.5
1
1.5
2
2.5
3
3.5
4
1 1.5 2 2.5 3 3.5 4
m10/T
T/Tc 0
0.5
1
1.5
2
1 1.5 2 2.5 3 3.5 4
T/Tc
m12/T
leading order perturbation theory:
mD(T,µq)
T= g(T)
√
1+Nf
6+
Nf
2π2
(µq
T
)2
Taylor expansion:
mD(T) = m0(T)+m2(T)(µq
T
)2+O (µ4
q)
m2(T) agrees with perturbation theory for T>∼1.5Tc
non-perturbative effects dominated by gluonic sector
Heavy quark free energies and screening in lattice QCD Hard Probes 2008, Illa da Toxa, June 10, 2008 – p.10/15
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
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0 0.5 1 1.5 2
rT
NQQ T/Tc = 1.002T/Tc = 1.02 T/Tc = 1.07 T/Tc = 1.16 T/Tc = 1.50
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)⟩ .
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