Heavy quark energy loss in a dynamical QCD medium Magdalena Djordjevic The Ohio State University
Lattice QCD results on heavy quark potentials bound …€¦ · 0.2 0.4 0.6 0.8 1 1.2 ... -...
Transcript of Lattice QCD results on heavy quark potentials bound …€¦ · 0.2 0.4 0.6 0.8 1 1.2 ... -...
Lattice QCD results on heavy quark potentialsand
bound states in the quark gluon plasma
Olaf Kaczmarek Felix Zantow
Universität Bielefeld
April 5, 2006
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.1/27
”Machines” for QCD - Experiments
RHIC@BNL LHC@CERN
STARdetector
=⇒
only indirect signalsfrom collision region
⇓theoretical input needed
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.2/27
”Machines” for QCD - lattice theory
QCDOC apeNEXT
Installation in Bielefeld
1999/2001 144 Gflops APEmille
2005/2006 5 Tflops apeNEXT
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.3/27
Charmonium suppression
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0 2 4 6 8 10L (fm)
Mea
sure
d / E
xpec
ted
J/ψ / DY4.2-7.0Pb-Pb
ψ , / DY4.2-7.0Pb-Pb
S-U
S-U
p-A
p-A
observed charmonium yields at SPS
nuclear absorption length L
using Bjorken formula (τ = 1 f m) + lattice EOS:
ε =dET/dη
τ AT
L [ f m] ε [GeV/ f m3] T/Tc
4 ∼ 1 ∼ 1.0
8 ∼ 3 ∼ 1.16
10 ∼ 4 ∼ 1.25
suppression patterns in a narrow temperature regime
detailed (lattice) equation of state needed
detailed knowledge on heavy quark bound states needed
What are the processes of charmonium formation/suppression?
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.4/27
Charmonium suppression
0.25
0.50
0.75
1.00
1 2 3 4 5
In−In, SPS
Au−Au, RHIC, |y| < 0.35
Pb−Pb, SPS
Au−Au, RHIC, |y|=[1.2,2.2]
ψS(J/ )
ε (GeV/fm )3
[F. Karsch,D. Kharzeev,H. Satz,hep-ph/0512239]
observed charmonium yields at SPS
nuclear absorption length L
using Bjorken formula (τ = 1 f m) + lattice EOS:
ε =dET/dη
τ AT
L [ f m] ε [GeV/ f m3] T/Tc
4 ∼ 1 ∼ 1.0
8 ∼ 3 ∼ 1.16
10 ∼ 4 ∼ 1.25
suppression patterns in a narrow temperature regime
detailed (lattice) equation of state needed
detailed knowledge on heavy quark bound states needed
What are the processes of charmonium formation/suppression?
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.4/27
Motivation - Heavy quark bound states above deconfinement
Quarkonium suppression as a probe for thermal properties of hot and dense matter [Matsui and Satz]
- heavy quark potential gets screened
- screening radius related to parton density
rD ∼ 1
g√
n/T
- at high T screening radius smaller than size of a quarkonium state
Typical length scales of heavy quark bound states: 1/ΛQCD ∼ 1 fm
- screening has to be strong enough to modify short distance behaviour
- detailed analysis of ”heavy quark potentials”
- temperature and r dependence
- screening properties above deconfinement
- What is the correct effective potential at finite temperature ?
F1(r,T) = U1(r,T)−T S1(r,T)
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.5/27
Heavy quark bound states above deconfinement
Strong interactions in the deconfined phase T>∼Tc
Possibility of heavy quark bound states?
Charmonium (χc,J/ψ) as thermometer above Tc
Suppression patterns of charmonium/bottomonium
=⇒ 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
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.6/27
The lattice set-up
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, ...]
)
−FQQ̄(r ,T)
TQQ̄ = 1, 8, av
Lattice data used in our analysis:
Nf = 0:323×4,8,16-lattices( Symanzik )
O. Kaczmarek,F. Karsch,P. Petreczky,F.Z. (2002, 2004)
Nf = 2:163×4-lattices( Symanzik, p4-stagg. )
mπ/mρ ≃ 0.7 (m/T = 0.4)
O. Kaczmarek, F.Z. (2005),O. Kaczmarek et al. (2003)
Nf = 3:163×4-lattices
mπ/mρ ≃ 0.4
P. Petreczky,K. Petrov (2004)
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.7/27
The lattice set-up
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, ...]
)
−FQQ̄(r ,T)
TQQ̄ = 1, 8, av
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
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.7/27
Heavy quark free energy
-500
0
500
1000
0 0.5 1 1.5 2 2.5 3
r [fm]
F1 [MeV]
0.76Tc0.81Tc0.90Tc0.96Tc1.00Tc1.02Tc1.07Tc1.23Tc1.50Tc1.98Tc4.01Tc
Renormalization of F(r,T)
bymatching with T=0 potential
e−F1(r,T)/T =(
Zr (g2))2Nτ 〈Tr (LxL
†y)〉
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.8/27
Heavy quark free energy
-500
0
500
1000
0 0.5 1 1.5 2 2.5 3
r [fm]
F1 [MeV]
0.76Tc0.81Tc0.90Tc0.96Tc1.00Tc1.02Tc1.07Tc1.23Tc1.50Tc1.98Tc4.01Tc
-1
-0.5
0
0.5
1
1.5
0.2 0.4 0.6 0.8 1 1.2 1.4
r σ1/2
F(r,T)/σ1/2
T/Tc0.961.001.071.161.231.501.98
T-independentr ≪ 1/
√σ
F(r,T) ∼ g2(r)/r
Renormalization of F(r,T)
bymatching with T=0 potential
e−F1(r,T)/T =(
Zr (g2))2Nτ 〈Tr (LxL
†y)〉
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.8/27
Heavy quark free energy
-500
0
500
1000
0 0.5 1 1.5 2 2.5 3
r [fm]
F1 [MeV]
0.76Tc0.81Tc0.90Tc0.96Tc1.00Tc1.02Tc1.07Tc1.23Tc1.50Tc1.98Tc4.01Tc
0
500
1000
1500
0 1 2 3 4T/Tc
F∞ [MeV] Nf=0Nf=2Nf=3
T-independentr ≪ 1/
√σ
F(r,T) ∼ g2(r)/r
String breakingT < Tc
F(r√
σ ≫ 1,T) < ∞
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.8/27
Heavy quark free energy
-500
0
500
1000
0 0.5 1 1.5 2 2.5 3
r [fm]
F1 [MeV]
0.76Tc0.81Tc0.90Tc0.96Tc1.00Tc1.02Tc1.07Tc1.23Tc1.50Tc1.98Tc4.01Tc
0
500
1000
1500
0 1 2 3 4T/Tc
F∞ [MeV] Nf=0Nf=2Nf=3
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
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.8/27
Heavy quark free energy
-500
0
500
1000
0 0.5 1 1.5 2 2.5 3
r [fm]
F1 [MeV]
0.76Tc0.81Tc0.90Tc0.96Tc1.00Tc1.02Tc1.07Tc1.23Tc1.50Tc1.98Tc4.01Tc
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
Complex r and T dependence
Small vs. large distance behaviorRunning coupling vs. screeningWhere do temperature effects set in?
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.8/27
Temperature depending running coupling
0
0.5
1
1.5
2
2.5
0.1 0.5 1
αqq(r,T)
r [fm]
T/Tc0.810.900.961.021.071.231.501.984.01
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
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.9/27
Temperature depending running coupling
0
0.5
1
1.5
2
2.5
0.1 0.5 1
αqq(r,T)
r [fm]
T/Tc0.810.900.961.021.071.231.501.984.01
non-perturbative confining part for r>∼0.4 fm
αqq(r) ≃ 3/4r2σ
present below and just above Tc
temperature effects set in at smaller r with increasing T
maximum due to screening
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
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.9/27
Temperature depending running coupling
0
0.5
1
1.5
2
2.5
0.1 0.5 1
αqq(r,T)
r [fm]
T/Tc0.810.900.961.021.071.231.501.984.01
non-perturbative confining part for r>∼0.4 fm
αqq(r) ≃ 3/4r2σ
present below and just above 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
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.9/27
Heavy quark bound states aboveTc?
0
0.5
1
1.5
0 1 2 3 4T/Tc
r [fm]
J/ψ
ψ’χc
rmedrD
bound states above deconfinement?
first estimate:
mean charge radii of charmonium statescompared to screening radius: V(rmed) ≡ F∞(T)
thermal modifications on ψ′ and χc already at Tc
J/ψ may survive above deconfinement
(a) (c)(b)
cloud2r r
〈rn〉 ≡ 1N
Z
d3r r n F1(r ,T)
High T: Using a screened Coulomb form〈r〉 ≃ 2/mD
T = 0: Using parameterization of V(r) at T = 0: 〈r〉T=0 ≃ 0.74 − 0.85 fm
0.01
0.1
1
0 5 10 15 20 25
rD [fm]
T/Tc
<r>rmed
rentropy2/mD
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.10/27
Heavy quark bound states aboveTc?
0
0.5
1
1.5
0 1 2 3 4T/Tc
r [fm]
J/ψ
ψ’χc
rmedrD
bound states above deconfinement?
first estimate:
mean charge radii of charmonium statescompared to screening radius: V(rmed) ≡ F∞(T)
thermal modifications on ψ′ and χc already at Tc
J/ψ may survive above deconfinement
Better estimates:
effective potentials in Schrödinger Equation
direct calculation using correlation functions
Better estimates:
Potential models, effective potential Ve f f(r,T)
Maximum entropy method → spectral function
But: Free energies vs. internal energies F(r,T) = U(r,T)−TS(r,T)
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.10/27
Free energy vs. Entropy at large separations
0
500
1000
1500
0 1 2 3 4T/Tc
F∞ [MeV] Nf=0Nf=2Nf=3
Free energies not only determinedby potential energy
F∞ = U∞ −TS∞
Entropy contributions play a role at finite T
S∞ = − ∂F∞∂T
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.11/27
Free energy vs. Entropy at large separations
0
1000
2000
3000
4000
0 1 2 3 4
U∞ [MeV]
T/Tc
S∞ = −∂F∞
∂T
U∞ = −T2 ∂F∞/T∂T
0
1000
2000
3000
4000
0 1 2 3
TS∞ [MeV]
T/Tc
Nf=0Nf=2Nf=3
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 fi-nite temperature energies is related toscreeningrather than to the temperaturedependence of masses of correspondingheavy-light mesons!
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.11/27
r-dependence of internal energies
0
500
1000
0 0.5 1 1.5
TS1 [MeV]
r [fm]
(b)
(a) (c)(b)
cloud2r r
The large distance behavior of the fi-nite temperature energies is related toscreeningrather than to the temperaturedependence of masses of correspondingheavy-light mesons!
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
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.12/27
r-dependence of internal energies
0
1000
2000
3000
4000
0 0.5 1 1.5 2 2.5 3
U1 [MeV]
r [fm]
0.88Tc0.93Tc0.98Tc
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
0
500
1000
1500
0 0.5 1 1.5 2
U1 [MeV]
r [fm]
1.09Tc1.13Tc1.19Tc1.29Tc1.43Tc1.57Tc1.89Tc
=⇒ Implications on heavy quark bound states?
=⇒ What is the correct Ve f f(r,T)?
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.12/27
Heavy quark bound states
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)
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.13/27
Estimates on bound states from Schrödinger equation
Schrödinger equation for heavy quarks:
[
2mf +1
mf∆2 +Ve f f(r,T)
]
Φ fi = E f
i (T)Φ fi , f = charm,bottom
T-dependent color singlet heavy quark potential mimics in-medium modifications of qq̄ interaction
reduction to 2-particle interaction clearly too simple, in particular close to Tc
recent analysis:
using Ve f f = F1: S.Digal, P.Petreczky, H.Satz, Phys. Lett. B514 (2001)57using Ve f f = V1: C.-Y. Wong, hep-ph/0408020using Ve f f = V1: W.M. Alberico, A. Beraudo, A. De Pace, A. Molinari, hep-ph/0507084
state J/ψ χc ψ′ ϒ χb ϒ′ χ′b ϒ′′
Eis[GeV] 0.64 0.20 0.005 1.10 0.67 0.54 0.31 0.20
r0[ f m] 0.50 0.72 0.90 0.28 0.44 0.56 0.68 0.78
Td/Tc 1.1 0.74 0.1-0.2 2.31 1.13 1.1 0.83 0.74
Td/Tc ∼ 2.1 ∼ 1.2 ∼ 1.2 ∼ 5.0 ∼ 1.95 ∼ 1.65 - -
Td/Tc 1.75-1.95 1.13-1.15 1.10-1.11 4.4-4.7 1.5-1.6 1.4-1.5 ∼ 1.2 ∼ 1.2
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.14/27
Correlation functions of hadronic states
1
10
100
1000
0 0.2 0.4 0.6 0.8 1
τ T
G(τ,T)/T3
0.6 Tc
pseudo-scalarscalar
1
10
100
1000
0 0.2 0.4 0.6 0.8 1
τ T
G(τ,T)/T3
1.5 Tc
pseudo-scalarscalar
Direct lattice calculations on bound states
Thermal correlation functions:
GH(τ, r,T) = 〈JH(τ, r)J†H(0,0)〉 with JH = q̄(τ, r)ΓHq(τ, r)
Example using light quarks, scalar (δ) and pseudo-scalar (π):
splitting below Tc due to chiral and axial U(1) symmetry breaking
symmetry restauration at high temperatures
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.15/27
Spectral functions of charmonium states
1
2
3
4
0.1 0.2 0.3 0.4 0.5
G(τ)/Grecon(τ)
τ[fm]
0.75Tc
AX+1.0 SC
1.12Tc1.5Tc
0.8
1
1.2
1.4
0.1 0.2 0.3 0.4
G(τ)/Grecon(τ)
τ[fm]
0.9Tc
PS+0.2 VC
1.5Tc2.25Tc
3Tc
Where do thermal effects on charmonium states set in?
χc,1
χc,0
ηc
J/ψ
strong effects already near Tc no effect in ηc up to 1.5Tc
modifications on J/ψ only of order 10% at 1.5Tc
bound states above Tc possible?
=⇒ reconstruction of spectral functions
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.16/27
Spectral functions of charmonium states
spectral representation of correlators =⇒ in-medium properties of hadrons
spectral representation of Euclidean correlation functions:
GβH(τ,~r) =
Z ∞
0dω
Z
d3~p(2π)3 σH(ω,~p,T) ei~p~r cosh(ω(τ−1/2T))
sinh(ω/2T)
calculate the most probablespectral function
Bayesian data analysis, e.g. Maximum Entropy Method (MEM)
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.16/27
Spectral functions of charmonium states
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20 25 30
ω[GeV]
σ(ω)/ω2
0.9Tc1.5Tc
0
0.2
0.4
0.6
0.8
0 5 10 15 20 25 30
ω[GeV]
σ(ω)/ω2
2.25Tc3Tc
ω [GeV]
0 5 10 15 20 25 30
T = 0.78Tc
T = 1.38Tc
T = 1.62Tc
0
0.5
1.5
2
2.5
0
0.5
1
1.5
2
1
T = 1.87Tc
T = 2.33Tc
J/ψ spectral function
M. Asakawa, T. Hatsuda,Phys.Rev.Lett.92 (2004) 012001
S. Datta et al.,Phys.Rev.D69 (2004) 094507
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20 25 30
ω[GeV]
σ(ω)/ω2
0.9Tc1.5Tc
0
0.2
0.4
0.6
0.8
0 5 10 15 20 25 30
ω[GeV]
σ(ω)/ω2
2.25Tc3Tc
ω [GeV]
0 5 10 15 20 25 30
T = 0.78Tc
T = 1.38Tc
T = 1.62Tc
0
0.5
1.5
2
2.5
0
0.5
1
1.5
2
1
T = 1.87Tc
T = 2.33Tc
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.16/27
Spectral functions of charmonium states
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20 25 30
ω[GeV]
σ(ω)/ω2
0.9Tc1.5Tc
0
0.2
0.4
0.6
0.8
0 5 10 15 20 25 30
ω[GeV]
σ(ω)/ω2
2.25Tc3Tc
ω [GeV]
0 5 10 15 20 25 30
T = 0.78Tc
T = 1.38Tc
T = 1.62Tc
0
0.5
1.5
2
2.5
0
0.5
1
1.5
2
1
T = 1.87Tc
T = 2.33Tc
J/ψ spectral function
M. Asakawa, T. Hatsuda,Phys.Rev.Lett.92 (2004) 012001
S. Datta et al.,Phys.Rev.D69 (2004) 094507
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20 25 30
ω[GeV]
σ(ω)/ω2
0.9Tc1.5Tc
0
0.2
0.4
0.6
0.8
0 5 10 15 20 25 30
ω[GeV]
σ(ω)/ω2
2.25Tc3Tc
ω [GeV]
0 5 10 15 20 25 30
T = 0.78Tc
T = 1.38Tc
T = 1.62Tc
0
0.5
1.5
2
2.5
0
0.5
1
1.5
2
1
T = 1.87Tc
T = 2.33Tc
J/ψ dissociates for 1.6Tc<∼T<∼1.9Tc
rather abrupt disappearance of J/ψJ/ψ gradually disappears for T>∼1.5Tc
strength reduced by 25% at T = 2.25Tc
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.16/27
Heavy quark bound states above deconfinement - Diquarks [OK,K. Hübner, O. Vogt]
Coloured bound states speculated just above Tc (SQGP)
- Is the interaction strong enough to support diquarks?
- Potential models for coloured bound states
- Diquark free and internal energies
Colour antitriplet (anti-symmetric) or color sextet (symmetric) state:
3⊗3 = 3̄⊕6.
C3qq(R,T) =
32〈Tr L(0)Tr L(R)〉− 1
2〈Tr L(0)L(R)〉
C6qq(R,T) =
34〈Tr L(0)Tr L(R)〉+ 1
4〈Tr L(0)L(R)〉
F3,6qq (R,T) = −T lnC3,6
qq (R,T)
[E.V. Shuryak,I. Zahed (2004/05)]
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.17/27
Z(3) symmetry and volume scaling
0.010
0.100
0.80 1.00 1.20 1.40 1.60 1.80
<|Tr L|>
T/Tc
Nτ=4
Nσ16243248
- Polyakov loop and diquark correlation functions not Z(3) symmetric
- In the confined phase all non Z(3) symmetric observables vanish
- Z(3) rotation such that ReL > 0
- At β = 0 the Polyakov loop scales like
〈|L|〉 = 〈| 1V ∑
~x
Tr L~x|〉 ∼1√V
.
- We assume this scaling behaviour for L and C3,6qq (r,T) for T < Tc
C3qq(r,T) ∝
(
1Nσ
)3ν(r,T)
= V−ν(r,T).
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.18/27
Z(3) symmetry and volume scaling
- Polyakov loop and diquark correlation functions not Z(3) symmetric
- In the confined phase all non Z(3) symmetric observables vanish
- Z(3) rotation such that ReL > 0
- At β = 0 the Polyakov loop scales like
〈|L|〉 = 〈| 1V ∑
~x
Tr L~x|〉 ∼1√V
.
- We assume this scaling behaviour for L and C3,6qq (r,T) for T < Tc
C3qq(r,T) ∝
(
1Nσ
)3ν(r,T)
= V−ν(r,T).
3.0
4.0
5.0
6.0
7.0
8.0
9.0
8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0
-ln C3qq
-ln(1/N3σ)
RT0.360.490.620.901.031.30
-ln <|TrL|> 0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.90 0.92 0.94 0.96 0.98 1.00 1.02
ν
T/Tc
RT0.360.490.620.901.03
<|TrL|>
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.18/27
Z(3) symmetry and volume scaling
- Polyakov loop and diquark correlation functions not Z(3) symmetric
- In the confined phase all non Z(3) symmetric observables vanish
- Z(3) rotation such that ReL > 0
- At β = 0 the Polyakov loop scales like
〈|L|〉 = 〈| 1V ∑
~x
Tr L~x|〉 ∼1√V
.
- We assume this scaling behaviour for L and C3,6qq (r,T) for T < Tc
C3qq(r,T) ∝
(
1Nσ
)3ν(r,T)
= V−ν(r,T).
0.055
0.060
0.065
0.070
0.075
0.080
0.085
0.090
0.095
0.100
0.0e+00 5.0e-05 1.0e-04 1.5e-04 2.0e-04 2.5e-04 3.0e-04 3.5e-04
C3qq
1/V
RT0.360.490.620.901.031.302.00
c<|TrL|>
- Below Tc the diquark free energies diverge
- Above Tc the Z(3) symmetry is spontanously broken
- In full QCD the Z(3) symmetry is explicitly broken at all T
- All observables are finite in the thermodynamic limit
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.18/27
Diquark free energies -qqvs.qq̄ in the deconfined phase
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5 1.0 1.5 2.0 2.5 3.0
∆F1q—q(R,T)/T
RT
2∆F3qq(R,T)/T T/Tc
1.0131.0311.1491.6822.9955.000
normalized free energy
∆Fi(r,T) := Fi(r,T)−Fi(r → ∞,T)
is a renormalization invariant quantity.
perturbative relation between diquark and quark-antiquark free energies
∆F3qq(r,T) ≃ ∆
12
F1qq̄(r,T)
good approximation above Tc.
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.19/27
Diquark free energies -qqvs.qq̄ in the deconfined phase
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5 1.0 1.5 2.0 2.5 3.0
∆F1q—q(R,T)/T
RT
2∆F3qq(R,T)/T T/Tc
1.0131.0311.1491.6822.9955.000
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
0.5 1 1.5 2 2.5
F1q—q(R,T)/σ1/2
Rσ1/2
F3qq(R,T)/σ1/2
T/Tc1.0051.0311.1491.6822.9955.000
normalized free energy
∆Fi(r,T) := Fi(r,T)−Fi(r → ∞,T)
is a renormalization invariant quantity.
perturbative relation between diquark and quark-antiquark free energies
∆F3qq(r,T) ≃ ∆
12
F1qq̄(r,T)
good approximation above Tc.
temperature dependence for all separations
=⇒ entropy contributions play a role for all r.
same asymptotic value for qq and qq̄
=⇒ quarks in both systems are screened
independently by the medium
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.19/27
3-quark free energies [ K. Hubner, OK, O. Vogt., hep-lat/0408031 ]
-8
-6
-4
-2
0
2
0 0.1 0.2 0.3 0.4 0.5 0.6
Rσ(1/2)
F(R,T)/σ(1/2)
6Tc
Tqqq=0average
singletoctet
decuplet
Different color channels: 3⊗3⊗3 = 10⊕8′⊕8⊕1
exp(
−F1qqq/T
)
=16
⟨
27Tr L1Tr L2Tr L3−9Tr L1Tr (L2L3)
−9Tr L2Tr (L1L3)−9Tr L3Tr (L1L2)
+3Tr (L1L2L3)+3Tr (L1L3L2)⟩
exp(
−F8qqq/T
)
=124
⟨
27Tr L1Tr L2Tr L3 +9Tr L1Tr (L2L3)
−9Tr L3Tr (L1L2)−3Tr (L1L3L2)⟩
exp(
−F8′qqq/T
)
=124
⟨
27Tr L1Tr L2Tr L3 +9Tr L3Tr (L1L2)
−9Tr L1Tr (L2L3)−3Tr (L1L2L3)⟩
exp(
−F10qqq/T
)
=160
⟨
27Tr L1Tr L2Tr L3 +9Tr L1Tr (L2L3)
+9Tr L2Tr (L1L3)+9Tr L3Tr (L1L2)
+3Tr (L1L2L3)+3Tr (L1L3L2)⟩
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.20/27
3-quark free energies [ K. Hubner, OK, O. Vogt., hep-lat/0408031 ]
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
F1qqq(R,T)/σ1/2
Rσ1/2
3(F3—
qq(R,T)-Fq(T))/σ1/2
T/Tc1.0051.0311.1491.6842.8586.000
-8
-6
-4
-2
0
2
0 0.1 0.2 0.3 0.4 0.5 0.6
Rσ(1/2)
F(R,T)/σ(1/2)
6Tc
Tqqq=0average
singletoctet
decuplet
- Renormalization of 3-quark Polyakov loop correlation functions
Fqqq(r,T) =(
ZR(g2))3Nτ 〈 f (Lx,Ly,Lz)〉
- Renormalization of n-point functions with the same ZR(g2)
- Comparison with qq free energies
Fqqq(r) ≃ ∑〈qq〉
Fqq(r,T)−3Fq(T) ≃ 32
Fqq̄(r,T) with Fq(T) = 1/2Fqq̄(r → ∞)
- Baryonic interaction dominated by two-particle interactions
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.20/27
3-quark free energies [ K. Hubner, OK, O. Vogt., hep-lat/0408031 ]
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
F1qqq(R,T)/σ1/2
Rσ1/2
3(F3—
qq(R,T)-Fq(T))/σ1/2
T/Tc1.0051.0311.1491.6842.8586.000
-3
-2
-1
0
1
2
3
0.5 1 1.5 2 2.5 3 3.5 4 4.5
F1qqq(R,T)/σ1/2
Rσ1/2
3(F3—
qq(R,T)-Fq(T))/σ1/2
T/Tc0.880.910.971.011.031.071.161.371.66
QuenchedFull QCD
- Renormalization of 3-quark Polyakov loop correlation functions
Fqqq(r,T) =(
ZR(g2))3Nτ 〈 f (Lx,Ly,Lz)〉
- Renormalization of n-point functions with the same ZR(g2)
- Comparison with qq free energies
Fqqq(r) ≃ ∑〈qq〉
Fqq(r,T)−3Fq(T) ≃ 32
Fqq̄(r,T) with Fq(T) = 1/2Fqq̄(r → ∞)
- Baryonic interaction dominated by two-particle interactions
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.20/27
qq and qqq entropy and internal energies
The r-dependence of static q̄q, qq and qqq interactions are related by Casimir factors
The relations for entropy and internal energy follow directly (Fq(T) = 1/2Fqq̄(r → ∞)):
F3qq(r,T) ≃ 1
2F1
q̄q(r,T)+Fq(T)
S3qq(r,T) ≃ 1
2S1
q̄q(r,T)+Sq(T)
U3qq(r,T) ≃ 1
2U1
q̄q(r,T)+Uq(T)
and for the baryonic system:
F1qqq(r,T) ≃ 3
2F1
q̄q(r,T)
S1qqq(r,T) ≃ 3
2S1
q̄q(r,T)
U1qqq(r,T) ≃ 3
2U1
q̄q(r,T)
Potential models based on this relations possible
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.21/27
SQGP - Strongly Coupled QGP ??? J. Liao, E.V. Shuryak, hep-ph/0508035
1 1.25 1.5 1.75 2 2.25 2.5T
�
T c
0�2�4�6Eb
�T c
� � � � � � � � � � � �� � � � �� � � � � � ��
� � � � � � �� meson bound states� diquark bound states baryon bound states 3 �gluon bound states
channel rep. charge factor no. of states
gg 1 9/4 9s
gg 8 9/8 9s∗16
qg+ q̄g 3 9/8 3c ∗6s∗2∗Nf
qg+ q̄g 6 3/8 6c ∗6s∗2∗Nf
q̄q 1 1 8s∗N2f
qq+ q̄q̄ 3 1/2 4s∗3c ∗2∗N2f
Bound states of quasi-particles above Tc?(here m∗ = 800 MeV)?
Is the interaction in the different channels strongenough to support bound states above Tc?
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.22/27
SQGP - Strongly Coupled QGP ??? J. Liao, E.V. Shuryak, hep-ph/0508035
1 1.25 1.5 1.75 2 2.25 2.5T
�
T c
0 2 4 6
Eb
�T c
� � � � � � � � � � � �� � � � �� � � � � � ��
� � � � � � �� meson bound states� diquark bound states� baryon bound states� 3 �gluon bound states
(a)(b)
(c)
(d)
T<Tc
T=Tc
Tc<T<1.5Tc
T > 3Tc
Polymer Chains are speculative
channel rep. charge factor no. of states
gg 1 9/4 9s
gg 8 9/8 9s∗16
qg+ q̄g 3 9/8 3c ∗6s∗2∗Nf
qg+ q̄g 6 3/8 6c ∗6s∗2∗Nf
q̄q 1 1 8s∗N2f
qq+ q̄q̄ 3 1/2 4s∗3c ∗2∗N2f
Bound states of quasi-particles above Tc?(here m∗ = 800 MeV)?
Is the interaction in the different channels strongenough to support bound states above Tc?
Binding energy Eb of the order of T already at Tc!
Coloured bound states and
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.22/27
What are the constituents of matter at high temperature? [S.Ejiri,F.Karsch,K.Redlich]
0.6 0.8 1 1.2 1.4 1.6 1.8 20
5
10
15
R4,2
T/T0
SB
q
HRG
0.6 0.8 1 1.2 1.4 1.6 1.8 20
0.5
1
1.5
2
R4,2
T/T0
SB
Q
HRG
Recent discussion of quark number and charge fluctuations inthe QGP
“Specific ratios of cummulants of (net) quark number and charge can characterize the
particular degrees of freedom which are relevant in the low and high temperature phase”
dx2 ≡
1VT3
∂2 lnZ∂(µx/T)2
∣
∣
∣
∣
µu=µd=0
dx4 ≡
1VT3
∂4 lnZ∂(µx/T)4
∣
∣
∣
∣
µu=µd=0
quark number
Rq4,2 =
dq4
dq2
charge
RQ4,2 =
dQ4
dQ2
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.23/27
What are the constituents of matter at high temperature? [S.Ejiri,F.Karsch,K.Redlich]
0.6 0.8 1 1.2 1.4 1.6 1.8 20
5
10
15
R4,2
T/T0
SB
q
HRG
0.6 0.8 1 1.2 1.4 1.6 1.8 20
0.5
1
1.5
2
R4,2
T/T0
SB
Q
HRG
Recent discussion of quark number and charge fluctuations inthe QGP
“Specific ratios of cummulants of (net) quark number and charge can characterize the
particular degrees of freedom which are relevant in the low and high temperature phase”
dx2 ≡
1VT3
∂2 lnZ∂(µx/T)2
∣
∣
∣
∣
µu=µd=0
dx4 ≡
1VT3
∂4 lnZ∂(µx/T)4
∣
∣
∣
∣
µu=µd=0
quark number
Rq4,2 =
dq4
dq2
charge
RQ4,2 =
dQ4
dQ2
Already for T > 1.5Tc quark number and charge are predominantly carried bystates with quantum numbers of quarks
See also V. Koch, A. Majumder, J. Randrup (2005)Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.23/27
Renormalized Polyakov loop
0
500
1000
1500
0 1 2 3 4T/Tc
F∞ [MeV] Nf=0Nf=2Nf=3
-500
0
500
1000
0 0.5 1 1.5 2 2.5 3
r [fm]
F1 [MeV]
0.76Tc0.81Tc0.90Tc0.96Tc1.00Tc1.02Tc1.07Tc1.23Tc1.50Tc1.98Tc4.01Tc
Lren = exp
(
−F(r = ∞,T)
2T
)
Defined by long distance behaviour of F(r,T).
Renormalized by renormalization of F(r,T)
at small distances.
Lren =(
ZR(g2))Nt Llattice
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.24/27
Renormalized Polyakov loop
0
0.5
1
0.5 1 1.5 2 2.5 3 3.5 4
Lren
T/Tc
2F-QCD: Nτ=4SU(3): Nτ=4
Nτ=8
0
500
1000
1500
0 1 2 3 4T/Tc
F∞ [MeV] Nf=0Nf=2Nf=3
-500
0
500
1000
0 0.5 1 1.5 2 2.5 3
r [fm]
F1 [MeV]
0.76Tc0.81Tc0.90Tc0.96Tc1.00Tc1.02Tc1.07Tc1.23Tc1.50Tc1.98Tc4.01Tc
Lren = exp
(
−F(r = ∞,T)
2T
)
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.24/27
Renormalized Polyakov loop
0
0.5
1
0.5 1 1.5 2 2.5 3 3.5 4
Lren
T/Tc
2F-QCD: Nτ=4SU(3): Nτ=4
Nτ=8
Lren = exp
(
−F(r = ∞,T)
2T
)
Quenched QCD:
Lren = 0 for T < Tc.
Finite gap at Tc
Full QCD:
Lren finite for all T.
Strong increase near Tc.
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.24/27
Renormalized Polyakov loop
0
0.5
1
0.5 1 1.5 2 2.5 3 3.5 4
Lren
T/Tc
2F-QCD: Nτ=4SU(3): Nτ=4
Nτ=8
Lren = exp
(
−F(r = ∞,T)
2T
)
Quenched QCD:
Lren = 0 for T < Tc.
Finite gap at Tc
Full QCD:
Lren finite for all T.
Strong increase near Tc.
Renormalized Polyakov loop- well defined in quenched and full QCD- non-zero for finite quark mass- strong increase near Tc
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.24/27
Renormalized Polyakov loop
0
0.5
1
1.5
0 5 10 15 20 25
Lren
T/Tc
Nτ=4Nτ=8
Lren = exp
(
−F(r = ∞,T)
2T
)
perturbation theory:Lren(T) approaches
high temperature limitfrom above
Lren(T) ≃ 1+23
mD(T)
Tα(T)
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.24/27
Polyakov loops in higher representations [S. Gupta,K. Hübner,OK]
use character property of direct product rep: χp⊗q(g) = χp(g)χq(g)
Z(3) symmetry: LD → eitφLD
triality (Z(3) charge): t ≡ p−q mod 3
adjoint link variable[
UD=8]
i j := 12Tr
[
UD=3λi(UD=3)†λ j]
D (p,q) t C2(r) dD = CD/CF LD(x)
3 (1,0) 1 4/3 1 L3
6 (2,0) 2 10/3 5/2 L23−L∗
3
8 (1,1) 0 3 9/4 |L3|2−1
10 (3,0) 0 6 9/2 L3L6−L8
15 (2,1) 1 16/3 4 L∗3L6−L3
15′ (4,0) 1 28/3 7 L3L10−L15
24 (3,1) 2 25/3 25/4 L∗3L10−L6
27 (2,2) 0 8 6 |L6|2−L8−1
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.25/27
Polyakov loops in higher representations [S. Gupta,K. Hübner,OK]
perturbation theory:
FD(r,T) = −CDαs(r)
rfor rΛQCD ≪ 1
renormalization of the Polykov loop:
〈LrenD 〉 =
(
ZD(g2))NτdD 〈Lbare
D 〉,
i.e. the renormalization constants are related by Casimir [G.Bali, Phys.Rev.D62 (2000) 114503]
-5
-4
-3
-2
-1
0
1
2
3
0.5 1 1.5 2 2.5
Fsing8 (r,T)/σ1/2
rσ1/2
T/Tcd8 V3(T=0)
1.0131.0311.1491.6823.000
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.25/27
Polyakov loops in higher representations [S. Gupta,K. Hübner,OK]
perturbation theory:
FD(r,T) = −CDαs(r)
rfor rΛQCD ≪ 1
renormalization of the Polykov loop:
〈LrenD 〉 =
(
ZD(g2))NτdD 〈Lbare
D 〉,
i.e. the renormalization constants are related by Casimir [G.Bali, Phys.Rev.D62 (2000) 114503]
1.1
1.2
1.3
1.4
1.5
1.6
0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
ZD(g2)
g2
r3 r6 r8
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.25/27
Polyakov loops in higher representations [S. Gupta,K. Hübner,OK]
Does Casimir scaling hold beyond leading order?
Singlet free energies of static quarks in representation D=3,8:
FsingD (r,T)
T= − ln
(
〈T̃rLD(x)L†D(y)〉
)
∣
∣
∣
∣
∣
GF
with LD made up of UD=3 and[
UD=8]
i j := 12Tr
[
UD=3λi(UD=3)†λ j]
-1.6
-1.4
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
∆FsingD (r,T)/C2(D)/T
D=8 D=3
rTc
T/Tc1.0311.1491.6823.0005.000
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.25/27
Polyakov loops in higher representations [S. Gupta,K. Hübner,OK]
Does Casimir scaling hold beyond leading order? Yes !
Even the Polyakov loops are related by Casimir
〈Ld〉 ≃ 〈Lr 〉dD ,
with dD = C2(D)/C2(3).
This relation holds for bare and renormalized Polykov loops:
0
0.1
0.2
0.3
0.4
0.5
0.6
5 10 15 20 25
LDbare
T/Tc
D=3 D=6 D=8 D=10D=15
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.25/27
Polyakov loops in higher representations [S. Gupta,K. Hübner,OK]
Does Casimir scaling hold beyond leading order? Yes !
Even the Polyakov loops are related by Casimir
〈Ld〉 ≃ 〈Lr 〉dD ,
with dD = C2(D)/C2(3).
This relation holds for bare and renormalized Polykov loops:
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1 2 3 4 5 6 7 8 9 10
Lren
T/Tc
L3 L6 L8 L10L15
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.25/27
Conclusions
- Heavy quark free and internal energies
Complex r and T dependence
Running coupling shows remnants of confinenement above Tc
Entropy contributions play a role at finite T
Separation of entropy and internal energy contributions possible
Potential energy larger than free energy
- Charmonium in the quark gluon plasma
First estimates from potential models
Higher dissociation temperature using V1
(directly produced) J/ψ exist well above Tc
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.26/27
Outlook
- Heavy quark free and internal energies
Smaller quark masses
Smaller lattice spacing to analyze small r dependence
Better understanding of the different contributions
- Charmonium in the quark gluon plasma
What is the correct Ve f f in potential models
Full QCD calculations of correlation/spectral functions
Relevant processes for charmonium production/dissociation ?
Lattice QCD results on heavy quark potentials and bound states in the quark gluon plasma Exploration of Hadron Structureand Spectroscopy, Seattle, April, 2006 – p.27/27