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Ágnes Mócsy
July 16th-19th, 2007 McGill University, Montréal, Canada
July 2007 Early Time Dynamics Montreal
AM
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MotivationMotivation
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In this talkIn this talk
• revisit how we got to “J/ survives up to 2Tc”
• from the same data get very different conclusion
• revisit how we got to “J/ survives up to 2Tc”
• from the same data get very different conclusion
offering new direction in which models can be modifiedoffering new direction in which models can be modified
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a more detailed motivation
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IntroductionIntroduction
Debye screening in the
deconfined matter leads
to quarkonium
dissociation when
rDebye rQuarkonium
confined
deconfinedJ/
r
V(r)
€
V r( ) = −4
3
α s
rexp −mDr( )€
V r( ) = −α
r+ rσ
The Matsui-Satz argument:
Quarkonium properties at high T interesting
• proposed signal of deconfinement Matsui,Satz, PLB 86
• matter thermometer ?!
Karsch,Mehr,Satz, ZPhysC 88
• bound states in deconfined medium ?! Shuryak,Zahed PRD 04
Quarkonium properties at high T interesting
• proposed signal of deconfinement Matsui,Satz, PLB 86
• matter thermometer ?!
Karsch,Mehr,Satz, ZPhysC 88
• bound states in deconfined medium ?! Shuryak,Zahed PRD 04
quarkonium discussed in terms of potential model
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IntroductionIntroduction
Quarkonium properties at high T interesting
• proposed signal of deconfinement Matsui,Satz, PLB 86
• matter thermometer ?!
Karsch,Mehr,Satz, ZPhysC 88
• bound states in deconfined medium ?! Shuryak,Zahed PRD 04
Quarkonium properties at high T interesting
• proposed signal of deconfinement Matsui,Satz, PLB 86
• matter thermometer ?!
Karsch,Mehr,Satz, ZPhysC 88
• bound states in deconfined medium ?! Shuryak,Zahed PRD 04
Static quark-antiquark free energyRBC-Bielefeld Collaboration 2007
Nf=2+1 Screening seen in lattice QCDScreening seen in lattice QCD
see talk by Péter Petreczky
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IntroductionIntroduction
Quarkonium properties at high T interesting
• proposed signal of deconfinement Matsui,Satz, PLB 86
• matter thermometer ?!
Karsch,Mehr,Satz, ZPhysC 88
• bound states in deconfined medium ?! Shuryak,Zahed PRD 04
Quarkonium properties at high T interesting
• proposed signal of deconfinement Matsui,Satz, PLB 86
• matter thermometer ?!
Karsch,Mehr,Satz, ZPhysC 88
• bound states in deconfined medium ?! Shuryak,Zahed PRD 04
Hierarchy in binding energies
T
0.9 fm 0.7 fm 0.4 fm 0.2 fm
J/(1S)
c(1P)’(2S)
b(1P)
b’(2P) (1S)’’(3S)
Quarkonia melting as QGP thermometerQuarkonia melting as QGP thermometer
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IntroductionIntroduction
Need to calculate quarkonium spectral function
• quarkonium well defined at T=0, but can broaden at finite T
• spectral function contains all information about a given channel unified treatment of bound states, threshold, continuum
• can be related to experiments
Need to calculate quarkonium spectral function
• quarkonium well defined at T=0, but can broaden at finite T
• spectral function contains all information about a given channel unified treatment of bound states, threshold, continuum
• can be related to experiments
Quarkonium properties at high T interesting
• proposed signal of deconfinement Matsui,Satz, PLB 86
• matter thermometer ?!
Karsch,Mehr,Satz, ZPhysC 88
• bound states in deconfined medium ?! Shuryak,Zahed PRD 04
Quarkonium properties at high T interesting
• proposed signal of deconfinement Matsui,Satz, PLB 86
• matter thermometer ?!
Karsch,Mehr,Satz, ZPhysC 88
• bound states in deconfined medium ?! Shuryak,Zahed PRD 04
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““J/J/ survival” in LQCD survival” in LQCD
Asakawa, Hatsuda, PRL 04
Datta et al PRD 04
Jakovác et al, PRD 07 Aarts et al hep-lat/0705.2198
Lattice Spectral Functions
Conclusion: 1S ground state survives above
TC
see talk by Péter Petreczky
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““J/J/ survival” in LQCD survival” in LQCD
Asakawa, Hatsuda, PRL 04
Datta et al PRD 04
Jakovác et al, PRD 07 Aarts et al hep-lat/0705.2198
Lattice Spectral Functionssee talk by Péter Petreczky
• large uncertainties• not directly measured• extracted from correlators through MEM
• large uncertainties• not directly measured• extracted from correlators through MEM
€
G τ ,T( ) = σ ω,T( )K τ ,ω,T( )dω∫
€
G τ ,T( ) = σ ω,T( )K τ ,ω,T( )dω∫
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““J/J/ survival” in LQCD survival” in LQCD
Temperature dependence of correlators
€
G τ ,T( ) = σ ω,T( )K τ ,ω,T( )dω∫
€
Grec τ ,T( ) = σ ω,T = 0( )K τ ,ω,T( )dω∫
c
Jakovác et al, PRD 07
Conclusions drawn from analysis of lattice data were
• c melts by 1.1 Tc
based on modification of G/Grec and spectral functions
from MEM
Conclusions drawn from analysis of lattice data were
• c melts by 1.1 Tc
based on modification of G/Grec and spectral functions
from MEM
G/Grec 1 implies modified spectral
function
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““J/J/ survival” in LQCD survival” in LQCD
Conclusions drawn from analysis of lattice data were
• c melts by 1.1 Tc
• J/ and c survive up to 1.5-2Tc “J/ survival”based on (un)modification of G/Grec and spectral functions from MEM
Conclusions drawn from analysis of lattice data were
• c melts by 1.1 Tc
• J/ and c survive up to 1.5-2Tc “J/ survival”based on (un)modification of G/Grec and spectral functions from MEM
c
Jakovác et al, PRD 07Jakovác et al, PRD 07
€
G τ ,T( ) = σ ω,T( )K τ ,ω,T( )dω∫
€
Grec τ ,T( ) = σ ω,T = 0( )K τ ,ω,T( )dω∫
c
Temperature dependence of correlatorsG/Grec = 1 implied unchanged spectral function?
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““J/J/ survival” in Potential survival” in Potential ModelsModels
Shuryak,Zahed PRD 04Wong, PRC 05Alberico et al PRD 05Cabrera, Rapp 06 Alberico et al PRD 07Wong,Crater PRD 07
series of potential model studies
Conclusions
• states survive
• dissociation temperatures quoted
• agreement with lattice is claimed
Conclusions
• states survive
• dissociation temperatures quoted
• agreement with lattice is claimed
Wong,Crater, PRD 07
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Strong screening of Q and antiQ interaction seen on lattice yet some quarkonium states still survive unaffected?
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€
c
Mócsy,Petreczky EJPC 05Mócsy,Petreczky PRD 06
model lattice
€
c
First Indication of First Indication of InconsistencyInconsistency
simplified spectral function: discrete bound states + perturbative continuum
T = 0T Tc
alsoCabrera, Rapp 06
It is not enough to have “surviving state”
Correlators calculated in this approach do not agree with lattice
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What is the source of these
inconsistencies?
validity of potential models?
finding the right potential?
relevance of screening for quarkonia
dissociation?
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our recent approach to determine quarkonium properties
Á. Mócsy, P. Petreczky 0705.2559 [hep-ph] 0706.2183 [hep-ph]
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Spectral Function Spectral Function
bound states/resonances & continuum above threshold
(GeV)
€
−1
m∇ 2 + V (
r r ) + E
⎡ ⎣ ⎢
⎤ ⎦ ⎥G
NR (r r ,
r r ',E) = δ 3(
r r −
r r ')
nonrelativistic Green’s function
~ MJ/ , s0 nonrelativistic
€
σ E( ) =2Nc
πImGNR r
r ,r r ',E( ) r
r =r r '= 0
€
σ E( ) =2Nc
π
1
m2
r ∇ ⋅
r ∇'ImGNR r
r ,r r ',E( ) r
r =r r '= 0
S-wave
P-wave
medium effects - important near threshold
PDG 06
re-sum ladder diagrams first in vector channel Strassler,Peskin PRD 91 also Casalderrey-Solana,Shuryak 04
S-wave also Cabrera,Rapp 07
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Spectral FunctionSpectral Function
€
σ pert ≅ω2 3
8π1+
11
3πα s
⎛
⎝ ⎜
⎞
⎠ ⎟
+
s0
perturbative
bound states/resonances & continuum above threshold
(GeV)
€
σ ∝1
πImGNR
€
−1
m∇ 2 + V (
r r ) + E
⎡ ⎣ ⎢
⎤ ⎦ ⎥G
NR (r r ,
r r ',E) = δ 3(
r r −
r r ')
nonrelativistic Green’s function
~ MJ/ , s0 nonrelativistic
PDG 06PDG 06
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Spectral FunctionSpectral Function
Unified treatment: bound states, threshold effects together with relativistic perturbative continuumUnified treatment: bound states, threshold effects together with relativistic perturbative continuum
bound states/resonances & continuum above threshold
(GeV)
+
s0
perturbative ~ MJ/ , s0 nonrelativistic
smooth matchingdetails do not influence the result
€
−1
m∇ 2 + V (
r r ) + E
⎡ ⎣ ⎢
⎤ ⎦ ⎥G
NR (r r ,
r r ',E) = δ 3(
r r −
r r ')
nonrelativistic Green’s function + pQCDnonrelativistic Green’s function + pQCD
PDG 06
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no temperature effects
Constructing the Potential Constructing the Potential at T>Tat T>Tcc
Potential assumed to share general features with the free energy
€
V∞ T( ) = rmed T( )σ > F1∞(T)
€
V r,T( ) = −α
r+ rσ
also motivated by Megías,Arriola,Salcedo PRD07
€
r < rmed
€
r > rmed
€
V r,T( ) = V∞ T( ) −α 1 T( )
re−μ T( )r
strong screening effects
Free energy - contains negative entropy contribution - provides a lower limit for the potential
Phenomenological potential constrained by lattice data Phenomenological potential constrained by lattice data
subtract entropy
€
F1 = E1 − TS
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quarkonia in a gluon plasma (quenched QCD)
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S-wave Charmonium in Gluon S-wave Charmonium in Gluon PlasmaPlasma
• resonance-like structures disappear already by 1.2Tc
• strong threshold enhancement
• contradicts previous claims
• resonance-like structures disappear already by 1.2Tc
• strong threshold enhancement
• contradicts previous claims
higher excited states gonecontinuum shifted1S becomes a threshold enhancement
lattice
Jakovác,Petreczky,Petrov,Velytsky, PRD07
c
Mócsy, Petreczky 0705.2559 [hep-ph]
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S-wave Charmonium in Gluon S-wave Charmonium in Gluon PlasmaPlasma
• resonance-like structures disappear already by 1.2Tc
• strong threshold enhancement above free case indication of correlation
• height of bump in lattice and model are similar
• resonance-like structures disappear already by 1.2Tc
• strong threshold enhancement above free case indication of correlation
• height of bump in lattice and model are similar
details cannot be resolveddetails cannot be resolved
Mócsy, Petreczky 0705.2559 [hep-ph]
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S-wave Charmonium in Gluon S-wave Charmonium in Gluon PlasmaPlasma
Mócsy, Petreczky 0705.2559 [hep-ph]
€
G τ ,T( ) = σ ω,T( )K τ ,ω,T( )dω∫
€
Grec τ ,T( ) = dωσ ω,T = 0( )∫ K ω,τ ,T( )
spectral function unchanged across deconfinement
€
G(τ ,T)
Grec (τ ,T)=1
LQCD measures correlators LQCD measures correlators
N.B.: 1st time2% agreement between model and lattice correlators for all states at T=0 and T>Tc
Unchanged LQCD correlators do not imply quarkonia survival: Lattice data consistent with charmonium dissolution just above Tc
N.B.: 1st time2% agreement between model and lattice correlators for all states at T=0 and T>Tc
Unchanged LQCD correlators do not imply quarkonia survival: Lattice data consistent with charmonium dissolution just above Tc
or… integrated area under spectral function unchanged
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P statesP states
b
“the b puzzle” b same size as the J/, so why are the b and J/ correlators so different ?
“the b puzzle” b same size as the J/, so why are the b and J/ correlators so different ?
Jakovác et al, PRD 07
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Agreement for P-wave as wellAgreement for P-wave as well
so look at the derivative following Umeda 07
constant contribution in the correlator at finite T
quark number susceptibili
ty1.5 Tc
Threshold enhancement in spf compensates for dissolution of states
Agreement with lattice data for scalar charmonium and bottomonium
Threshold enhancement in spf compensates for dissolution of states
Agreement with lattice data for scalar charmonium and bottomonium
cb
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P-waveP-wave
>>deconfined confined
in free theory
behavior explained using ideal gas expression for susceptibilities:
indicates deconfined heavy quarks carry the quark-number at 1.5 Tc
behavior explained using ideal gas expression for susceptibilities:
indicates deconfined heavy quarks carry the quark-number at 1.5 Tc
charm1.5 Tc
bottom1.5 Tc
b “puzzle” resolved
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quarkonia in a quark-gluon plasma (full QCD)
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S-wave Quarkonium in QGPS-wave Quarkonium in QGP
• J/, c at 1.1Tc is just a threshold enhancement
• (1S) survives up to ~2Tc with unchanged peak position, but reduced binding energy
• Strong enhancement in threshold region - Q and antiQ remain correlated
• J/, c at 1.1Tc is just a threshold enhancement
• (1S) survives up to ~2Tc with unchanged peak position, but reduced binding energy
• Strong enhancement in threshold region - Q and antiQ remain correlated
€
Ebin = s0 − M
c
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upper limits on dissociation temperatures
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Most Binding PotentialMost Binding Potential
need strongest confining effects = largest possible rmed
Find upper limit for binding Find upper limit for binding
rmed = distance where exponential screening
sets in
NOTE: uncertainty in potential - have a choice for rmed or V∞
our choices physically motivated all yield agreement with correlator data
distance where deviation from T=0 potential starts
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Binding Energy Upper LimitsBinding Energy Upper Limits
Upsilon remains strongly bound up to 1.6Tc
Other states are weakly bound above 1.2Tc
Upsilon remains strongly bound up to 1.6Tc
Other states are weakly bound above 1.2Tc
€
Ebin < Tweak binding
When binding energy drops below T• state is weakly bound• thermal fluctuations can destroy the resonance
€
Ebin > Tstrong binding
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for weak binding Ebin<T
for strong binding Ebin>T
Thermal Dissociation Widths Thermal Dissociation Widths
Rate of escape into the continuum due to thermal activation = thermal width related to the binding energy
€
Ebin = s0 − MQQ
€
=LT( )
2m
3πexp −
Ebin
T
⎛
⎝ ⎜
⎞
⎠ ⎟
€
=4
L
T
2πm
€
L ≈ rmed − rQQ
Kharzeev, McLerran, Satz PLB 95
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Can Quarkonia Survive?
Upper bounds on dissociation temperatures
condition: thermal width > 2x binding energy
Upper bounds on dissociation temperatures
condition: thermal width > 2x binding energy
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ConclusionsConclusions
Quarkonium spectral functions can be calculated within a potential model with screening - description of quarkonium dissociation at high T
Lattice correlators have been explained correctly for the 1st time
Unchanged correlators do not imply quarkonia survival: lattice data consistent with charmonium dissolution just above Tc
Contrary to previous statements, we find that all states except and b are dissolved by at most by ~1.3Tc
Threshold enhancement found: spectral function enhanced over free propagation =>> correlations between Q-antiQ may remain strong
OutlookOutlookImplications for heavy-ion phenomenology need to be considered
see also Laine,hep-ph/0704.1720Brau,Buisseret,hep-ph/0706.4012