Ágnes Mócsy - RBRC
Zimányi 75 Memorial Workshop, Budapest 07 03 07
Quarkonium Properties Above
Deconfinement
Zimányi 75
MEMORIAL WORKSHOP ON
HADRONIC and QUARK MATTER
July 2 - 4 (Mon - Wed), 2007
Budapest, Hungary
Ágnes Mócsy
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Ágnes Mócsy - RBRC
Zimányi 75 Memorial Workshop, Budapest 07 03 07
Motivation
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Ágnes Mócsy - RBRC
Zimányi 75 Memorial Workshop, Budapest 07 03 07
• revisit how we got to “J/psi survives up to 2Tc”
• from same data get very different conclusion
offering new direction in which models can be modified
Motivation
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Ágnes Mócsy - RBRC
Zimányi 75 Memorial Workshop, Budapest 07 03 07
a more detailed motivation
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Ágnes Mócsy - RBRC
Zimányi 75 Memorial Workshop, Budapest 07 03 07
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
V(r)
confined
V r  
J/

r
The Matsui-Satz argument:
 r
deconfined


V r  
r
4 s
expmD r
3 r
Debye screening in the
deconfined matter leads to
quarkonium dissociation when
rDebye rQuarkonium

Introduction
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Ágnes Mócsy - RBRC
Zimányi 75 Memorial Workshop, Budapest 07 03 07
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
RBC-Bielefeld Collaboration 2007
Static quark-antiquark free energy
Nf=2+1
Screening seen in lattice QCD
Introduction
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Ágnes Mócsy - RBRC
Zimányi 75 Memorial Workshop, Budapest 07 03 07
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
’(2S)
0.9 fm
c(1P)
J/(1S)
’’(3S) b’(2P)
b(1P)
(1S)
0.4 fm
0.2 fm
0.7 fm
T
Quarkonia as QGP thermometer
Introduction
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Ágnes Mócsy - RBRC
Zimányi 75 Memorial Workshop, Budapest 07 03 07
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
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
Introduction
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Ágnes Mócsy - RBRC
Zimányi 75 Memorial Workshop, Budapest 07 03 07
Spectral Functions
Asakawa, Hatsuda, PRL 04
Jakovác et al, PRD 07
Datta et al PRD 04
extracted from
Correlators
c
G,T 
Grec ,T 
 ,TK,,Td
Aarts et al hep-lat/0705.2198
  ,T  0K,,Td

c

Jakovác et al, PRD 07
Jakovác et al, PRD 07
Conclusions drawn from analysis of lattice data were
• J/ and c survive up to ~1.5-2Tc  “J/ survival”
• c melts by 1.1 Tc
based on (un)modification of G/Grec and spectral functions from MEM
“J/ survival” in LQCD
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Ágnes Mócsy - RBRC
Zimányi 75 Memorial Workshop, Budapest 07 03 07
series of potential model studies
Shuryak,Zahed PRD 04
Wong, PRC 05
Alberico et al PRD 05
Cabrera, Rapp 06
Alberico et al PRD 07
Wong,Crater PRD 07
Conclusions
• states survive
• dissociation temperatures quoted
• agreement with lattice is claimed
Wong,Crater, PRD 07
“J/ survival” in Potential Models
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Ágnes Mócsy - RBRC
Zimányi 75 Memorial Workshop, Budapest 07 03 07
simplified spectral function: discrete bound states + perturbative continuum
Mócsy,Petreczky EJPC 05
and PRD 06
model
T Tc
T=0
c
lattice
c
it is not enough to have “surviving state”
correlators calculated
in thisapproach do not agree with lattice

What is the source of these inconsistencies?
validity of potential models?
finding the right potential?
relevance of screening for quarkonia dissociation?
First Indication of Inconsistency
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Ágnes Mócsy - RBRC
Zimányi 75 Memorial Workshop, Budapest 07 03 07
our recent approach to determine quarkonium properties
Á. Mócsy, P. Petreczky 0705.2559 [hep-ph]
0706.2183 [hep-ph]
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Ágnes Mócsy - RBRC
Zimányi 75 Memorial Workshop, Budapest 07 03 07
 bound states/resonances
&
 continuum above threshold
PDG 06
 (GeV)
 ~ MJ/ , s0 nonrelativistic
medium effects - important near threshold
re-sum ladder diagrams
first in vector channel Strassler,Peskin PRD 91
also Casalderrey-Solana,Shuryak 04
 E  
2Nc
 E  
2Nc 1
 ' ImGNR r,r ', E r  r ' 0
2
 m

ImGNR r,r ', E r  r ' 0
S-wave
P-wave
 1 2
 NR



V
(r
)

E
G (r ,r ', E)   3 (r  r ')


 m

nonrelativistic Green’s function
S-wave also Cabrera,Rapp 07

Spectral Function
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Ágnes Mócsy - RBRC
Zimányi 75 Memorial Workshop, Budapest 07 03 07
 bound states/resonances
&
 continuum above threshold
PDG 06
06
PDG
 (GeV)
 ~ MJ/ , s0 nonrelativistic
  s0 perturbative
+
 pert   2
nonrelativistic Green’s function
 1 2
 NR



V
(r
)

E
G (r ,r ', E)   3 (r  r ')


 m

1
  ImG



NR
3  11 
 s 
1
8  3 

Spectral Function
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Ágnes Mócsy - RBRC

Zimányi 75 Memorial Workshop, Budapest 07 03 07
 bound states/resonances
&
 continuum above threshold
PDG 06
 (GeV)
 ~ MJ/ , s0 nonrelativistic
  s0 perturbative
smooth matching
details do not influence the result
+
 1 2
 NR



V
(r
)

E
G (r ,r ', E)   3 (r  r ')


 m

nonrelativistic Green’s function + pQCD
Unified treatment: bound states, threshold effects
together with relativistic perturbative continuum
Spectral Function
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
Ágnes Mócsy - RBRC
Zimányi 75 Memorial Workshop, Budapest 07 03 07
T>0 potential is unknown
use a phenomenological potential constrained by lattice data
Free energy - contains negative entropy contribution see talk by Péter Petreczky
- provides a lower limit for the potential
Potential assumed to share general features with the free energy
r  rmed
no temperature effects

V r,T     r
r  rmed
strong screening effects
 T 
V r,T   V T   1 e  T r
r
r

 subtract entropy
V T  rmed T   F1 (T)
also motivated by
Megías,Arriola,Salcedo PRD07
Constructing the Potential at T>Tc

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Ágnes Mócsy - RBRC
Zimányi 75 Memorial Workshop, Budapest 07 03 07
quarkonia in a gluon plasma (quenched QCD)
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Ágnes Mócsy - RBRC
Zimányi 75 Memorial Workshop, Budapest 07 03 07
Mócsy, Petre czky 0705.2559 [hep-ph]
c
higher excited states gone
continuum shifted
1S becomes a threshold
enhancement
lattice
Jakovác,Petreczky,
Petrov,Velytsky, PRD07
• resonance-like structures disappear already by 1.2Tc
• strong threshold enhancement
• contradicts previous claims
S-wave Charmonium in Gluon Plasma
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Ágnes Mócsy - RBRC
Zimányi 75 Memorial Workshop, Budapest 07 03 07
Mócsy, Petre czky 0705.2559 [hep-ph]
details cannot be resolved
• 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
S-wave Charmonium in Gluon Plasma
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Ágnes Mócsy - RBRC
Zimányi 75 Memorial Workshop, Budapest 07 03 07
Mócsy, Petre czky 0705.2559 [hep-ph]
N.B.: 1st time
2% 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
LQCD measures correlators
Grec ,T   d ,T  0K,,T
G,T    ,TK,,Td

G( ,T)
1
Grec ( ,T)
spectral function unchanged across deconfinement
or… integrated area under spectral function unchanged

S-wave Charmonium in Gluon Plasma
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Ágnes Mócsy - RBRC
Zimányi 75 Memorial Workshop, Budapest 07 03 07
Jakovác et al, PRD 07
b
“the b puzzle”
b same size as the J/, so
why are the b and J/ correlators so different ?
P states
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Ágnes Mócsy - RBRC
Zimányi 75 Memorial Workshop, Budapest 07 03 07
constant contribution in the correlator at finite T
so look at the derivative
following Umeda 07
1.5 Tc
quark number
susceptibility
c
b
Threshold enhancement of spf compensates for dissolution of states
Agreement with lattice data for scalar charmonium and bottomonium
Agreement for P-wave as well
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Ágnes Mócsy - RBRC
Zimányi 75 Memorial Workshop, Budapest 07 03 07
charm
1.5 Tc
in free theory
bottom
1.5 Tc
deconfined
>>
confined
 b “puzzle” resolved
behavior explained using ideal gas expression for susceptibilities:
indicates deconfined heavy quarks carry the quark-number at 1.5 Tc
P-wave
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Ágnes Mócsy - RBRC
Zimányi 75 Memorial Workshop, Budapest 07 03 07
quarkonia in a quark-gluon plasma (full QCD)
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Ágnes Mócsy - RBRC
Zimányi 75 Memorial Workshop, Budapest 07 03 07
c

E bin  s0  M
• 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
S-wave Quarkonium in QGP
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Ágnes Mócsy - RBRC
Zimányi 75 Memorial Workshop, Budapest 07 03 07
upper limits on dissociation temperatures
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Ágnes Mócsy - RBRC
Zimányi 75 Memorial Workshop, Budapest 07 03 07
Find upper limit for binding
need strongest confining effects = largest possible rmed
distance where deviation
from T=0 potential starts
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
Most Binding Potential
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Ágnes Mócsy - RBRC
Zimányi 75 Memorial Workshop, Budapest 07 03 07
When binding energy drops below T
• state is weakly bound
• thermal fluctuations can destroy the resonance
weak binding
E bin  T
strong binding
E bin  T


Upsilon remains strongly bound up to 1.6Tc
Other states are weakly bound above 1.2Tc
Binding Energy Upper Limits
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Ágnes Mócsy - RBRC
Zimányi 75 Memorial Workshop, Budapest 07 03 07
Rate of escape into the continuum due to thermal activation
= thermal width   related to the binding energy
E bin  s0  MQQ
Kharzeev, McLerran, Satz PLB 95
for weak binding Ebin<T


4
T
L 2m
L  rmed  rQQ


for strong binding Ebin>T
LT m exp E bin 

2
3


 T 


Thermal Dissociation Widths
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Ágnes Mócsy - RBRC
Zimányi 75 Memorial Workshop, Budapest 07 03 07
Upper bounds on dissociation temperatures
condition: thermal width > 2x binding energy
Can Quarkonia Survive?
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Ágnes Mócsy - RBRC
Zimányi 75 Memorial Workshop, Budapest 07 03 07
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 1.3 Tc
Threshold enhancement found: spectral function enhanced over free
propagation =>> correlations between Q-antiQ may remain strong
Outlook
Implications for heavy-ion phenomenology need to be considered
Conclusions
31
Ágnes Mócsy - RBRC
Zimányi 75 Memorial Workshop, Budapest 07 03 07
****The END****
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