Quarkonium Correlators

1
Quarkonium Correlators
Péter Petreczky

• in collaboration with
• Jakovác, P.P., Petrov, Velytsky, PRD 75 (07)
  014506
• Á. Mócsy, P.P. arXiv.0705.2559 and
  arXiv0706.2183 

2
Introduction
Correlation functions of static charges indicate
strong screening
Strong color screening in QGP leads to reduced
binding and quarkonium melting above
deconfinement Quarkonium suppression (Matsui
and Satz)
Kaczmarek, Karsch, P.P., Zantow,PLB 543 (02) 41
Quarkonium properties at Tgt0 are encoded in the
spectral functions
On the lattice we calculate
constraints on s(?,T)
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Spectral Function from lattice at T0
For the spectral
function is sensitive to lattice cut-off Strong
default model dependence in the continuum region
Jakovác, P.P., Petrov, Velytsky, PRD 75 (07)
014506
4
T-dependence of quarkonium correlators
temperature dependene of
If there is no T-dependence in the spectral
function,
PS
SC
Datta et al, PRD 69 (04) 094507
in agreement with previous calculations
5
Spectral functions from LQCD at Tgt0
ground state peak is shifted, excited states are
not resolved when become small
no temperature dependence in the PS spectral
functions within errors

6
Default model dependence at Tgt0
constant default model
default model from the high enetgy part of the
T0 spectral function

• the shape of the spectral functions depends on
  the default model
• the T-dependence of the spectral functions is
  small for all default models
• no strong evidence for the resonance peak

7
Bottomonium correlators at Tgt0
Jakovác, P.P., Petrov, Velytsky, PRD 75 (07)
014506
PS
SC
?b
?b
the ?b puzzle - same size as the J/? why are
the ?b and J/? correlators so different
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Spectral Function
? bound states/resonances
? continuum above threshold
PDG 06

• ?? s0 perturbative
• calculations

? MJ/? , s0 ladder resummation
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Spectral Function
? bound states/resonances
? continuum above threshold
PDG 06
? MJ/? , s0 nonrelativistic
many gluon exchanges important near threshold
re-summation of ladder diagrams
first in vector channel Strassler,Peskin PRD 91
also Casallderey-Solana,Shuryak,04
S-wave
nonrelativistic Greens function
P-wave
S-wave also Cabrera,Rapp 07
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Spectral Function
? bound states/resonances
? continuum above threshold
PDG 06
? ?? s0 perturbative
? MJ/? , s0 nonrelativistic
smooth matching details do not influence the
result
nonrelativistic Greens function pQCD
Unified treatment bound- and scattering states,
threshold effects
together with relativistic perturbative
continuum
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Constructing the Potential
Constrain the potential by lattice data
what we know
Free energy of static Q-Qbar pair in deconfined
phase
Kaczmarek, Karsch, P.P., Zantow,PLB 543 (02) 41
no temperature effects
strong screening effects
Free energy - contains negative entropy
contribution -
provides a lower limit for the potential V(r,T)
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Constructing the Potential
Constrain the potential by lattice data
Potential assumed to share general features with
the free energy
no temperature effects
strong screening effects
other choices of the potential consistent
with lattice results is possible but give very
similar results for quarkonium correlators
also motivated by Megías,Arriola,Salcedo PRD07
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S-wave Charmonium in Gluon Plasma
Mócsy, Petreczky arXiV.0705.2559hep-ph

• higher excited states gone
• continuum shifted
• 1S becomes a threshold enhancement

?c

• resonance-like structures disappear already by
  1.2Tc
• strong threshold enhancement
• contradicts previous claims

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S-wave Charmonium in Gluon Plasma
Mócsy, Petreczky hep-ph/0705.2559
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

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S-wave Charmonium in Gluon Plasma
N.B. 1st time 2 agreement between model and
lattice correlators for all states at T0 and
TgtTc Unchanged LQCD correlators do not imply
quarkonia survival Lattice data consistent with
charmonium dissolution just above Tc
Mócsy, Petreczky hep-ph/0705.2559
LQCD measures correlators
if the spectral function unchanged across
deconfinement
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Bottomonium
ground state survives deconfinement other states
dissolved medium modification of the 1S peak is
small agreement found with lattice correlators
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Scalar Channel
constant contribution (Gilow) to the correlator
at finite T
so look at the derivative
following Umeda 07
quark number susceptibility
1.5 Tc
Threshold enhancement of spf compensates for
dissolution of states Agreement with lattice data
for scalar charmonium and bottomonium
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Scalar Channel
charm 1.5 Tc
in free theory
bottom 1.5 Tc
gtgt
deconfined
confined
Similar enhancement was observed in the vector
correlators P.P., Teaney, PRD 73 (2006) 014508
behavior explained using ideal gas expression for
susceptibilities seems to indicate deconfined
heavy quarks carry the quark-number at 1.5 Tc
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Conclusions
Lattice data does not necessarily imply survival
of quarkonia all states except 1S bottomonia are
dissolved by 1.2 Tc
Threshold is enhanced over free propagation,
correlations between Q-Qbar may remain strong
in the plasma
The thershold enhancement obtained in potential
model with screening togethe with the transport
contribution to the spectral function can
describe the T-dependence of the quarkonium
correlators calculated on the lattice
The size of the transport contribution to the
correlators seems to be consistent with the
expectations based on free quarks
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The END
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Most binding
Most binding possibility
J/?
?

• Note the reduced binding energy for the J/?
  already at 1.2 Tc!
• Even for maximal binding J/? at 1.6 Tc is just
  a threshold enhancement
• ? survives up to 2Tc with peak position
  unchanged
• Also note strong enhancement in threshold
  region
• Q and Qbar remain correlated

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note on Correlators
LQCD measures correlators
if spectral function unchanged across
deconfinement
?b
lattice data from Jakovác,Petreczky,Petrov,Velytsk
y, PRD 07
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T?0 Spectral Function

• gluon plasma with heavy quarks

results for the ?c
model
lattice
Jakovac,Petreczky,Petrov,Velytsky, PRD 07
ground state peak, excited states, and continuum
identified
reasonably good agreement between model and data
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lQCD Correlators
look directly at the correlator
if spectral function unchanged across
deconfinement
Datta,Karsch,Petreczky,Wetzorke, PRD 04
?c
?c
?c survives to 2Tc ?c melts at 1.1Tc
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T0 Continuum in Quenched QCD
G does not depend on the parameters good
agreement between model and data
relativistic continuum seen on lattice
this contradicts statements made in the recent
literature
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charm
bottom

• With this potential
• 1S charmonium peaks found unmodified at 1.2Tc
• binding energy (Ebindings0-M) is small so
  dissociation by thermal fluctuations is likely
• all states, except 1S bottomonium, are gone by
  1.5Tc

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Internal Energy as Potential
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Screened Cornell