Predictions for Quarkonium Properties Above Deconfinement

1
Predictions for Quarkonium Properties Above
Deconfinement
Ágnes Mócsy RIKEN-BNL

• in collaboration with Péter Petreczky
• ref hep-ph/0705.2559 and in preparation

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Introduction

• Quarkonium properties at high T interesting
• proposed signal of deconfinement, matter
  thermometer,
• possibility of bound states in deconfined medium

• Need to calculate quarkonia spectral function
• quarkonium well defined at T0, but can
  significantly broaden at finite temperature
• contains all information about a given channel
  unified treatment of bound states, threshold
  effects, and the continuum
• can be related to experiments

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Spectral Function
? bound states/resonances
? continuum above threshold
PDG 06
? MJ/? , s0 nonrelativistic
medium effects - important near threshold
re-sum 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
? MJ/? , s0 nonrelativistic
? ?? s0 perturbative
nonrelativistic Greens function
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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,Zantow,Petreczky, PRD 04
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
also motivated by Megías,Arriola,Salcedo PRD07
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S-wave Charmonium in Gluon Plasma
Mócsy, Petreczky hep-ph/0705.2559

• 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
spectral function unchanged across
deconfinement
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S-wave Quarkonium in QGP
J/?
?

• J/? at 1.1Tc is just a threshold enhancement
• ? survives up to 2Tc with unchanged peak
  position,
• but
  reduced binding energy
• Strong enhancement in threshold region - Q and
  Qbar remain correlated

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Most Binding Potential
Find upper limit for binding
need strongest confining effects largest
possible rmed
rmed distance where exponential screening
sets in
NOTE uncertainty in potential - have a choice
for rmed or V8, our choices
physically motivated all yield
agreement with correlator data
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Binding Energy Upper Limits
strong binding
weak binding

• When binding energy drops below T
• state is weakly bound
• thermal fluctuations can destroy the resonance
• Upsilon remains strongly bound up to 1.6Tc
• Other states are weakly bound above 1.2Tc

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Thermal Dissociation Widths ?
Rate of escape into the continuum due to thermal
activation ? ? related to the binding energy
weak binding
for weak binding EbinltT for strong binding
EbingtT Kharzeev, McLerran, Satz PLB 95
?
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Conclusions
lattice data does not necessarily imply survival
of quarkonia all states except ? and ?b are
dissolved by 1.2 Tc
Dissociation condition thermal width gt 2 binding
energy upper limits
Upsilon suppressed at LHC but less suppresed at
RHIC
Threshold is enhanced over free propagation gtgt
correlations between Q-Qbar may remain strong
regeneration from primordially correlated, not
independent Q-Qbar
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The END
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Lattice etac
most recent results
Jakovác,Petreczky,Petrov,Velytsky, PRD 07
pseudoscalar spf unchanged up to 1.5Tc within
errors, but details cannot be resolved
?c
?c
if spectral function unchanged across
deconfinement
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Lattice Spectral Function
most recent results
pseudoscalar spf unchanged up to 1.5T within
errors, but details cannot be resolved
Jakovac,Petreczky,Petrov,Velytsky, PRD 07
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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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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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lQCD J/? survival
Spectral function at finite T from Lattice
quenched QCD
Euclidean correlation function
Asakawa, Hatsuda, PRL 04
current knows about the channels
spectral decomposition
MEM
Peak still present at J/? mass at 1.62Tc! Gone
only at higher T
Note no T0 data for comparison
other features identified with lattice artifacts
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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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lQCD Bottomonium
Jakovac,Petreczky,Petrov,Velytsky, PRD 07
?b
?b
the ?b puzzle - same size as the J/? why are
the ?b and J/? correlators so different
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Full LQCD
recent full LQCD results show similar behavior
S-waves survive up to 2Tc
P-waves melt away below 1.2Tc
Aarts,Allton,Oktay,Peardon,Skullerud,
hep-lat/0705.2198
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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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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
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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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
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Wong Potential
? admixture of free and internal energies
Wong 05

• apparent agreement
• but

1.) reports 1S charmonium dissociation at 1.62Tc
binding
energy 0.2MeV
undetectable
2.) assumes only ground state contributes to
correlation function
contrary to lattice findings
3.) neglects contribution from the wave fct at
the origin,
which decreases when screened
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hybrid potentials in quenched QCD
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internal energy as potential

• big jump in the critical region
• huge increase in mass

? no agreement w/ lattice
Cabrera, Rapp hep-ph/0611134
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etab