Quarkonia from Lattice and Potential Models

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Quarkonia from Lattice and Potential Models
Ágnes Mócsy
based on work with Péter Petreczky
Characterization of QGP with Heavy Quarks Bad
Honnef Germany, June 25-28 2008
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Confined Matter
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Deconfined Matter
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Deconfined Matter
Screening
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Deconfined Matter
Screening
J/? melting
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Deconfined Matter
Screening
J/? melting
J/? yield suppressed
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Sequential suppression
QGP thermometer
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Screening seen in lattice QCD
Free energy of static Q-Qbar pair F1
RBC-Bielefeld Coll. (2007)
The range of interaction between Q and Qbar is
strongly reduced. Need to quantify what this
means for quarkonia.
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J/? suppression measured
PHENIX, QM 2008

• but interpretation not
  understood
• Hot medium effects - screening?
• Must know dissociation
  temperature, in-medium properties
• Cold nuclear matter effects ?
• Recombination?

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Studies of quarkonium in-medium
Matsui, Satz, PLB 178 (1986) 416 Digal,
Petreczky, Satz, PRD 64 (2001) 094015 Wong PRC 72
(2005) 034906 PRC 76 (2007)
014902 Wong, Crater, PRD 75 (2007)
034505 Mannarelli, Rapp, PRC 72 (2005)
064905 Cabrera, Rapp, Eur Phys J A 31 (2007) 858
PRD 76 (2007)
114506 Alberico et al,PRD 72 (2005) 114011
PRD 75 (2007) 074009
PRD 77 (2008) 017502 Mócsy,
Petreczky, Eur Phys J C 43 (2005) 77
PRD 73 (2006) 074007
PRD 77(2008) 014501
PRL 99 (2007) 211602
Umeda et al Eur. Phys. J C 39S1 (2005) 9 Asakawa,
Hatsuda, PRL 92 (2004) 012001 Datta et al PRD 69
(2004) 094507 Jakovac et al PRD 75 (2007) 014506
Aarts et al Nucl Phys A785 (2007) 198 Iida et al
PRD 74 (2006) 074502 Umeda PRD 75 (2007) 094502
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Studies of quarkonium in-medium
Assume medium effects can be understood in
terms of a temperature-dependent screened
potential
Still inconclusive (discretization effects,
statistical errors)
Contains all info about a given channel. Melting
of a state corresponds to disappearance of a
peak.
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Quarkonium from lattice

• Euclidean-time correlator measured on the lattice
• Spectral functions extracted from correlators
• inverting the integrals using Maximum
  Entropy Method

Kernel cosh?(?-1/2T)/sinh?/2T
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Spectral function from lattice

• Shows no large T-dependence
• Peak has been commonly interpreted as ground
  state
• Uncertainties are significant!
• limited data points
• limited extent in tau
• systematic effects
• prior-dependence

Details cannot be resolved.
Jakovac et al, PRD (2007)
..it is difficult to make any conclusive
statement based on the shape of the spectral
functions Jakovác et al PRD (2007)
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Ratio of correlators
Compare high T correlators to correlators
reconstructed from spectral function at low T
Pseudoscalar
Scalar
Datta et al PRD (2004)
Initial interpretation

T-dependence of correlator ratio determines
dissociation temperatures ?c survives to 2Tc
?c melts at 1.1Tc
Seemingly in agreement with spectral function
interpretation.
2004 J/? melting replaced by J/? survival
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Recently Zero-mode contribution
Low frequency contribution to spectral function
at finite T, scattering states of single heavy
quarks (commonly overlooked)
Quasi-free heavy quarks interacting with the
medium
Bound and unbound Q-Qbar pairs (?gt2mQ)
Gives constant contribution to correlator gtgt
Look at derivatives
Umeda, PRD 75 (2007) 094502
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Ratio of correlator derivatives
Datta, Petreczky, QM 2008, arXiv0805.1174hep-lat

All correlators are flat.

• Flatness is not related to survival no change
  in the derivative scalar up to 3Tc ! ?c
  survives until 3Tc???
• Almost the entire T-dependence comes from
  zero-modes. Understood in terms of quasi-free
  quarks with some effective mass - indication of
  free heavy quarks in the deconfined phase

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From the lattice
Dramatic changes in spectral function are not
reflected in the correlator
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Lessons from Lattice QCD
Small change in the ratio of correlators does not
imply (un)modification of states.
Dominant source of T-dependence of correlators
comes from zero-modes (low energy part of
spectral function). Understood in terms of free
heavy quark gas.
High energy part which carries info about bound
states shows almost no T-dependence until 3Tc in
all channels.
Although spectral functions obtained with MEM do
not show much T-dependence, the details (like
bound state peaks) are not resolved in the
current lattice data.
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Would really the J/? survive in QGP up to 1.5-2Tc
even though strong screening is seen in the
medium?
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Potential model at T0

• Interaction between heavy quark (Qc,b) and its
  antiquark Qbar described by a potential Cornell
  potential
• Non-relativistic treatment
• Solve Schrödinger equation
• - obtain properties, binding energies
• Describes well spectroscopy
• Verified on the lattice
• Derived from QCD.

V(r)
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Potential model at finite T

• Matsui-Satz argument Medium effects on the
  interaction between Q and Qbar described by a
  T-dependent screened potential
• Solve Schrödinger equation
• for non-relativistic Greens function
• - obtain spectral function
• Utilize lattice data

V(r,T)
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Lattice Potential models
Reliable
Not yet reliable
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First lattice-based potential
Free energy of static Q-Qbar pair F1
RBC-Bielefeld Coll. (2007)
Free energy F1? Potential V Contains entropy
F1E1-ST
Digal, Petreczky, Satz, PRD (2001)
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Lattice-based potentials
Most confining potential
Wong potential
T0 potential
Our physical potential
- upper limit
Internal energy
- lower limit
Free energy
r2
r1
Mócsy, Petreczky 2008

• Deeper potentials stronger binding, higher Tdiss
• Open charm (bottom) threshold 2mQVinf(T)
• Explore uncertainty assuming the general features
  of F1
• r lt r1(1/T) vacuum potential
• r gt r2(1/T) exponential screening

Can we constrain them using correlator lattice
data?
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Pseudoscalar correlators
with set of potentials within the allowed ranges
Set of potentials all agree with lattice data
yield indistinguishable results.
No, we cannot determine quarkonium properties
from such comparisons If no agreement found,
model is ruled out We can set upper limits.
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Pseudoscalar spectral function
using most confining potential
?c
Mocsy, Petreczky 08

• Large threshold (rescattering) enhancement even
  at high T
• indication of Q-Qbar correlation
• compensates for melting of states
• keeping correlators flat

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Pseudoscalar spectral function
using most confining potential
?c
Mocsy, Petreczky 08
Ebin 2mqV8(T)-M
State is dissociated when no peak structure is
seen. At which T the peak structure disappears?
Ebin0 ?!
Warning! Widths are not physical - broadening not
included
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Binding energies
Binding energies decrease as T increases. True
for all potential models. Whats the meaning of
a J/? with 0.2 MeV binding? With Ebinlt T a state
is weakly bound and thermal fluctuations can
destroy it
Mocsy, Petreczky, PRL 08
Do not need to reach Ebin0 to dissociate a state.
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Upper limit melting temperatures
Ebin 2mQV8(T)-MQQbar lt T
Estimate dissociation rate due to thermal
activation (thermal width)
Dissociation condition
Kharzeev, McLerran, Satz, PLB (1995)
J/? melts before it bounds.
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Lessons from potential models
Set of potentials (between the lower and upper
limit constrained by lattice free energy data)
yield agreement with lattice data on correlators
(S- and P-wave) Precise quarkonium properties
cannot be determined this way, only upper limit.
Decrease in binding energies with increasing
temperature.
Upper limit potential predicts that all bound
states melt by 1.3Tc, except the upsilon, which
survives until 2Tc. Lattice results are
consistent with quarkonium melting.
Large threshold enhancement above free
propagation even at high T - compensates for
melting of states (flat correlators) -
correlation between Q and Qbar persists
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Implications for RHICollisions
Karsch et al
J/?
?survival?
? survival ?
?

• Consequences
• J/? RAA J/? should melt at SPS and RHIC
• ? suppressed at RHIC (centrality dependent?)
  definitely at LHC
• expect correlations of heavy-quark pairs
• ? DD correlations?
• ? non-statistical recombination?

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Final note

• All of the above discussion is for isotropic
  medium
• Anisotropic plasma Q-Qbar might be more strongly
  bound in an anisotropic medium, especially if it
  is aligned along the anisotropy of the medium
  (beam direction)

Dumitru, Guo, Strickland, PLB 62 (2008) 37
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Final note II
The future is in Effective field theories from
QCD at finite T
Hierarchy of energy scales
NRQCDHTL
T
mD gT
pNRQCDHTL
Brambilla, Ghiglieri, Petreczky, Vairo,
arXiv0804.0993hep-ph
Real and Imaginary part of potential derived
r distance between Q and Qbar Ebin binding
energy
Also Laine et al 2007, Blaizot et al 2007
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The QGP thermometer
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The END