ATHIC 2010T. Umeda (Hiroshima Univ.)1 Heavy Quarkonium in QGP on the Lattice Takashi Umeda 3rd Asian...

ATHIC 2010 T. Umeda (Hiroshima Univ.) 1

Heavy Quarkonium in QGP on Heavy Quarkonium in QGP on the Latticethe Lattice

Takashi UmedaTakashi Umeda

3rd Asian Triangle Heavy-Ion Conference3rd Asian Triangle Heavy-Ion ConferenceCCNU, Wuhan, China, October 18-20, 2010CCNU, Wuhan, China, October 18-20, 2010

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Contents of this talk

IntroductionIntroduction

-- J/-- J/ψψ suppression suppression

-- Lattice studies with Maximum Entropy Method (MEM)-- Lattice studies with Maximum Entropy Method (MEM)

-- Sequential J/ψ dissociation -- Sequential J/ψ dissociation

Zero mode contributionsZero mode contributions

Other approaches to study charmonium dissociationOther approaches to study charmonium dissociation

SummarySummary

from the Phenix group web-site

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J/ψ suppression as a signal of QGP

Static quark free energyStatic quark free energyWHOT-QCD Collab. (’07)WHOT-QCD Collab. (’07)

NNff=2+1 QCD result=2+1 QCD result

Confined phase:Confined phase: linear raising potentiallinear raising potential bound state of c – cbound state of c – c

De-confined phase:De-confined phase: Debye screeningDebye screening scattering state of c - cscattering state of c - c ( J/ψ dissociation )( J/ψ dissociation )

T.Hashimoto et al.(’86), T.Hashimoto et al.(’86), Matsui&Satz(’86)Matsui&Satz(’86)

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Maximum Entropy Method (MEM)

J/ c Charmonium spectral func.Charmonium spectral func.Asakawa & Hatsuda (’04)Asakawa & Hatsuda (’04)

Quench QCD (NQuench QCD (Nff=0)=0)

Maximum Entropy MethodMaximum Entropy Method

J/ψ & ηJ/ψ & ηcc survive till 1.62 Tsurvive till 1.62 Tcc

dissociate at 1.87Tdissociate at 1.87Tcc

Charmonium spectral func.Charmonium spectral func.Asakawa & Hatsuda (’04)Asakawa & Hatsuda (’04)

Quench QCD (NQuench QCD (Nff=0)=0)

Maximum Entropy MethodMaximum Entropy Method

J/ψ & ηJ/ψ & ηcc survive till 1.62 Tsurvive till 1.62 Tcc

dissociate at 1.87Tdissociate at 1.87Tcc

Charmonium correlator on the lattice Spectral function (SPF)

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Results on P-wave states Results on P-wave states A.Jakovac et al. (’07)A.Jakovac et al. (’07)

Drastic change in Drastic change in χχcc correlator above T correlator above Tcc

MEM results indicateMEM results indicate

χχcc dissociation just above Tdissociation just above Tcc (?) (?)

P-wave states (χc) in charmonium

Grecon is a charmonium correlator constructed with SPF at T=0. No change in SPF at T>0

leads to G/Grecon = 1

““Default model” is Default model” is input information for MEM analysisinput information for MEM analysisDefault model dependence is Default model dependence is one of systematic errors one of systematic errors

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Possible J/ψ suppression scenario

E705 Collab.(’93) E705 Collab.(’93)

When When χχcc or/and ψ’ dissociate just above T or/and ψ’ dissociate just above Tcc, ,

part of J/part of J/ψψ suppression occurs suppression occurs even if J/even if J/ψψ survives in QGP. survives in QGP.

Sequential charmonium dissociationSequential charmonium dissociationF. Karsch et al. (’05)F. Karsch et al. (’05)

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-- Sequential J/ψ suppression -- Sequential J/ψ suppression



SummarySummary


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exp(-mqt) x exp(-mq(Lt-t)) = exp(-mqLt)

mq is single quark energyLt = 1/T = temporal extent

Zero mode in meson correlators

T. Umeda (’07)T. Umeda (’07)

“An Introduction to Quantum Field Theory” Michael E. Peskin, Perseus books (1995)

zero mode

The zero mode is part of Landau dumping but it is not relevant whether charmonium dissociates or survives.

One can remove the zero mode effects by derivative of correlators

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Zero mode in meson correlators

Spectral changes in χc0 w/ zero mode w/o zero mode

A.Jakovac et al. (’07)A.Jakovac et al. (’07)

Mocsy & Petreczky (’08)Mocsy & Petreczky (’08) The drastic change of correlatorsis due to the zero mode

No change in χc SPF within statistical errors

Grecon is a charmonium correlator constructed with SPF at T=0. No change in SPF at T>0

leads to G/Grecon = 1/19


J/ψ results taking account of zero mode

Zero mode in J/ψ correlatorZero mode in J/ψ correlator

H.Ding et al. (’09)

Spectral changes in J/ψ w/ & w/o zero mode

T/Tc=1.5

No change in J/ψ SPF within statistical error

T/Tc=0.75

T/Tc=1.5

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J/ψ results taking account of zero mode

Zero mode in J/ψ correlatorZero mode in J/ψ correlator

H.Ding et al. (’09)

Spectral changes in J/ψ w/ & w/o zero mode

T/Tc=1.5

No change in J/ψ SPF within statistical error

T/Tc=0.75

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T/Tc=1.5


Zero mode & MEM results

No significant change in correlators at T>0except for the zero mode effect.

Zero mode is not relevant to charmonium dissociations.

The default model is necessary in MEM analysis. No good default model for charmonium SPFs. default model dependence

a systematic error in MEM

T. Ding et al. (’09) shows that both SPFs w/ & w/o J/ψ peak can be extracted from common charmonium correlator at 1.5Tc by MEM.

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-- Sequential J/ψ suppression -- Sequential J/ψ suppression



SummarySummary


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infinite volume case finite volume case

In a finite volume (e.g. Lattice simulations), In a finite volume (e.g. Lattice simulations), discrete spectra does not always indicate bound states !discrete spectra does not always indicate bound states !

Spectral functions in a finite volume

Momenta are discretized in finite (V=LMomenta are discretized in finite (V=L33) volume) volume

ppii/a = 2n/a = 2niiππ/L (n/L (nii=0,±1,±2,…) for Periodic boundary condition=0,±1,±2,…) for Periodic boundary condition

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H. Iida et al. (’06)

M

BC BC’

bound

M

BC BC’

scattering

r

φ(r)bound

0

r

φ(r)scattering

0

The wave functions are localized,their energies are insensitive to B.C.

The momenta depends on BC,the scattering state energies are sensitive to B.C.

Other approaches to study charmonium dissociation

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Quark boundary conditions (B.C.) in space (finite volume on the lattice)

ηc(2S)

χc0(2P)

Ψ(2S)

χc1(2P)

ηc(1S) J/Ψ(1S)

χc0(1P) χc1(1P)

PBCAPBC

PBCAPBC

PBCMBC

PBCMBC


No significant differences in the different B.C.

PBC : b=( 1, 1, 1)PBC : b=( 1, 1, 1)APBCAPBC : b=(-1,-1,-1) : b=(-1,-1,-1) MBCMBC : b=(-1, 1, 1) : b=(-1, 1, 1)

Charmonium spectra in various boundary conditions

an expected gapan expected gapin V=(2fm)in V=(2fm)33

(free quark case)(free quark case) ~ 200MeV~ 200MeV

H. Ohno et al. (’08)H. Ohno et al. (’08)

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J/ψ(1S)

ψ(2S)

Charmonium wave function on the lattice

Clear signals of bound states even at T=2.3TClear signals of bound states even at T=2.3Tcc

χχc1c1(1P)(1P)

χχc1c1(2P)(2P)

H. Ohno et al. (’08)H. Ohno et al. (’08)

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(Bethe-Salpeter) (Bethe-Salpeter) “Wave function” at T=2.3T“Wave function” at T=2.3Tcc


Summary on lattice studies of charmonium dissociations

Because of MEM results on the lattice,Because of MEM results on the lattice,- J/ψ state survives till 1.5T- J/ψ state survives till 1.5Tcc or more or more

and, dissociates around 1.5-2.0Tand, dissociates around 1.5-2.0Tcc

-- χ χcc states dissociate just above T states dissociate just above Tcc

are widely believed.are widely believed.

Analysis taking the zero mode into accountAnalysis taking the zero mode into accountNo significant spectral changes in QGP (except for zero mode)No significant spectral changes in QGP (except for zero mode)

MEM results include large default model dependenceMEM results include large default model dependence


indicate no clear signal of dissociationindicate no clear signal of dissociation

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Summary and Outlook

Puzzle of J/ψ suppression in QGPPuzzle of J/ψ suppression in QGP

J/ψ should dissociate at very high temperatureJ/ψ should dissociate at very high temperature

because of the asymptotic freedom.because of the asymptotic freedom.

Lattice QCD has never seen such evidences yet (except for MEM).Lattice QCD has never seen such evidences yet (except for MEM).

High temperature calculations are time consuming on the lattice.High temperature calculations are time consuming on the lattice.

Non-MEM studies at very high temperature (T/TNon-MEM studies at very high temperature (T/Tcc=3~5) are desired.=3~5) are desired.

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Thank you for your attention !

Buckup slides



Temp. dependence of ( Bethe-Salpeter ) Temp. dependence of ( Bethe-Salpeter ) “Wave function” “Wave function”

Wave functions at finite temperature

using the eigen functions of the variational methodusing the eigen functions of the variational method

we can extract the wave functions of each stateswe can extract the wave functions of each states

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Summary and future plan

We investigated TWe investigated Tdisdis of charmonia from Lattice QCD of charmonia from Lattice QCD

using another approach to study charmonium at T>0 using another approach to study charmonium at T>0

without Bayesian analysiswithout Bayesian analysis

- boundary condition dependence- boundary condition dependence

- Wave function (Volume dependence)- Wave function (Volume dependence)

The result may affect the scenario of J/The result may affect the scenario of J/ψψ suppression. suppression.

Future planFuture plan Interpretations of the experimental results on J/Interpretations of the experimental results on J/ψψ suppression suppression Higher Temp. calculations ( T/Tc=3~5 )Higher Temp. calculations ( T/Tc=3~5 )

Full QCD calculations ( Nf=2+1 Wilson is now in progress )Full QCD calculations ( Nf=2+1 Wilson is now in progress )

No evidence for unbound c-c quarks up to T = 2.3 TcNo evidence for unbound c-c quarks up to T = 2.3 Tc


Maximum Entropy Method (MEM)

Other lattice studies:Other lattice studies:

T.Umeda et al.(’02), S.Datta et al.(’04), T.Umeda et al.(’02), S.Datta et al.(’04),

Asakawa&Hatsuda(’04), A.Jakovac et al.(’07), G.Aatz et al.(’06)Asakawa&Hatsuda(’04), A.Jakovac et al.(’07), G.Aatz et al.(’06)

all calculations conclude thatall calculations conclude that J/J/ψψ survives till 1.5T survives till 1.5Tcc or higher or higher

ATHIC 2010T. Umeda (Hiroshima Univ.)1 Heavy Quarkonium in QGP on the Lattice Takashi Umeda 3rd Asian...

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