Ágnes Mócsy

Ágnes Mócsy - RBRC

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Ágnes Mócsy

July 16th-19th, 2007 McGill University, Montréal, Canada

July 2007 Early Time Dynamics Montreal

AM


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MotivationMotivation


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In this talkIn this talk

• revisit how we got to “J/ survives up to 2Tc”

• from the same data get very different conclusion

• revisit how we got to “J/ survives up to 2Tc”

• from the same data get very different conclusion

offering new direction in which models can be modifiedoffering new direction in which models can be modified


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a more detailed motivation


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IntroductionIntroduction

Debye screening in the

deconfined matter leads

to quarkonium

dissociation when

rDebye rQuarkonium

confined

deconfinedJ/

r

V(r)

€

V r( ) = −4

3

α s

rexp −mDr( )€

V r( ) = −α

r+ rσ

The Matsui-Satz argument:

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






quarkonium discussed in terms of potential model


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Static quark-antiquark free energyRBC-Bielefeld Collaboration 2007

Nf=2+1 Screening seen in lattice QCDScreening seen in lattice QCD

see talk by Péter Petreczky


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Hierarchy in binding energies

T

0.9 fm 0.7 fm 0.4 fm 0.2 fm

J/(1S)

c(1P)’(2S)

b(1P)

b’(2P) (1S)’’(3S)

Quarkonia melting as QGP thermometerQuarkonia melting as QGP thermometer


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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

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












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““J/J/ survival” in LQCD survival” in LQCD

Asakawa, Hatsuda, PRL 04

Datta et al PRD 04

Jakovác et al, PRD 07 Aarts et al hep-lat/0705.2198

Lattice Spectral Functions

Conclusion: 1S ground state survives above

TC

see talk by Péter Petreczky


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Asakawa, Hatsuda, PRL 04

Datta et al PRD 04

Jakovác et al, PRD 07 Aarts et al hep-lat/0705.2198

Lattice Spectral Functionssee talk by Péter Petreczky

• large uncertainties• not directly measured• extracted from correlators through MEM

• large uncertainties• not directly measured• extracted from correlators through MEM

€

G τ ,T( ) = σ ω,T( )K τ ,ω,T( )dω∫

€

G τ ,T( ) = σ ω,T( )K τ ,ω,T( )dω∫


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Temperature dependence of correlators

€

G τ ,T( ) = σ ω,T( )K τ ,ω,T( )dω∫

€

Grec τ ,T( ) = σ ω,T = 0( )K τ ,ω,T( )dω∫

c

Jakovác et al, PRD 07

Conclusions drawn from analysis of lattice data were

• c melts by 1.1 Tc

based on modification of G/Grec and spectral functions

from MEM



based on modification of G/Grec and spectral functions

from MEM

G/Grec 1 implies modified spectral

function


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• J/ and c survive up to 1.5-2Tc “J/ survival”based on (un)modification of G/Grec and spectral functions from MEM



• J/ and c survive up to 1.5-2Tc “J/ survival”based on (un)modification of G/Grec and spectral functions from MEM

c

Jakovác et al, PRD 07Jakovác et al, PRD 07

€

G τ ,T( ) = σ ω,T( )K τ ,ω,T( )dω∫

€

Grec τ ,T( ) = σ ω,T = 0( )K τ ,ω,T( )dω∫

c

Temperature dependence of correlatorsG/Grec = 1 implied unchanged spectral function?


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““J/J/ survival” in Potential survival” in Potential ModelsModels

Shuryak,Zahed PRD 04Wong, PRC 05Alberico et al PRD 05Cabrera, Rapp 06 Alberico et al PRD 07Wong,Crater PRD 07

series of potential model studies

Conclusions

• states survive

• dissociation temperatures quoted

• agreement with lattice is claimed

Conclusions

• states survive

• dissociation temperatures quoted

• agreement with lattice is claimed

Wong,Crater, PRD 07


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Strong screening of Q and antiQ interaction seen on lattice yet some quarkonium states still survive unaffected?


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€

c

Mócsy,Petreczky EJPC 05Mócsy,Petreczky PRD 06

model lattice

€

c

First Indication of First Indication of InconsistencyInconsistency

simplified spectral function: discrete bound states + perturbative continuum

T = 0T Tc

alsoCabrera, Rapp 06

It is not enough to have “surviving state”

Correlators calculated in this approach do not agree with lattice


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What is the source of these

inconsistencies?

validity of potential models?

finding the right potential?

relevance of screening for quarkonia

dissociation?


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our recent approach to determine quarkonium properties

Á. Mócsy, P. Petreczky 0705.2559 [hep-ph] 0706.2183 [hep-ph]


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Spectral Function Spectral Function

bound states/resonances & continuum above threshold

(GeV)

€

−1

m∇ 2 + V (

r r ) + E

⎡ ⎣ ⎢

⎤ ⎦ ⎥G

NR (r r ,

r r ',E) = δ 3(

r r −

r r ')

nonrelativistic Green’s function

~ MJ/ , s0 nonrelativistic

€

σ E( ) =2Nc

πImGNR r

r ,r r ',E( ) r

r =r r '= 0

€

σ E( ) =2Nc

π

1

m2

r ∇ ⋅

r ∇'ImGNR r

r ,r r ',E( ) r

r =r r '= 0

S-wave

P-wave

medium effects - important near threshold

PDG 06

re-sum ladder diagrams first in vector channel Strassler,Peskin PRD 91 also Casalderrey-Solana,Shuryak 04

S-wave also Cabrera,Rapp 07


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Spectral FunctionSpectral Function

€

σ pert ≅ω2 3

8π1+

11

3πα s

⎛

⎝ ⎜

⎞

⎠ ⎟

+

s0

perturbative


(GeV)

€

σ ∝1

πImGNR

€

−1

m∇ 2 + V (

r r ) + E

⎡ ⎣ ⎢

⎤ ⎦ ⎥G

NR (r r ,

r r ',E) = δ 3(

r r −

r r ')

nonrelativistic Green’s function

~ MJ/ , s0 nonrelativistic

PDG 06PDG 06


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Spectral FunctionSpectral Function

Unified treatment: bound states, threshold effects together with relativistic perturbative continuumUnified treatment: bound states, threshold effects together with relativistic perturbative continuum


(GeV)

+

s0

perturbative ~ MJ/ , s0 nonrelativistic

smooth matchingdetails do not influence the result

€

−1

m∇ 2 + V (

r r ) + E

⎡ ⎣ ⎢

⎤ ⎦ ⎥G

NR (r r ,

r r ',E) = δ 3(

r r −

r r ')

nonrelativistic Green’s function + pQCDnonrelativistic Green’s function + pQCD

PDG 06


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no temperature effects

Constructing the Potential Constructing the Potential at T>Tat T>Tcc

Potential assumed to share general features with the free energy

€

V∞ T( ) = rmed T( )σ > F1∞(T)

€

V r,T( ) = −α

r+ rσ

also motivated by Megías,Arriola,Salcedo PRD07

€

r < rmed

€

r > rmed

€

V r,T( ) = V∞ T( ) −α 1 T( )

re−μ T( )r

strong screening effects

Free energy - contains negative entropy contribution - provides a lower limit for the potential

Phenomenological potential constrained by lattice data Phenomenological potential constrained by lattice data

subtract entropy

€

F1 = E1 − TS


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quarkonia in a gluon plasma (quenched QCD)


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S-wave Charmonium in Gluon S-wave Charmonium in Gluon PlasmaPlasma

• resonance-like structures disappear already by 1.2Tc

• strong threshold enhancement

• contradicts previous claims


• strong threshold enhancement

• contradicts previous claims

higher excited states gonecontinuum shifted1S becomes a threshold enhancement

lattice

Jakovác,Petreczky,Petrov,Velytsky, PRD07

c

Mócsy, Petreczky 0705.2559 [hep-ph]


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• strong threshold enhancement above free case indication of correlation

• height of bump in lattice and model are similar


• strong threshold enhancement above free case indication of correlation

• height of bump in lattice and model are similar

details cannot be resolveddetails cannot be resolved



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€

G τ ,T( ) = σ ω,T( )K τ ,ω,T( )dω∫

€

Grec τ ,T( ) = dωσ ω,T = 0( )∫ K ω,τ ,T( )

spectral function unchanged across deconfinement

€

G(τ ,T)

Grec (τ ,T)=1

LQCD measures correlators LQCD measures correlators

N.B.: 1st time2% 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

N.B.: 1st time2% 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

or… integrated area under spectral function unchanged


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P statesP states

b

“the b puzzle” b same size as the J/, so why are the b and J/ correlators so different ?

“the b puzzle” b same size as the J/, so why are the b and J/ correlators so different ?

Jakovác et al, PRD 07


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Agreement for P-wave as wellAgreement for P-wave as well

so look at the derivative following Umeda 07

constant contribution in the correlator at finite T

quark number susceptibili

ty1.5 Tc

Threshold enhancement in spf compensates for dissolution of states

Agreement with lattice data for scalar charmonium and bottomonium

Threshold enhancement in spf compensates for dissolution of states

Agreement with lattice data for scalar charmonium and bottomonium

cb


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P-waveP-wave

>>deconfined confined

in free theory

behavior explained using ideal gas expression for susceptibilities:

indicates deconfined heavy quarks carry the quark-number at 1.5 Tc

behavior explained using ideal gas expression for susceptibilities:

indicates deconfined heavy quarks carry the quark-number at 1.5 Tc

charm1.5 Tc

bottom1.5 Tc

b “puzzle” resolved


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quarkonia in a quark-gluon plasma (full QCD)


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S-wave Quarkonium in QGPS-wave Quarkonium in QGP

• 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

• 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

€

Ebin = s0 − M

c


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upper limits on dissociation temperatures


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Most Binding PotentialMost Binding Potential

need strongest confining effects = largest possible rmed

Find upper limit for binding Find upper limit for binding

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

distance where deviation from T=0 potential starts


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Binding Energy Upper LimitsBinding Energy Upper Limits

Upsilon remains strongly bound up to 1.6Tc

Other states are weakly bound above 1.2Tc

Upsilon remains strongly bound up to 1.6Tc

Other states are weakly bound above 1.2Tc

€

Ebin < Tweak binding

When binding energy drops below T• state is weakly bound• thermal fluctuations can destroy the resonance

€

Ebin > Tstrong binding


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for weak binding Ebin<T

for strong binding Ebin>T

Thermal Dissociation Widths Thermal Dissociation Widths

Rate of escape into the continuum due to thermal activation = thermal width related to the binding energy

€

Ebin = s0 − MQQ

€

=LT( )

2m

3πexp −

Ebin

T

⎛

⎝ ⎜

⎞

⎠ ⎟

€

=4

L

T

2πm

€

L ≈ rmed − rQQ

Kharzeev, McLerran, Satz PLB 95


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Can Quarkonia Survive?

Upper bounds on dissociation temperatures

condition: thermal width > 2x binding energy

Upper bounds on dissociation temperatures

condition: thermal width > 2x binding energy


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ConclusionsConclusions

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 by ~1.3Tc

Threshold enhancement found: spectral function enhanced over free propagation =>> correlations between Q-antiQ may remain strong

OutlookOutlookImplications for heavy-ion phenomenology need to be considered

see also Laine,hep-ph/0704.1720Brau,Buisseret,hep-ph/0706.4012


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****The END********The END****

Ágnes Mócsy

Documents

zahed prd

petreczky prd

crater prd

quarkonium states

datta et

alberico et

aarts et

lattice spectral functionssee