Quarkonia above Deconfinement and Potential Models

Ágnes MócsyÁgnes Mócsy QWG Meeting BNL June 27-30 06QWG Meeting BNL June 27-30 06

11

Quarkonia above Quarkonia above DeconfinementDeconfinement

and Potential Modelsand Potential Models

Quarkonia above Quarkonia above DeconfinementDeconfinement

and Potential Modelsand Potential Models

Ágnes MócsyÁgnes Mócsy

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22summarysummarysummarysummary

potential models vs lattice QCD potential models vs lattice QCD

some features of quarkonia spectral some features of quarkonia spectral

functions agree BUT there are unreconciled functions agree BUT there are unreconciled

inconsistenciesinconsistencies

1st analysis of correlators from potential 1st analysis of correlators from potential

modelsmodels

our attempts to understand the discrepancies our attempts to understand the discrepancies


33

J/J/ suppression “unambiguous” signal of suppression “unambiguous” signal of deconfinementdeconfinement

T. Matsui, H. Satz 1986T. Matsui, H. Satz 1986

in quark-gluon plasma the color Coulomb-force in quark-gluon plasma the color Coulomb-force

between heavy Q and between heavy Q and Q gets Debye-screenedQ gets Debye-screened

RRscreeningscreening < R < RQQQ Q quarkonium dissociatesquarkonium dissociates

sequential suppressionsequential suppression F. Karsch, M. Mehr, H. Satz 1988F. Karsch, M. Mehr, H. Satz 1988

modification of quarkonia properties with modification of quarkonia properties with

temperature could tell about deconfinementtemperature could tell about deconfinement

it all started in 1986it all started in 1986it all started in 1986it all started in 1986

T

’’(2S)(2S) cc(1P)(1P) J/J/(1S)(1S)0.9fm0.9fm 0.7f0.7f

mm0.4f0.4fmm


44since 2004 from QCDsince 2004 from QCDsince 2004 from QCDsince 2004 from QCD

correlationcorrelation functions of hadronic currentsfunctions of hadronic currents reliably calculated reliably calculated

spectral function spectral function ((,T),T)

€

G τ ,T( )Grecon τ ,T( )

=σ ω,T( )K τ ,ω,T( )dω∫

σ ω,T = 0( )K τ ,ω,T( )dω∫

also: T. Umedaalso: T. UmedaT. Hatsuda, M. AsakawaT. Hatsuda, M. Asakawa

S. Datta et al 2004S. Datta et al 20041P charmonium is gone at 1.16T1P charmonium is gone at 1.16Tcc

P. Petreczky et al 2006P. Petreczky et al 2006

M E MM E M

€

=1⇒ σ (ω,T) = σ (ω,T = 0)

c0c0


55from from from from

1S charmonium survives 1S charmonium survives

up to 1.5Tup to 1.5Tcc

correlatorcorrelator spectral function spectral function

does not changedoes not change spectral function spectral function properties properties do not changedo not changecontradiction with early potential model predictionscontradiction with early potential model predictions

S. Datta et al 2004S. Datta et al 2004

cc


66

At what temperature do heavy quark bound At what temperature do heavy quark bound

states disappear? states disappear?

Can modification of quarkonia properties Can modification of quarkonia properties

be understood via a temperature-dependent be understood via a temperature-dependent

screened potential? screened potential?

If yes, what is the potential? If yes, what is the potential?

If not, how can we explain quarkonium If not, how can we explain quarkonium

dissociation? What is the mechanism behind dissociation? What is the mechanism behind

quarkonia melting? quarkonia melting?


77potential MODELpotential MODELpotential MODELpotential MODEL

heavy Q-heavy Q-Q interactions are mediated by a potentialQ interactions are mediated by a potential

confinedconfined

deconfineddeconfinedJ/

r

V(r)V( )

ar r

r=− + T = T =

00

T > TT > Tcc

( ) ( ) ( )2

2 2

110

dV r E u r

m dr mr

+⎛ ⎞− + + − =⎜ ⎟⎝ ⎠

l l( ) ( )u r

R rr

=

success for spectroscopysuccess for spectroscopylattice confirmedlattice confirmedobtainable from QCDobtainable from QCD

we don’t knowwe don’t know

assume a temperature-dependent potential V(r,T) assume a temperature-dependent potential V(r,T)

& solve Schrödinger’s equation to obtain properties of Q& solve Schrödinger’s equation to obtain properties of QQQ


88screened potentialsscreened potentialsscreened potentialsscreened potentials

screened Cornell potential:screened Cornell potential:

fitted lattice internal energy:fitted lattice internal energy:

Wong potential: Wong potential:

mixture of lattice internal & free energymixture of lattice internal & free energy

Common: Common:

all could keep the J/all could keep the J/ up to 1.5 T up to 1.5 Tcc

Is this enough to be consistent with lattice?Is this enough to be consistent with lattice?

( ) ( )

( )( )( )T TV ,T 1

Tr ra

r e er

μ μσ

μ− − = − + −

E. Shuryak, I. Zahed, E. Shuryak, I. Zahed, 20042004W. Alberico et al W. Alberico et al 20052005

C. Y. Wong C. Y. Wong 20052005

F. Karsch, M. Mehr, H. Satz, 1988F. Karsch, M. Mehr, H. Satz, 1988

O. Kaczmarek et al 2004O. Kaczmarek et al 2004


99

bound states/resonances + bound states/resonances + continuumcontinuum

I. model spectral functionI. model spectral functionI. model spectral functionI. model spectral function

€

(ω)

€

2M i∑ Fi2δ ω2 − M i

2( )

€

m0ω2 f ω,s0( )θ ω − s0( )++=

€

G τ ,T( ) = σ ω,T( )K τ ,ω,T( )dω∫

€

G T > Tc( )Grecon

ÁM, P. Petreczky, ÁM, P. Petreczky, hep-ph/0411262hep-ph/0411262 hep-ph/0512156hep-ph/0512156 hep-ph/0606053hep-ph/0606053

Schrödinger eq with V(r,T) Schrödinger eq with V(r,T)

MMii(T) bound state mass(T) bound state mass

FFii(T) amplitude(T) amplitude

asymptotic value of V(r,T)asymptotic value of V(r,T)

ss00(T) threshold(T) threshold


1010c0c0 correlator correlatorc0c0 correlator correlator

the the c0c0 is gone just above T is gone just above Tcc

increase in correlator due to continuumincrease in correlator due to continuum

qualitative agreement with lattice qualitative agreement with lattice

ÁM, P. Petreczky ÁM, P. Petreczky 20052005

S. Datta et al S. Datta et al 20042004


1111cc correlator correlatorcc correlator correlator

cc correlator does not agree with lattice correlator does not agree with lattice

increase due to continuum, decrease due to amplitude reductionincrease due to continuum, decrease due to amplitude reduction

correlator implies change in spectral functioncorrelator implies change in spectral function

disagrees with lattice disagrees with lattice

feature for all screened potentialsfeature for all screened potentials

ÁM, P. Petreczky ÁM, P. Petreczky 20052005

S. Datta et al S. Datta et al 20042004


1212

no assumption for spectral function neededno assumption for spectral function needed

drastic change in 1S mass & amplitudedrastic change in 1S mass & amplitude

inconsistent with latticeinconsistent with lattice

even though 1S survives the spectral function is even though 1S survives the spectral function is strongly modifiedstrongly modifiedII. nonrelativistic Green’s II. nonrelativistic Green’s

functionfunctionII. nonrelativistic Green’s II. nonrelativistic Green’s

functionfunction

lattice internal energy

S-waveS-wave

A. Jakovác et al A. Jakovác et al 20062006ÁM, P. Petreczky, J. Casalderrey-ÁM, P. Petreczky, J. Casalderrey-

Solana, in prep.Solana, in prep.


1313Green’s fct. cont.Green’s fct. cont.Green’s fct. cont.Green’s fct. cont.

inconsistency with lattice data is even worseinconsistency with lattice data is even worse

how could we - can we - produce agreement with how could we - can we - produce agreement with

lattice?lattice?

Wong potentialÁM, P. Petreczky ÁM, P. Petreczky hep-ph/0606053hep-ph/0606053

A. Jakovác et al A. Jakovác et al 20062006


1414instead consider a toy instead consider a toy

modelmodelinstead consider a toy instead consider a toy

modelmodel

no temperature-dependent screeningno temperature-dependent screening

no modification of the 1S properties - use PDGno modification of the 1S properties - use PDG

melting of 2S and 3S statesmelting of 2S and 3S states

melting of the 1P statemelting of the 1P state

continuum threshold scontinuum threshold s00 reduction reduction

1S1S 2S2S 3S3S

T = 0T = 0

T T TTcc

11PP

ÁM ÁM hep-ph/0606124hep-ph/0606124

ss00 ss00ss00 ss00


1515the toy modelthe toy modelthe toy modelthe toy model

cc

c0c0

choice of schoice of s0 0 can reproduce lattice correlatorscan reproduce lattice correlators

cc unchanged & unchanged & c0 c0 increased increased

compensate for the melting of higher excited states compensate for the melting of higher excited states above Tabove Tcc with the decrease of the threshold with the decrease of the threshold

ÁM 2006ÁM 2006


1616with nonrelativistic with nonrelativistic

Green’s fct.Green’s fct.with nonrelativistic with nonrelativistic

Green’s fct.Green’s fct.

maybe works BUT note: “screened” not maybe works BUT note: “screened” not screened screened

screening might not be the mechanism screening might not be the mechanism governing quarkonia melting governing quarkonia melting ttscreeningscreening>t>tQQQQ

ÁM, P. Petreczky, J. Casalderrey-ÁM, P. Petreczky, J. Casalderrey-Solana, in prep.Solana, in prep.

“screened” Cornell potential


1717conclusionconclusionconclusionconclusion

temperature-dependent screened potentials have temperature-dependent screened potentials have problems even though 1S can survive and 1P melts problems even though 1S can survive and 1P melts

two different analysis of spectral functions and two different analysis of spectral functions and correlators not consistent with lattice QCDcorrelators not consistent with lattice QCD

medium modification cannot be described by a medium modification cannot be described by a simple Debye screening picture simple Debye screening picture

gluo-dissociation effect gluo-dissociation effect finite width finite width Green’s fctGreen’s fct

current investigationcurrent investigation


1818my thanks tomy thanks tomy thanks tomy thanks to

Péter PetreczkyPéter Petreczky

Jorge Casalderrey-SolanaJorge Casalderrey-Solana

Dima KharzeevDima Kharzeev

Helmut SatzHelmut Satz


1919

T << ET << EQQ QQ gluo-gluo-dissociation dissociation effecteffect discrete states discrete states dominate dominate

ground state ground state unaffectedunaffected

T >TT >Tcc gluon sector gluon sector relevantrelevant

F. F. Karsch et al 1996Karsch et al 1996

Rate of J/Rate of J/ escape into the continuum escape into the continuum

€

∝exp −MQQ

T

⎛

⎝ ⎜

⎞

⎠ ⎟

D. Kharzeev, L. McLerran, H. D. Kharzeev, L. McLerran, H. Satz 1995Satz 1995

€

∝T 3 / 2 exp −E

QQ

T

⎛

⎝ ⎜

⎞

⎠ ⎟

€

EQQ

= s0 − MQQ

€

Z(T) = ZQQ

(T) + Zcont (T)

€

R∝1

Z(T)T 2 exp −

EQQ

T

⎛

⎝ ⎜

⎞

⎠ ⎟

E. Shuryak 1978E. Shuryak 1978G. Bhanot, M.Peskin 1979G. Bhanot, M.Peskin 1979

binding energybinding energy

T >> ET >> EQQ QQ screeningscreening

continuum continuum dominatesdominates all states get all states get modifiedmodified

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Quarkonia above Deconfinement and Potential Models