Ágnes Mócsy Quark Matter 06

1

Quarkonium Survival in a Quarkonium Survival in a Gluon Plasma:Gluon Plasma:

Spectral Function AnalysisSpectral Function Analysis

Ágnes Mócsy

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with Péter Petreczky (BNL) and Jorge Casalderrey-Solana (LBNL)

Ágnes Mócsy Quark Matter 06

2motivation for this study motivation for this study

Quarkonium - could probe deconfinement must understand its modification in a hot medium !

Traditionally - Debye screening in qgp rDebye rquarkonium quarkonium dissociation Hierarchy in binding energy - qgp thermometer

Our approach - use spectral function - contains all info - from full nonrelativistic Green’s function

also:

TT0.90.9 0.70.7 0.40.4 0.20.2

J/J/(1S)(1S)cc(1P)(1P)’’(2S)(2S)bb(1P)(1P)bb’(2P’(2P

))(1S)(1S)’’’’(3S)(3S)

rr221/2 1/2 fmfm

€

V r( ) = −4

3

α s

rexp −mDr( )

€

mD ∝ gT

Matsui,Satz 86

Karsch,Mehr,Satz 88 Satz 06

AM, Petreczky, hep-ph/0606053AM, Petreczky, Casalderrey-Solana, hep-ph/0609205,hep-ph/0612…

Strassler,Peskin 91; Casalderrey-Solana,Shuryak 04; Cabrera, Rapp 06; Wong 06

Ágnes Mócsy Quark Matter 06

3motivation - why spectral functionmotivation - why spectral function

€

σ ω( )ω 2

~ R =σ e+e− → H( )

σ e+e− → μ +μ−( )

€

σ(ω) =1

πImDR (ω)

T0 heavy ion dilepton rates

defined through the meson propagator

measured on the lattice

PDG 06 T0 spectral function

€

G τ ,r p ,T( ) = d3∫ xe i

r p

r x jH τ ,

r x ( ) jH

+ 0,r 0 ( )

€

jH = q ΓHq

NA50

Ágnes Mócsy Quark Matter 06

4potential modelpotential model

models valid if tgluon tquarkonium “instantaneous interaction”

V( )a

r rr

σ=− +

T0 hierarchy of energy/timescales

QCDQCD

NRQCDNRQCD

pNRQCDpNRQCD

potential modelpotential model

mvmv22

mv mv

mm

1/mv2 ~ tquarkonium

1/mv ~ tgluon

potential can be derivedpotential can be derived

mass mQ QCD nonrelativistic Q velocity v 1

Ágnes Mócsy Quark Matter 06

5potential models T0potential models T0

( ) ( )

( )( )( )T TV ,T 1

Tr ra

r e er

μ μσ

μ− − = − + −

Karsch,Mehr,Satz 88

T0 ??? no analogous effective theory:extra scales T, gT, g2T make derivation too complicated

(T) model parameter

other potentials Shuryak,Zahed; Alberico,Rapp; Wong; Nardi;

(T) = mD

AM,Petreczky 05

mass mQ QCD nonrelativistic Q velocity v 1

assume a phenomenological potential:

models valid if tgluon tquarkonium “instantaneous interaction”

potential is unknownpotential is unknown

Ágnes Mócsy Quark Matter 06

6spectral function approachspectral function approach

€

σ pert ≅ω2 3

8π1+

11

3πα s

⎛

⎝ ⎜

⎞

⎠ ⎟

+

bound states/resonances continuumω ~ MJ/ - nonrelativistic ω MJ/ - perturbative

medium effects in the gluon propagator

PDG 06

€

σ =−1

πImΠ ∝

1

πImGNR

€

−1

m∇ 2 + V (

r r ) + E + iΓ

⎡ ⎣ ⎢

⎤ ⎦ ⎥G(

r r ,

r r ',E + iΓ) = δ 3(

r r −

r r ')

nonrelativistic Green’s function - contains all states

goal: calculate the spectral function at finite T

€

D00(k) =c

k 2 − μ T( )2

( )2 +

1

k 2 + μ T( )2

M (GeV)

match

Ágnes Mócsy Quark Matter 06

7c spectral function T0c spectral function T0

pure gluon plasma

Jakovác,Petreczky,Petrov,Velytsky,hep-lat/0611017

€

rp = 0

talk by K. Petrov

Ágnes Mócsy Quark Matter 06

8c spectral function TTcc spectral function TTc

pure gluon plasma

€

rp = 0

Ágnes Mócsy Quark Matter 06

9c spectral function TTcc spectral function TTc

higher excited states gone continuum shifted 2S becomes merely a threshold

enhancement

spf unchanged within errors, but details cannot be resolved

strong modification of 1S incompatible w/ data

ground state identified

Jakovác et al hep-lat/0611017

Ágnes Mócsy Quark Matter 06

10c correlator c correlator

€

G τ ,T( ) = σ ω,T( )K τ ,ω,T( )dω∫

€

Grecon = dωσ ω,T = 0( )∫ K ω,τ ,T( )

calculated and lattice correlators not compatible up to 1.5Tc

decrease in correlator due to 1S amplitude reduction

- not seen on the lattice

calculated and lattice correlators not compatible up to 1.5Tc

decrease in correlator due to 1S amplitude reduction

- not seen on the lattice

G/Grecon 1 means spectral function unchanged

correlation of hadronic currents

Jakovác et al hep-lat/0611017

Ágnes Mócsy Quark Matter 06

11b spectral function b spectral function

lattice spectral function

not yet reliable

Jakovác et al hep-lat/0611017

1S survives with decrease

in amplitude & some shift in mass

Ágnes Mócsy Quark Matter 06

12b correlator b correlator

no agreement at all with the lattice data

Jakovác et al hep-lat/0611017

Ágnes Mócsy Quark Matter 06

13if 1S unchangedif 1S unchanged

if the ground state properties are unchanged at finite T then the lattice correlators are recovered

dissolution of excited states is compensated by threshold reduction

lattice correlator compatible w/ dissolution of higher excited states

AM hep-ph/0606124

Ágnes Mócsy Quark Matter 06

14concluding/closing remarksconcluding/closing remarks

• we calculated the quarkonium spectral function– nonrelativistic Green’s function + relativistic continuum

useful apparatus to study quarkonium properties in medium

• we found that: – potentials don’t agree with lattice quarkonium data at

finite T - tgluon tquarkonium not satisfied

need to think harder – the dissolution of higher excited states is compensated by

threshold reduction– lattice correlator compatible w/ dissolution of higher

excited states

• future:– “short distance confinement”– pNRQCD at finite T ?! – finite momentum: quarkonium in motion