Quarkonia from Lattice and Potential Models

Ágnes Mócsy, Bad Honnef 08 1

Quarkonia from Lattice and Potential Models

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Characterization of QGP with Heavy Quarks

Bad Honnef Germany, June 25-28 2008

Ágnes Mócsy

based on work with Péter Petreczky


Confined Matter


Deconfined Matter


Deconfined Matter

Screening


Deconfined Matter

Screening

J/ melting


Deconfined Matter

Screening

J/ melting

J/ yield suppressed


T/TC 1/r [fm-1]

(1S)

J/(1S)

c(1P)

’(2S)

b’(2P)

’’(3S)

Sequential suppression

QGP thermometer QGP thermometer


Screening seen in lattice QCD

no T effects

€

r < r1(T)

strong screening

€

r > rmed (T)

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.


J/ suppression measured

… but interpretation not understood

• Hot medium effects - screening? Must know dissociation temperature, in-medium

properties • Cold nuclear matter effects ? • Recombination?

PHENIX, QM 2008


Studies of quarkonium in-medium

Potential Models

Lattice QCD

Matsui, Satz, PLB 178 (1986) 416Digal, Petreczky, Satz, PRD 64 (2001) 094015Wong PRC 72 (2005) 034906; PRC 76 (2007) 014902Wong, Crater, PRD 75 (2007) 034505Mannarelli, Rapp, PRC 72 (2005) 064905Cabrera, Rapp, Eur Phys J A 31 (2007) 858; PRD 76 (2007) 114506Alberico et al,PRD 72 (2005) 114011; PRD 75 (2007) 074009 PRD 77 (2008) 017502Mócsy, 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) 9Asakawa, Hatsuda, PRL 92 (2004) 012001Datta et al PRD 69 (2004) 094507Jakovac et al PRD 75 (2007) 014506 Aarts et al Nucl Phys A785 (2007) 198Iida et al PRD 74 (2006) 074502Umeda PRD 75 (2007) 094502


Studies of quarkonium in-medium

Potential Models

Lattice QCD

Spectral functions

Still inconclusive(discretization effects,

statistical errors)

Assume: medium effects can be understood in terms of

a temperature-dependent screened

potential

Contains all info about a given channel.Melting of a state corresponds to disappearance of a peak.


Quarkonium from lattice

• Euclidean-time correlator measured on the lattice

• Spectral functions extracted from correlators inverting the integrals using Maximum Entropy Method

€

G τ ,r p ,T( ) = d3∫ xe i

r p

r x jH τ ,

r x ( ) jH

+ 0,r 0 ( )

€

G τ ,T( ) = σ ω,T( )K τ ,ω,T( )dω∫

Kernel cosh[(-1/2T)]/sinh[/2T]

q qγ5

q qμγ

q qμγ γ5

j =

scalar

pseudoscalar

vector

axialvector

c b

c0 b0

J/

c1 b1

q q


Spectral function from lattice

• Shows no large T-dependence • Peak has been commonly interpreted as ground

state • Uncertainties are significant!

limited # data pointslimited extent in tau systematic effectsprior-dependence

c

Details cannot be resolved.

“..it is difficult to make any conclusive statement based on the shape of the spectral functions … ”

Jakovác et al PRD (2007)

Jakovac et al, PRD (2007)


Ratio 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∫

Compare high T correlators to correlators “reconstructed” from

spectral function at low T

Pseudoscalar Scalar

Datta et al PRD (2004) T-dependence of correlator ratiodetermines dissociation temperatures: c survives to ~2Tc & c melts at 1.1Tc

Initial interpretation

Seemingly in agreement with spectral function interpretation.

2004: “J/ melting” replaced by “J/ survival”


Recently: Zero-mode contribution

Bound and unbound Q-Qbar pairs

(>2mQ)

Bound and unbound Q-Qbar pairs

(>2mQ)

Quasi-free heavy quarks interacting with the

medium

Quasi-free heavy quarks interacting with the

medium€

σ ,T( ) = Tχ s T( )ωδ ω( ) + σ high ω,T( )

€

σ ,T( ) = Tχ s T( )ωδ ω( ) + σ high ω,T( )

Low frequency contribution to spectral function at finite T,scattering states of single heavy quarks (commonly overlooked)

Gives constant contribution to correlator =>> Look at derivativesUmeda, PRD 75 (2007) 094502

€

G τ ,T( ) = σ ω,T( )K τ ,ω,T( )dω∫


Ratio of correlator derivatives

• 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

All correlators are flat.

Datta, Petreczky, QM 2008, arXiv:0805.1174[hep-lat]


From the lattice

Dramatic changes in spectral function are not reflected in the correlator


Lessons from Lattice QCD

Small change in the ratio of correlators does not imply (un)modification of states. 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.

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. 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.

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.


Would really the J/ survive in QGP up to 1.5-2Tc even though strong screening is seen in the medium?

Would really the J/ survive in QGP up to 1.5-2Tc even though strong screening is seen in the medium?


Potential model at T=0

• Interaction between heavy quark (Q=c,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.

heavy quark massmQ>>QCD

and velocityv<<1

V(r)Confined

r

V(r)

€

−1

m∇ r

2 + V r( ) ⎡ ⎣ ⎢

⎤ ⎦ ⎥ψ r( ) = Eψ r( )


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 equationfor non-relativistic Green’s function - obtain spectral function

• Utilize lattice data

V(r,T) Confined

Deconfined T>Tc

r

V(r)

€

−1

m∇ 2 + V (

r r ) + E

⎡ ⎣ ⎢

⎤ ⎦ ⎥G

NR (r r ,

r r ',E) = δ 3(

r r −

r r ')

€

σ E( ) =2Nc

πImGNR r

r ,r r ', E( ) r

r =r r '= 0


Lattice & Potential models

Potential Models

Lattice QCD

Quarkonium correlators

ReliableReliable

Spectral functions

Free energy of static quarks

Potential from pNRQCD


Spectral functions

Not yet reliableNot yet reliable


First lattice-based potentialFree energy of static Q-Qbar pair: F1

Digal, Petreczky, Satz, PRD (2001)

RBC-Bielefeld Coll. (2007)

Free energy F1≠ Potential VContains entropy F1=E1-ST


Lattice-based potentials Most confining potential

Our physical potential

– Deeper potentials: stronger binding, higher Tdiss

– Open charm (bottom) threshold = 2mQ+Vinf(T)– Explore uncertainty assuming the general features of F1

• r < r1(1/T): vacuum potential • r > r2(1/T): exponential screening

Wong potential1.2Tc

1.2Tc

T=0 potential

Internal energyTS

- lower limit

- upper limit

Mócsy, Petreczky 2008

Free energy

r1r2

Can we constrain them using correlator lattice data?


Pseudoscalar correlators

1.2Tc

No, we cannot determine quarkonium properties from such comparisons;If no agreement found, model is ruled out; We can set upper limits.

Set of potentials all agree with lattice data; yield indistinguishable

results.

with set of potentials within the allowed ranges

~ 1-2%


Pseudoscalar spectral function

c

most confining potentialusing most confining potential

Mocsy, Petreczky 08

Large threshold (rescattering) enhancement even at high T- indication of Q-Qbar correlation

- compensates for melting of states keeping correlators flat

~ 1-2%


Pseudoscalar spectral function

c

most confining potentialusing most confining potential

Mocsy, Petreczky 08

State is dissociated when no peak structure is seen.At which T the peak structure disappears? Ebin=0 ?!

Ebin = 2mq+V∞(T)-M

Warning! Widths are not physical - broadening not included


Binding energies

€

Ebin < Tweak binding

€

Ebin > Tstrong binding

Binding energies decrease as T increases. True for all potential models.

What’s the meaning of a J/ with 0.2 MeV binding?

With Ebin< T a state is weakly bound and thermal fluctuations can destroy it

Mocsy, Petreczky, PRL 08

Do not need to reach Ebin=0 to dissociate a state.Do not need to reach Ebin=0 to dissociate a state.


Upper limit melting temperatures

Estimate dissociation rate due to thermal activation (thermal width)

Dissociation condition:

Ebin = 2mQ+V∞(T)-MQQbar < T

€

Γ T( ) ≥ 2Ebin T( )

Kharzeev, McLerran, Satz, PLB (1995)

Broadening in agreement with:pQCD calculation QCD sum ruleImaginary part in resummed pQCD

pNRQCD at finite T

Laine,PhilipsenLee, Morita

Park et al

Brambilla et al

J/ melts before it bounds.

T/TC 1/r [fm-1]

(1S)

J/(1S) ’(2S)

c(1P) ’(2S)b’(2P) ’’(3S)TC

2

1.2

b(1P)


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.

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.

Large threshold enhancement above free propagation even at high T

- compensates for melting of states (flat correlators) - correlation between Q and Qbar persists

Large threshold enhancement above free propagation even at high T

- compensates for melting of states (flat correlators) - correlation between Q and Qbar persists

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.

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.

Decrease in binding energies with increasing temperature. Decrease in binding energies with increasing temperature.


Implications for RHICollisions

survival J/ survival

Karsch et al

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?


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


Final note IIThe future is in:

Effective field theories from QCD at finite T

QCD

NRQCD

pNRQCDpotential model

Ebin~mv2

1/r ~ mv

m

Hierarchy of energy scales

r: distance between Q and QbarEbin: binding energy

Brambilla, Ghiglieri, Petreczky, Vairo, arXiv:0804.0993[hep-ph]

TmD ~gT

NRQCDHTL

pNRQCDHTL

Real and Imaginary part of potential derived

Also: Laine et al 2007, Blaizot et al 2007


The QGP thermometer

Potential Models Lattice QCD

ExtractedSpectral Functions

Free energyof q-antiq


Quarkoniumcorrelators

Spectral Functions

T/TC 1/r [fm-1]

(1S)

J/(1S) ’(2S)

c(1P) ’(2S)

b’(2P) ’’(3S)TC

2

1.2

b(1P)


****The END****

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Quarkonia from Lattice and Potential Models