Overview of Potential models at finite temperature

Péter Petreczky Physics Department and RIKEN-BNL

QWG2008, Nara, December 2-5, 2008

Brief history :

• Potential models with screening and quarkonium dissociation in the quark gluon plasma (1986-2003): J/psi melts at T<1.2Tc, Upsilon melts at T~2Tc, excited charmonium states melt around Tc (Matsui, Satz, 1986, ….)

• Lattice calculations of quarkonium correlators and spectral functions (2003-2006): J/psi survives till T~1.6Tc, Upsilon does not melt, excited charmonium states melt around Tc (Umeda 2002, Asakawa, Hatsuda, 2003, Datta et al, 2003)

• Role of zero mode contribution and threshold enhancement (2006-2008) :zero mode contribution mock melting of 1P quarkonium states (Umeda , 2006, Mocsy, P.P, 2007),threshold enhancement leads to almost T-independent quarkonium correlators ( Mocsy, P.P, 2007)

Color screening in QCD and quarkonia melting

Confined

Deconfined

r

V(r)

Matsui and Satz, 1986

T/TC 1/r [fm-1]

(1S)

J/(1S)

c(1P)

’(2S)

b’(2P)

’’(3S)

use quarkonia as thermometerof the matter created in RHIC

Color screening reduces the effective rangeof interactions in QGP

Other medium effects (e.g. Landau damping)produce an imaginary part for the potential

(Laine et al, 2006, Blaizot 2007, Brambilla et al, 2008,Escobeto and Soto, 2008)

RBC-Bielefeld Collaboration, 2+f lattice QCD

Color screening in QCD and quarkonia melting

),(),(),(,)0,0(),(),,( 3 xqxqxJJxJexdTpG HHHHxpi

Meson correlators and spectral functions

5,,5,1H

)(),( iDTG

Imaginary time Real time

0 ))2/(sinh(

))2/(1(cosh(),(),(

T

TTdTG

LGT )()(Im1

2

)()(

RDDD

MEM),,( TpG ),,( Tp

If there is no T-dependence in

the spectral function

Study the ratio

1

m2 V (

r ) E

GNR (

r ,

r ', E) 3(

r

r ')

E 2Nc

ImGNR

r ,r ',E

r r '0

E 2Nc

1

m2

'ImGNR

r ,r ',E

r r '0

S-wave P-wave

many gluon exchanges important near threshold

Quarkonium spectral functions in potential models

pert 2 3

81

11

3 s

+

~ MJ/ , s0 nonrelativistic

s0 perturbative

PRD77 (08) 014501, EPJC ST 155 (08) 101 Mócsy, P.P., PRL 99 (07) 211602,

use lattice data on the quark anti-quark free energy to construct the potential

compare to lattice QCD results

• resonance-like structures disappear already by 1.2Tc

• strong threshold enhancement above free case indication of correlations

• height of bump in lattice and model are similar

•The correlators do not change significantly despitethe melting of the bound states

• resonance-like structures disappear already by 1.2Tc

• strong threshold enhancement above free case indication of correlations

• height of bump in lattice and model are similar

•The correlators do not change significantly despitethe melting of the bound states

c

• resonance-like structures disappear already by 1.2Tc

• strong threshold enhancement above free case indication of correlations

• height of bump in lattice and model are similar

•The correlators do not change significantly despitethe melting of the bound states

• resonance-like structures disappear already by 1.2Tc

• strong threshold enhancement above free case indication of correlations

• height of bump in lattice and model are similar

•The correlators do not change significantly despitethe melting of the bound states

c

• resonance-like structures disappear already by 1.2Tc

• strong threshold enhancement above free case indication of correlations

• height of bump in lattice and model are similar

•The correlators do not change significantly despitethe melting of the bound states

• resonance-like structures disappear already by 1.2Tc

• strong threshold enhancement above free case indication of correlations

• height of bump in lattice and model are similar

•The correlators do not change significantly despitethe melting of the bound states

bc ,

Quarkonium binding energy and thermal width

Using lattice data on the static quark anti-quark free energy in 2+1f QCD the binding energy of different quarkonium states can be estimated Mócsy, P.P., PRL 99 (07) 211602 Kharzeev, McLerran, Satz, PLB356 (95) 349

Quarkonium binding energy in different models

binding energy decreases with T, but there are large uncertanties from modeling of V

Alberico et al, PRD72 (05) 114011

Quarkonium width in different models

Zhao, Rapp, PLB664 (08) 253Park et al, PRC76 (07) 044907

Reduced binding energy => larger width;thermal width increases with T abovedeconfinement

NLO pQCD + in-medium binding energy

quark gluon

quasi-free dissociation in-medium binding energy

Spectral functions with complex potential

Burnier, Laine, Vepsalainen JHEP 0801 (08) 043

The imaginary part of the potential washes out the bound state peak making it amere threshold enhancement even for b-quarks !Large threshold enhancement is observed

Summary

• Lattice and perturbative calculations show that in-medium modification of the potential is sufficiently strong to lead to quarkonium dissociation in the deconfined phase

• Residual interaction of quark and anti-quark are important threshold enhancement very small T-dependence of Euclidean correlators conclusions reached in lattice calculations of the Euclidean correlators and spectral functions about the survival of 1S state (Umeda et al, 2002; Asakawa, Hatsuda, 2003, Datta et al, 2003) were premature ! MEM is not sufficiently accurate

• Potential model calculations based on lattice results on singlet free energy reproducethe temperature (in)dependence of the Euclidean time correlatorsCrosscheck : threshold enhancement effects weaken with decreasing quark masses larger T-dependence for quarkonium correlators (consistent with lattice calculations of Datta et al)

• Lattice calculations based on “wave function method” indicate survival of charmoniumstates till 2.3Tc (Umeda et al, 2000, 2008)Problems : even highly excited states, e.g. 2P states survive to such high T the notion of well defined states is problematic due to finite width effectCrosscheck : consider the light quark case where no bound states are expected, c.f. lattice calculations of fluctuations of conserved charges.

Outlook

• Combine EFT techniques in the weak coupling regime with available latticedata on the static meson correlators to obtain a reliable potential model typeof framework with all medium effect included.

• Calculate charm fluctuations to find the relevant degrees of freedom : bound states or free quark. Determine the quasi-particle properties at high T

• Extend the lattice “wave function analysis” to light quark sector to check the consistency of the approach

Backup slides