Heavy quark and quarkonia at finite temperature

Péter Petreczky

Physics Department and RIKEN-BNL

xQCD 2008, NCSU, July 21-23, 2008

• Introduction : Deconfinement at high temperature and color screening

• Quarkonium correlators and spectral functions from lattice

• Quarkonium spectral functions in potential models

• Effective field theory approach for heavy quark bound states

• Static meson correlators T>0 in Euclidean time

• Conclusions and Outlook

RBC-Bielefeld Collaboration

Color screening in QCD and quarkonia melting

Does this imply quarkonium melting ?

Matsui and Satz PLB 178 (86) 416

see also

Digal et al, PLB 514 (01) 57 ; PRD 64 (01) 094015,

),(),(),(,)0,0(),(),,( 3 xqxqxJJxJexdTpG HHHH

xpi

Meson correlators and spectral functions

5,,5,1H

)(),( iDTG

Imaginary time Real time

0 ))2/(sinh(

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

T

TTdTG

LGT

Experiment, dilepton rate)()(Im

1

2

)()(

RDDD

MEM),,( TpG ),,( Tp

Quarkonium spectral functions above deconfinement

E.g. free theory :

P.P., Teaney, PRD 73 (2006) 014508

interactions :

calculate the area under the peak using

lattice QCD !

quark number susceptibility

+

If there is no T-dependence in the spectral

function,

0 ))2/(sinh(

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

T

TTdTG

temperature dependene of ),( TG

Charmonia correlators at T>0

Datta et al, PRD 69 (04) 094507

Charmonia correlators at T>0

zero mode contribution is not present in the time derivative of the correlatorUmeda, PRD 75 (2007) 094502

Datta, P.P., Quark Matter 2008, arXiv:0805.1174

Charmonia correlators at T>0

zero mode contribution is not present in the time derivative of the correlatorUmeda, PRD 75 (2007) 094502

Datta, P.P., Quark Matter 2008, arXiv:0805.1174

Estimating the zero mode contribution

vector axial-vector

Heavy quark susceptibility in quasi-particle picture

Zero mode contribution in quasi-particle picture

Datta, P.P., Quark Matter 2008, arXiv:0805.1174

Jakovác, P.P., Petrov, Velytsky, PRD 75 (07) 014506

Charmonium spectral functions at finite temperature

no large T-dependence but details are not resolved

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

8111

3s

+

~ 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

• resonance-like structures disappear already by 1.2Tc

• strong threshold enhancement above free case indication of correlations

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

c

• all P-states disappear already by 1.2Tc

but the derivatives of the of the correlators don not show any significant T-dependence

bc ,

Effective field theory approach for heavy quark bound states

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

The heavy quark mass provides a hierarchy of different energy scales

there are also different thermal scales in the weak coupling regime

potential is the matching parameter of EFT !

singlet-octet transition : Landau damping :

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

pNRQCD at finite temperature for static quarks

static limit : LO in 1/m -expansion

EFT for energy scale

If there are thermal contribution to the potentials

The potential for :

The potential for :

The potential for :

Laine, Philipsen, Romatschke, Tassler, JHEP 073 (2007) 054

Static meson correlators in SU(N) gauge theory

cyclic Wilson loops, Laine, Philipsen, Romatschke, Tassler, JHEP 073 (‘07) 054

Jahn, Philipsen, PRD 70 (’04) 074504

Numerical results in SU(2) gauge theory

Bazavov, P.P., Velytsky arXiv:0807.xxxx [hep-lat]

( adjoint triplet )

Summary and outlook

• The temperature dependence of quarkonium correlators in Euclidean time

is dominated by the zero mode contribution and are not sensitive to the change

in the spectral function related to melting of the bound states

• The zero mode contribution can be very well described by a quasi-particle model

• Potential models at finite temperature predict melting of all charmonium states,

yet are consistent with lattice data on the Eulcidean correlators

• In the weak coupling regime potential models at T>0 can be justified in the

EFT framework, however T>0 the potential has an imaginary part;

for r < Debye radius the thermal corrections go like powers of r

for r > Debye radius the real part of the potential is exponentially screened

• Static mesons correlators at T>0 can be studied in lattice QCD and indicate

survival of singlet states smaller than ~0.5/T and melting of octet states

Back-up slides

Juge et al, hep-lat/0103008

The color octet correlator only fixes the relative color orientation of static

quark anti-quark pair.

Perturbative relation between

to the color singlet free energy at high

temperatures