21-26 June 2004, Lattice 2004

Fermi National Accelerator Laboratory, IL, USA

Takashi Umeda ( YITP, Kyoto-Univ. )

Hideo Matsufuru ( CRC, KEK )

Lattice 2004 / 21-26 June 2004

created by

Charmonium properties at finite temperature

on quenched anisotropic lattices

Contents

15

1) Introduction

2) Our approach

3) Spectral function of charmonium

4) Heavy quark free energy

5) Discussion & Summary

Charmonium properties at T>0 as signals of QGP

Charmonium spectral function

reconstructed from temporal correlators

Potential model analysis

with heavy quark free energies

Lattice 2004 / 21-26 June 2004

Introduction

15

Charmonium is an important signal for formation of QGP

in heavy ion collision experiments.

Theoretical understanding

potential models

Mass shift near Tc

T.Hashimoto et al., Phys. Rev. Lett. 57 (1986) 2123.

suppression above Tc

T.Matsui and H.Satz, Phys. Lett. B178 (1986) 416.

Lattice QCD

Meson correlators

T.Umeda et al., Int. J. Mod. phys. A16 (2000) 2215.

strong spatial correlation at T~1.5Tc

J

/



Lattice 2004 / 21-26 June 2004

Charmonium spectral function at T>0

15

Bielefeld group (light mesons, diquark, charmonium)

F.Karsch et al., Phys. Lett. B530 (2002) 147.

I.Wotzorke et al., Nucl. Phys. B(PS)106 (2002) 513.

S.Datta et al., hep-lat/0208012(Lattice02) hep-lat/0312037.

Asakawa, Hatsuda and Nakahara (light meson, charmonium)

M..Asakawa et al., hep-lat/0208059(Lattice02).

M.Asakawa and T.Hatsuda, Phys.Rev.Lett.92 (2004) 012001.

Our works (charmonium, light mesons)

K.Nomura et al., hep-lat/0209139 (Lattice02).

T.Umeda et al., hep-lat/0211003 (Eur.Phys.J.dirC).

T.Umeda et al., hep-lat/0309178 (Lattice03).

Lattice 2004 / 21-26 June 2004

All study supports an existence of hadronic mode just above Tc

Our approach for spectral function

15

Anisotropic lattice

Analysis procedures

Maximum entropy method (MEM)

Y.Nakahara et al., Phys. Rev. D60 (1999) 091503.

Constrained curve fitting

P.Lepage et al., Nucl. Phys. B(PS)106 (2002) 12.

We use these two methods in complementary manner

smearing operators

enhancement of low frequency modes

this may cause artificial peak even in free quark case

we have to investigate a smearing function dependence

Lattice 2004 / 21-26 June 2004

Lattice setup

15

Nt 160 32 30 29 27 26 24 20 16

T/Tc ~0 0.88 0.93 0.97 1.04 1.08 1.17 1.40 1.75

Anisotropic quenched lattices:

T.R.Klassen, Nucl. Phys. B533 (1998) 557.

GeV (set by hadronic radius )

Quark action:

O(a) improved Wilson action

H.Matufuru et al., Phys. Rev. D64 (2001) 114503.

Temperatures : phase transition occurs at just Nt=28

statistics: 1000conf. x 16src. (500conf. for T=0)



=

a

s

/

a

t

=

4

a

s

−

1

=

2.030



13



Lattice 2004 / 21-26 June 2004

r

0

20

3

×

Nt

Our lattices cover T/Tc=0~1.75 with same lattice cutoff

Temporal correlator of charmonium

15

No change of correlators below Tc

Significant change appears above Tc

Lattice 2004 / 21-26 June 2004

temperature dependence of effective mass for PS & V channels

Result above Tc

15

correlators change gradually as temperature increases

peak structure suvives above Tc,

peak positions are similar to the result at T=0

vector channel shows large change at high T

Lattice 2004 / 21-26 June 2004

Result above Tc

15

comparison between smeared and half-smeared results

at T/Tc=1.4 and 1.75 ( Nt=20 and 16 )

in PS channel at T=1.40Tc

smeared & half-smeared results have similar peaks

==> physical peak exists at T=1.40Tc

The others show artificial peaks / MEM does not work

Lattice 2004 / 21-26 June 2004

Constrained curve fitting analysis

15

Constrained curve fit results have large systematic uncertainties

due to input parameters as prior knowledge

small or no mass shift above and below Tc

wider peak structure above Tc

preliminary

preliminary

Lattice 2004 / 21-26 June 2004

Heavy quark free energy

15

Lattice 2004 / 21-26 June 2004

These results are inconsistent with some Potential model predictions

What do we use as a “heavy quark potential” ?

c.f. O.Kaczmarek et al., Phys. Lett. B543 (2002) 41.

“Potential” for a system with T, V=const. (Hermholtz) free energy

The free energy can be extracted from polyakov loop correlations

exp



−

F

ave



r



T



〈

Tr

L



r



Tr

L



0



〉

exp



−

F

sing



r



T



〈

Tr

L



r



L



0



〉

( color averaged )

( color singlet )

∝

∝













exp



−

F



r



t



〈

W



r

,

t



〉

∝

( ground state of

color singlet potential )





and also from Wilson loop , W(r,t) (same analysis as T=0)

†

†

Heavy quark potentials at T<Tc

15

Lattice 2004 / 21-26 June 2004

effective masses at T/Tc = 0~1.75

==> no change below Tc

Schrödinger eq. with singlet free energy at T<Tc

==> 50~80MeV larger than T=0

lowest peak of spectral function x thermal averaged singlet potential

O ground state of singlet potential

Heavy quark potentials at T>Tc

15

Lattice 2004 / 21-26 June 2004

Schrödinger eq.

with singlet free energies

(T=1.08Tc) bound state with

170MeV smaller mass than T=0

(T 1.40Tc) no bound state

or too wide wave function

Charmonium bound states survive above Tc

roughly consistent with the results of spectral function

But more discussion is needed !

≥

Relation to the QGP signals

15

Lattice 2004 / 21-26 June 2004

Charmonium mass shift below Tc

==> lowest peak position of charmonium spectral function

no mass shift in our lattice results

J/psi suppression above Tc

estimation of actual amount of produced J/psi in experiments

is related to mechanism of J/psi production

c.f. P.Crochet, Nucl. Phys. A715 (2003) 359.

==> pair can bound or not in the deconfinement phase

(*) most of pairs are produced as color octet pair

c.f. M.Gluck et al., Phys. Rev. D17 (1978) 2324.

Contribution of octet potential may also be important.

c



c

c



c

Summary

15

KEK Workshop / 28-30 Jan. 2004

We study charmonium properties

on quenched anisotropic lattices at T/Tc=0.88~1.75

Reconstruction of spectral functions from temporal correlators

below Tc

no change from T=0

above Tc

peak structure may survive upto T=1.4Tc

peak width grows as temperature increases

Potential model with the heavy quark free energy

lowest peak of charmonium spectral function

<==> ground state of color singlet free energy

It is important to discuss the signals of QGP formation

using these data from lattice QCD calculations

Takashi Umeda

2003-09-04T17:47:02

Takashi Umeda