MEM Analysis of Glueball Correlators at T>0

speaker

Noriyoshi ISHII (RIKEN, Japan)

in collaboration with

Hideo SUGANUMA (TITECH, Japan)

START

Introduction/backbround

At T>0 (even below Tc)

QCD vacuum changes• reduction of the string tension• partial restoration of the chiral symmetry

hadronic properties change• light • charmonium• glueball

qq

Important precritical phenomena of QCD phase transition

The glueball mass reduction near Tc is suggested by the dual Meissner picture of the confinement.

H.Ichie et al., Phys.Rev.D52 (1995) 2944.

Recently, tested by the quenched lattice QCD.

N.Ishii et al., Phys.Rev.D66 (2002) 014507.N.Ishii et al., Phys.Rev.D66 (2002) 094506.

Reiew of the result of the χ² fit analyses •N.Ishii et al., Phys.Rev.D66(2002)014507.

•N.Ishii et at., Phys.Rev.D66(2002)094506.

SU(3) lattice QCD result of glueball correlator at T>0.

Narrow peak ansatz

Pole mass reduction

)(300MeV

The Breit-Wigner ansatzThermal width broadening

Modest reduction of peak center

MeV 300)( CT

MeV 1000

)(

0

)(),()( AKdG

2/sin

)2/(cosh),(

K

χ² analysis needs ansatz on the shape of A(ω)

It is not always easy to determine which ansatz is the most probable one.

Maximum Entropy Method(MEM)

This can be solved by MEM.

MEM requires no such ansatz. ⇒reconstructed spectral function directly based on the lattice QCD data.

Our aim is to use MEM

to reconstruct the spectral function A(ω)

to perform further studies of the properties of the glueball peak at finite temperature.

cf.) M.Asakawa et al., Prog.Part.Nucl.Phys. 46 (2001) 459.

SmearingUse of the extended operator (smearing) is one of the most useful techniques to enhance the low energy spectra.

However, it has a disadvantage that it makes the interpretation of resulting peak nontrivial. --- it can create an unphysical peak !

Example [free gg O(α ｓ⁰） ]

4)( A

4/)(exp)( 24 A

non-smeared case

smeared case with the smearing size ρ

Still, we emphasize that the smearing works as an useful tool to obtain information about the mass and the width of an established resonance. --- although it fails to provide an information on the corresponding decay constant

smearing

Our aim is to study the properties (mass and thermal width) of the established glueball peak below Tc

We are going to use the smearing technique.

)0()( akl

akl

aij

aij GGGG

More about the use of the smearing

1. Our numerical results for nonsmeared case are still unstable (due to just limited time).

2. The glueball peak is negligibly small in the unsmeared spectral function.

We use the smearing method, and concentrate on the properties of the lowest glueball peak in the region T<Tc～

– Gauge config by anisotropic Wilson action:

– Lattice spacings are determined from the string tension:

– Lattice size: 20³×Nt with various Nt.

– number of gauge config: 5,000-9,900, (bin size: 100)

– For each T, we pick up gauge configs every 100 sweeps after skipping 20,000 sweeps for thermalization.

– The critical temperature is determined

from the Polyakov loop susceptibility:

Tc = 280 MeV

4/ anisotropy lattice fm 021.0 fm, 084.0 tsts aaaa

)25.62( Clatt N

MeV 440Lattice Parameter Setup

MEM reconstruction of the spectrum

We apply the MEM to the normalized correlator G(τ)/G(0). (This artifitial normalization is just due to our fault. We are going to remove it in the near future.)

We adopt the suitable smearing. As the default model function m(ω), we adopt the free gg (with smearing with size ρ).

N is the normalization factor, which is determined as

(This is due to the artifitial normalization introduced above.)

We in principle follow the procedure explained in

M.Asakawa et al., Prog.Part.Nucl.Phys.46 (2001) 459.

4/)(exp)( 24 Nm

0

)(),0(1 mKd

T=130 MeV (low temperature case)

The solid line denotes the reconstructed spectrum

The reconstructed spectrum is devided into bins of the size ω=0.25 GeV. The such bin average is shown by the histogram.

The errorbars are estimated for the bin average.

T=253 MeV (high temperature case)

The solid line denotes the reconstructed spectrum

The reconstructed spectrum is devided into bins of the size ω=0.25 GeV. The such bin average is shown by the histogram.

The errorbars are estimated for the bin average.

T=275 MeV ( = Tc case)～

The solid line denotes the reconstructed spectrum

The reconstructed spectrum is devided into bins of the size ω=0.25 GeV. The such bin average is shown by the histogram.

The errorbars are estimated for the bin average.

Temperature dependence of the peak

We see the tendency that the peak becomes broader with the temperature.

Summary and Outlook

Summary:

We have applied Maximum Entropy Method (MEM) to the suitably smeared glueball correlator constructed with the anisotropic SU(3) lattice QCD below Tc.

We have seen the tendency that the peak becomes broader with the temperature, which supports the thermal width broadening of the glueball at finite temperature..

Outlook:

It is very interesting to consider the situation above Tc.

What happens to the glueball correlation above Tc ??

It is very important and interesting to apply MEM to non-smeared correlators. (So far, the numerical results are still unstable.)