Charmonium spectrum with the disconnected diagram in full QCD

JPS meeting

9 - 12 September 2003 Miyazaki Japan

T.Umeda ( YITP, Kyoto-Univ. )

and

H.Matsufuru ( YITP, Kyoto-Univ. )

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JPS meeting 2003 Sep. @Miyazaki

Contents

Introduction

Quenched study

Neglected effects

Calculation of disconnected diagrams

Lattice setup

Numerical results

Summary & Outlook

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Charmonium hyperfine splitting on the lattice

Introduction

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Charmonium spectrum on the lattice QCD

NRQCD

HQET

Fermilab

Anisotropic lattice

Good agreement with the experimental value

except for the hyperfine splitting

Quenched lattice QCD

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JHEP08(2003)022

QCD-TARO Collabration

Isotropic lattice

with a = 0.1~0.04 fm

( 1/a = 2~5 GeV )

Non-perturbative Csw

Nucl.Phys.B491(1997)323

M. Lüscher et al.

m(J/psi) – m(eta_c) = 77(2)(6) MeV in the continuum limit

30−40% smaller than the experimental value = 117 MeV

Dynamical quark effects

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Nucl. Phys. B(PS)119(2003)586

M.di Pierro et al.

valenc quark : Fermilab action

sea quark : KS quark

Nf = 0, 3, 2+1

no continuum limit a = 0.13 fm

Other full QCD studies Dynamical quark effects ~ 10%

T.Manke et al., Phys. Rev. D62 (2000) 114508.

C.Stewart and R.Koniuk, Phys. Rev. D63(2001) 054503.

OZI forbidden “disconnected” diagram

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Disconnected diagrams are neglected

because high cost & very small contribution

however, it may contribute to HFS ~ O(10) MeV ?

Charmonium correlators

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: quark propagator

( Pseudoscalar, Vector )

source & sink operators are extended with

disconnected diagrams are evaluated with

the complex Z2-noise method

Lattice setup

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Sea quark : Nf=2 KS quark : m_q=0.1

plaquette gauge : beta=5.50

lattice size : 12^3 x 24

lattice spacing : a=0.16fm (1/a=1.2GeV) set by r_0

16,000 traj. ( measurement at every 5 traj. )

Valence quark : Fermilab action

Csw : tadpole improved tree-level (u_0 in Landau gauge)

kappa=0.09342 set by m(J/psi)

Z2-noise method

N_noise=600

Smeared operators

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Effective mass plot

of connected diagram C(t)

Smearing functions are

determined from wavefunction

Ground states dominate at t~2

m(J/psi) – m(eta_c) = 0.0676 ( ~ 81 MeV )

Disconnected diagram contributions

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very preliminary

When ground state dominates,

We have

Too noisy at large t

Contributions of the disconnected diagram to HFS ~ O(1)MeV ?

Summary & Outlook

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We discuss the problem of charmonium HFS

and consider a possibility of disconnected diagram contributions

Disconnected diagram contributions are very small

or hidden by large error

more config. or/and Z2-noise sample

improved noise method

Same calculations with smaller valence quark mass

extrapolation from light quark mass region

Cutoff & sea-quark mass dependences

Appendix: light quark region

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Appendix: Z2-noise method

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Takashi Umeda

2003-09-04T17:47:02

Takashi Umeda