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We study the possible significance of four-quark states in the iso-singletscalar mesons ($J^{PC}=0^{++}$, $I=0$) by performing two-flavor full latticeQCD simulations on an $8^3 \times 16$ lattice using the improved gauge actionand the clover-improved Wilson quark action. In particular, we evaluate thepropagators of molecular and tetra-quark operators together with singlydisconnected diagrams. In the computation of the singly disconnected diagramswe employ the $Z_2$-noise method with the truncated eigenmode approach. We showthat the quark loops given by the disconnected diagrams play an essential rolein propagators of tetraquark and molecular operators.

Lattice QCD study of four-quark components of the isosinglet scalar mesons: Significance of disconnected diagrams