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

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