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

TL;DR

This study uses lattice QCD simulations to investigate the role of four-quark components and disconnected diagrams in iso-singlet scalar mesons, revealing their essential contribution to meson structure.

Contribution

First lattice QCD analysis emphasizing the importance of disconnected diagrams in four-quark state contributions to scalar mesons.

Findings

Disconnected diagrams are crucial for understanding tetraquark and molecular operator propagators.

Quark loops significantly influence the structure of iso-singlet scalar mesons.

The study demonstrates the importance of including disconnected diagrams in lattice QCD analyses.

Abstract

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.