pISSN 0374-4914 eISSN 2289-0041

## Research Paper

New Physics: Sae Mulli 2014; 64: 526-530

Published online May 30, 2014 https://doi.org/10.3938/NPSM.64.526

## Analysis of the Scalar Meson $f_{0}$(980) as a Bound State of Two $\eta$ Mesons within the QCD Sum Rule Including the Contribution from the Instanton

Hee-Jung LEE*

Department of Physics Education, Chungbuk National University, Cheongju 361-763, Korea

Correspondence to:hjl@cbnu.ac.kr

Received: April 1, 2014; Revised: April 21, 2014; Accepted: April 21, 2014

This is an open-access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

### Abstract

Using the quantum chromodynamics (QCD) sum rule including the contributions from the instanton and the anti-instanton, we re-analyze whether the scalar meson $f_{0}$(980) can be described as a simple bound state of two pseudoscalar $\eta$ mesons. We calculate the contributions to the QCD sum rule from the instanton and the anti-instanton, which act in two quarks and three quarks of different flavors, by interpolating the current of $f_{0}$(980) for simple bound state of the two pseudoscalar $\eta$ mesons. According to the analysis with the QCD sum rule including the contributions both from operators up to the energy dimension 10 with the operator product expansion (OPE) and from the instanton and anti-instanton, describing $f_{0}$(980) as a simple bound state of two $\eta$ mesons as in the case without the instanton-anti-instanton contributions included in the QCD sum rule, appears difficult.

Keywords: Instanton, Scalar mesons, QCD sum rule, OPE