pISSN 0374-4914 eISSN 2289-0041

## Research Paper

New Phys.: Sae Mulli 2020; 70: 836-840

Published online October 30, 2020 https://doi.org/10.3938/NPSM.70.836

## Discussion on the $J^{PC}=0^{--}$ Tetraquark of $u$ and $d$ Quarks within the QCD sum rule

Hee-Jung LEE*

Department of Physics Education, Chungbuk National University, Cheongju 28644 Korea

Correspondence to:hjl@cbnu.ac.kr

Received: July 17, 2020; Revised: August 11, 2020; Accepted: August 13, 2020

### Abstract

Using the QCD sum rule including the contributions from the instanton and the operator product expansion up to the dimension 10 operators of $O(\alpha_{s})$, we discuss the tetraquark state with the quantum numbers $J^{PC}=0^{--}$ consisting of a scalar diaquark and a pesudoscalar diquark of $u$ and $d$ quarks. From the QCD sum rule analysis, we found that the above tetraquark state of $J^{PC}=0^{--}$ would not exist for masses below 2 GeV. This result is similar to the result from a previous study\cite{5} in which the QCD sum rule without the contribution from the instanton was applied to analyze the tetraquark state with $u$ and $s$ quarks that had the same structure of the tetraquark state as in this work.

Keywords: Tetraquark, QCD sum rule, OPE, Instanton