OPE and quark-hadron duality for two-point functions of tetraquark currents in $1/N_c$ expansion

TL;DR

This paper analyzes the Operator Product Expansion and quark-hadron duality for tetraquark currents' two-point functions, highlighting the role of factorizable and nonfactorizable parts within the $1/N_c$ expansion in QCD.

Contribution

It clarifies that factorizable parts of the OPE are saturated by ordinary hadrons, while potential tetraquark states appear only in nonfactorizable, $1/N_c$-suppressed contributions.

Findings

Factorizable OPE parts are saturated by ordinary hadrons.

Tetraquark states may only appear in nonfactorizable, suppressed contributions.

Exotic tetraquarks are consistent with large-$N_c$ QCD properties.

Abstract

We discuss the Operator Product Expansion (OPE) and quark-hadron duality for two-point Green functions of tetraquark currents. We emphasize that the factorizable part of the OPE series for such Green functions, including nonperturbative contributions described by QCD condensates, is saturated by the full system of ordinary hadrons and therefore cannot have any relationship to the possible tetraquark bound states. Possible tetraquark bound states may be contained in nonfactorizable parts of these Green functions. In the framework of the $1/N_c$ expansion in QCD$(N_c)$, nonfactorizable parts of the two-point Green functions of tetraquark currents provide $N_c$-suppressed contributions compared to the $N_c$-leading factorizable parts. A possible exotic tetraquark state may appear only in $N_c$-subleading contributions to the QCD Green functions, in full accord with the well-known rigorous properties of large-$N_c$ QCD.