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

TL;DR

This paper critiques the common assumption that factorizable diagrams in QCD sum rules are unrelated to tetraquark states, arguing that such contributions are essential and challenge previous conclusions about tetraquark formation in the large N_c limit.

Contribution

It highlights the importance of including factorizable diagrams in QCD sum rules and questions the standard interpretation of their role in tetraquark state formation.

Findings

Factorizable diagrams contribute significantly to the sum rules.

Tetraquark couplings scale as N_c, not constant.

The assumption that tetraquarks only appear in subleading contributions is challenged.

Abstract

Without excluding the contributions of factorizable Feynman diagrams in the color space to the QCD sum rules by hand, we cannot obtain the conclusion that the factorizable parts of the operator product expansion series cannot have any relationship to the possible tetraquark bound states. The tetraquark couplings $f_T$ are of the order $\mathcal{O}(N_c)$ rather than of the order $\mathcal{O}(N^0_c)$ in the large $N_c$ limit, the conclusion "a possible exotic tetraquark state may appear only in $N_c$-subleading contributions to the QCD Green functions" is a paradox.