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.
Highlights
The correlation functions of two local colorless currents are the simplest gauge-invariant Green functions that have a unique decomposition in terms of the physical hadron states
We emphasize that the factorizable part of the operator product expansion (OPE) series for such Green functions, including nonperturbative contributions described by QCD condensates, is saturated by the full system of ordinary hadrons and cannot have any relationship to the possible tetraquark bound states
We discussed in great detail the OPE for two-point Green functions of the bilinear and quadrilinear colorless quark currents at large Nc and emphasized the qualitative differences between these two objects: 014012-8
Summary
The correlation functions of two local colorless currents are the simplest gauge-invariant Green functions that have a unique decomposition in terms of the physical hadron states. For the discussion of exotic states of any structure [in QCDðNcÞ one may have a very rich structure of colorless hadron states] the following features of large-Nc QCD are of special significance: as shown by Witten [7], large-Nc Green functions are saturated by noninteracting ordinary mesons This means, in particular, that any possible exotic states may appear only in Nc-subleading contributions to the QCDðNcÞ Green functions [7,8]. (i) We show that the T-adequate sum rules in SUðNcÞ should be based on appropriate nonfactorizable parts of the OPE for two-point functions of the tetraquark currents In this way, the tetraquark contributions are compatible with the well-known rigorous property of QCD at large Nc: the Nc-leading Green functions are saturated by the ordinary mesons; any exotic states may appear only in Nc-subleading contributions.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
