^{1}

^{1,2,3}

^{4}

^{3}.

We study details of QCD sum rules

Motivated by increasing experimental evidence for narrow near-threshold hadron resonances with favorable interpretation as tetraquark and pentaquark hadrons (of minimal parton configurations consisting of four and five quarks, respectively)

For a proper QCD analysis of possible tetraquarks and for the selection of the appropriate Feynman diagrams, the understanding of the four-quark singularities of Feynman diagrams plays a crucial role. In Refs.

Independently of this line of research, numerous works deal with the analysis of tetraquark states by QCD sum rules (see Refs.

For Green functions of currents

References

We will prove that the procedures adopted in SR analyses of exotic states

QCD sum rules utilize local interpolating currents, so it suffices to consider tetraquark interpolating currents in the form of products of two colorless bilinear quark currents

The parameter

All previous QCD SR applications to exotic states

We will show that quark-hadron duality relations for Green functions involving exotic tetraquark currents exhibit a specific feature: an exact cancellation of the

Let us consider tetraquarks involving two quarks of flavors

An appropriate definition of

Figure

Feynman diagrams for a direct two-point function of tetraquark currents

To show that this indeed happens, we inspect the OPE and the hadron representation for the two-point direct correlation function

QCD SR for the two-point function

Conventional QCD SR for the two-point function

Final tetraquark QCD SR relating the nonfactorizable OPE contributions to the two-point function

Direct Green functions

Feynman diagrams for a direct three-point function as obtained by merging vertices in

For correlators with recombination topology (Fig.

Feynman diagrams for a recombination two-point function of tetraquark currents as obtained by merging vertices in the recombination four-point function of bilinear quark currents. Diagrams (a) and (b) on the lhs do not contain four-quark singularities in the

We scrutinized the derivation of SVZ sum rules for exotic correlation functions of tetraquark currents

The duality relations for exotic correlators are fundamentally different from those for correlators of bilinear quark currents: the

This result is quite general and valid for any color structure of

For clarity, we demonstrated the aforementioned general property by considering currents

The cancellation of

The proper application of tetraquark QCD SR requires the knowledge of presently unknown nonfactorizable

The authors are grateful to V. Anisovich, T. Cohen, L. Gladilin, F.-K. Guo, M. Knecht, L. Maiani, B. Moussallam, A. Polosa, V. Riquer, S. Simula, B. Stech, and W. Wang for valuable discussions. D. M. acknowledges support from the Austrian Science Fund (FWF), Project No. P29028. D. M. and H. S. are grateful for support under joint CNRS/RFBR Grant No. PRC Russia/19-52-15022. D. M. has the pleasure of thanking L. Maiani and W. Wang for hospitality during his visit to the T. D. Lee Institute.