Tetraquark-adequate formulation of QCD sum rules

We study details of QCD sum rules \`a la Shifman-Vainshtein-Zakharov for exotic tetraquark states. We point out that duality relations for correlators involving exotic currents have fundamental differences compared with the duality relations for the correlators of bilinear quark currents: namely, the $O(1)$ and $O(\alpha_s)$ [$\alpha_s$ the strong coupling constant] terms in the operator product expansion for the exotic correlators exactly cancel against the contributions of the two-meson states on the hadron side of QCD sum rules. As a result, the tetraquark properties turn out to be related to the specific non-factorizable parts of the exotic Green functions; the relevant non-factorizable diagrams start at order $O(\alpha_s^2)$.