Abstract
We discuss the specific features of extracting properties of the exotic polyquark hadrons (tetraquarks, pentaquarks) compared to the usual hadrons by the QCD sum-rule approach. In the case of the ordinary hadrons, already the one-loop leading-order correlation functions provide the bulk of the hadron observables, e.g., of the form factor; inclusion of radiative corrections modifies already nonzero one-loop contributions. In the case of an exotic hadron, the situation is qualitatively different: discussing strong decays of an exotic tetraquark meson, which provide the main contribution to its width, we show that the disconnected leading-order diagrams are not related to the tetraquark properties. For a proper description of the tetraquark decay width, it is mandatory to calculate specific radiative corrections which generate the connected diagrams.
Highlights
One of the most famous applications of the method of QCD sum rules is the calculation of the hadronic ground-state properties from the QCD correlation functions involving power corrections
Let us emphasize, that not all contributions to two-point functions of exotic interpolating currents are related to the properties of exotic states
These are the form factors related to the connected parts of the three-point functions involving two exotic interpolating currents, T ; so far, no operator product expansion (OPE) calculations for the corresponding quantities are available in the literature
Summary
To recall the basics of the method, we briefly review QCD sum rules arising from two-point functions. One considers the correlation functions, i.e., the vacuum expectation values of the T -products of the interpolating currents. The basic concept of the method is the difference between the physical QCD vacuum, |Ω , which has a complicated structure, and the perturbative QCD vacuum, |0 : properties of the physical vacuum |Ω are characterized by the condensates — nonzero expectation values of gauge-invariant operators over the physical vacuum: Ω| : O(0, μ) : |Ω 0 (see [5, 6] for the recent determinations). As soon as we have an algorithm [10, 11] of fixing the effective threshold seff(τ) at our disposal, Eq (8) provides the decay constant f. To this end, we need either to know the hadron mass M or to set τ = 0
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