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Aiming at self-consistent descriptions of multiquark hadrons (such as tetraquarks, pentaquarks, hexaquarks) by means of QCD sum rules, we note that the totality of contributions to two-point or three-point correlation functions that involve, respectively, either two or just a single operator capable of interpolating the particular multiquark under study can be straightforwardly disentangled into two disjoint classes defined by unambiguously identifiable members. The first is formed by so-called multiquark-phile contributions which indeed might support multiquarks. In the case of flavour-exotic tetraquarks, by definition composed of four (anti–) quarks of mutually different flavours, a tetraquark-phile contribution has to exhibit two or more gluon exchanges of appropriate topology. The second consists of contributions evidently not bearing any relation to multiquarks; these must be discarded when studying multiquarks by QCD sum rules. The first class only should enter the “multiquark-adequate” QCD sum rules for exotic hadrons.

We propose to increase the factual reliability of descriptions of exotic multiquark hadrons utilizing the approach to bound states of strongly interacting constituents known as QCD sum rules, by allowing exclusively all contributions that potentially bear some relevance for multiquark states to enter the correlation functions that form the main ingredient of this framework. The route to this goal is illustrated for the (presumably least involved) special case of tetraquark states.

Rare B-decays induced by flavour-changing neutral currents (FCNC) is one of the promising candidates for probing physics beyond the Standard model. However, for identifying potential new physics from the data, reliable control over QCD contributions is necessary. We focus on one of such QCD contributions – the charming loops – that potentially can lead to difficulties in disentangling new physics effects from the observable and discuss the possibility to gain control over theoretical predictions for charming loops.

Frequently, theoretical discussions of multiquark hadron states prove to be contaminated or even dominated by contributions of conventional hadrons. For the approach to QCD bound states in terms of QCD sum rules, we show how to get rid of all unwanted ordinary-hadron ballast by boiling down the traditional QCD sum-rule formalism to the nonconventional aspects in the focus of interest.

The properties of possibly existing tetraquarks are studied in the large-Nc limit of QCD by means of four-point correlation functions of meson currents. The necessity of a detailed analysis of the singularities of Feynman diagrams, by means of the Landau equations, to recognize those diagrams that might contribute to the formation of tetraquark states, is emphasized. It is found, in general, that tetraquarks, if they exist, should have narrow widths of the order of N-2c.

We embark on systematic explorations of the behaviour of tetraquark mesons, i.e., colour-singlet bound states of two quarks and two antiquarks, in the (idealized) limit of a large number of colour degrees of freedom, Nc,; of quantum chromodynamics, QCD. Considering the scattering of two ordinary mesons into two ordinary mesons, we start off with formulating a set of selection criteria that should enable us to unambiguously single out precisely those contributions to all encountered scattering amplitudes that potentially will develop tetraquark poles. Assuming that tetraquark mesons do exist and, if so, emerge in the contributions compatible with our criteria at largest admissible order of Nc; we deduce, for the categories of tetraquarks that exhibit either four or only two different open quark flavours, that the decay rates of these tetraquark types are, at least, of order 1/N2c and that internal consistency requires all the members of the first species to exist pairwise, distinguishable by their favoured two-ordinary-meson decay channels.

Two-ordinary-meson scattering in large-Nc QCD implies consistency criteria for intermediate-tetraquark contributions. Their fulfilment at Nc-leading order constrains the nature of the spectrum of genuinely exotic tetraquark states.

Applying the QCD sum-rule machinery in the so-called local-duality shape to heavy-light mesons reveals that, as a consequence of the non-zero mass gap between up and down quarks, the leptonic decay constants of the neutral and charged versions of the D, D*, B and B* mesons differ by approximately 1 MeV.

This presentation reviews the main results of our recent work [1] on rare radiative leptonic decays Bd,s → γμ+μ- and Bd,s → γe+e- induced by flavour-changing neutral currents (FCNC) in the Standard Model.

Compared with lattice QCD, isospin breaking of heavy-meson decay constants from QCD sum rules agrees for D mesons but disagrees (by a factor of four) for B mesons.

We formulate rigorous criteria for selecting diagrams to be taken into account in the analysis of potential polyquark (tetra or penta) poles in QCD. The central point of these criteria is the requirement that the Feynman diagrams for the relevant Green functions contain four-or five-quark intermediate states and the corresponding cuts. It is shown that some diagrams which “visually”7 seem to contain the four-quark cuts, turn out to be free of these singularities and therefore should not be taken into account when calculating the tetraquark properties. We then consider large-Nc QCD which in many cases provide qualitatively correct picture of hadron properties and discuss in detail the tetraquark states. For the “direct” and the “recombination” four-point Green functions, which may potentially contain the tetraquark poles, we formulate large-Nc consistency conditions which strongly restrict the behaviour of the tetraquark-to-ordinary meson transition amplitudes. In the end, these conditions allow us to obtain constraints on width of the potential tetraquark states at large Nc. We report that both flavor-exotic and cryptoexotic (i.e., flavor-nonexotic) tetraquarks, if the corresponding poles exist, have a width of order O 1 / N c 2 , i.e. they should be parametrically narrower compared to the ordinary q ¯ q mesons with a width of order O(1/Nc). Moreover, for flavor-exotic states, the large-Nc consistency conditions require two narrow flavor-exotic states, each of these states coupling dominantly to one specific meson-meson channel.

We determine the strong couplings of three mesons that involve, at least, one ηc or J/ψ meson, within the framework of a constituent-quark model by means of relativistic dispersion formulations. For strong couplings of J/ψ mesons to two charmed mesons, our approach leads to predictions roughly twice as large as those arising from QCD sum rules.

Revisiting the QCD sum-rule description of exotic hadron states, we argue that, in order to arrive at trustable analyses of, for instance, strong decay widths of multiquarks, it is inevitable to adopt the QCD sum-rule approach beyond the leading perturbative level.

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 O(α0s) correlation functions provide the bulk of the hadron observables, e.g., of the form factor; inclusion of radiative corrections O(αs) 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.

Revisiting the strong couplings of three mesons, each of which involves at least one charm quark, proves clear disaccord between quark-model and QCD sum-rule results.

We obtain predictions for B(s) → e+e−γ and B(s) → μ+μ−γ decays. All the contributions containing long-distance QCD effects are calculated in the framework of relativistic quark model. The contributions of the light vector-meson resonances related to the virtual photon emission from valence quarks of the B-meson are included. The highest branching ratios for the radiative leptonic B-decays are B(B̄0s → e+e−γ) = 18.8×10−9 and B(B0s → μ+μ−γ) = 12.2×10−9. We also give the distribution of the foward-backward asymmetry.

QCD sum rules for decay constants of heavy mesons with u or d quark yield for B mesons much less isospin breaking than lattice QCD but good agreement for D mesons.

In spite of undeniable similarities of the applied techniques, somewhat different challenges are encountered when extracting, from QCD sum rules derived from two-point correlators of appropriate interpolating heavy–light quark currents, the decay constants of charmed mesons of pseudoscalar nature, on the one hand, or of vector nature, on the other hand. This observation justifies a rather careful reassessment of the corresponding results.

Our recently completed analysis of the decay constants of both pseudoscalar and vector beauty mesons reveals that in the bottom-quark sector two specific features of the sum-rule predictions show up: (i) For the input value of the bottom-quark mass in the M̅S̅ scheme m̅b(m̅b) ≈ 4:18 GeV; the sum-rule result fB ≈ 210–220 MeV for the B meson decay constant is substantially larger than the recent lattice-QCD finding fB ≈ 190 MeV: Requiring QCD sum rules to reproduce the lattice-QCD value of fB yields a significantly larger b-quark mass: m̅b(m̅b) = 4:247 GeV: (ii) Whereas QCD sum-rule predictions for the charmed-meson decay constants fD; fDs, fD* and fDs* are practically independent of the choice of renormalization scale, in the beauty sector the results for the decay constants—and especially for the ratio fB* / fB—prove to be very sensitive to the specific scale setting.