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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., 6 pages, 6 figures

This talk presents our recent results [1] on nonfactorizable charm-loop contributions to the amplitudes of rare exclusive $B$-decays induced by flavour-changing neutral currents (FCNC). We show that such contributions induced by a soft-gluon emission from the charm-quark loop may be expressed via three-particle quark-antiquark-gluon distribution amplitude (3DA) of the $B$-meson, $\langle 0|\bar q(x)G_{\mu\nu}(y)b(0)|B(p)\rangle$, and the knowledge of the full functional dependence of the latter quantity on the variable $(x-y)^2$ is necessary for a proper summation of potentially large terms $O\left(\left(\Lambda_{QCD}m_b/m_c^2\right)^n\right)$ in the amplitudes of FCNC $B$-decays.

We discuss the general properties of the $B$-meson decay form factors $F(q^2,q'^2)$, describing $B$-meson decays induced by two currents, e.g., $B$-decays into four leptons in the final state. We study the analytic properties of these complicated objects and identify those regions of $q^2$ and $q'^2$, where perturbative QCD can be applied for obtaining predictions for the physical form factors.

The generalization of the color gauge group SU(3) to SU ( N c ) , with N c taking arbitrarily large values, as had been proposed and developed by ’t Hooft, has allowed for a decisive progress in the understanding of many qualitative, as well as quantitative, aspects of QCD in its nonperturbative regime. In particular, the notion of valence quarks receives there a precise meaning. The present work reviews the various aspects of the extension of this approach to the case of tetraquark states, which are a category of the general class of exotic states, also called multiquark states, whose internal valence-quark structure does not match with that of ordinary hadrons, and which have received, in recent years, many experimental confirmations. The primary question of describing, or probing, on theoretical grounds, multiquark states is first examined. The signature of such states inside Feynman diagrams in relation with their singularities is highlighted. The main mechanisms of formation of tetraquark states, provided by the diquark model and the molecular scheme, are considered together with their specific implications. The properties of tetraquark states at large N c are analyzed through the Feynman diagrams that describe two-meson scattering amplitudes. It turns out that, in that limit, the possible formation of tetraquark states is mainly due to the mutual interactions of their internal mesonic clusters. These essentially arise from the quark-rearrangement, or quark-interchange, mechanism. In coupled-channel meson–meson scattering amplitudes, one may expect the occurrence of two independent tetraquark states, each having privileged couplings with the two mesons of their dominant channel. The question of the energy balance of various schemes in the static limit is also analyzed. The clarification of the mechanisms that are at work in the formation of tetraquarks is the main outcome from the large- N c approach to this problem.

In perturbation theory, the spectral densities of two-point functions develop non-integrable threshold singularities at higher orders. In QCD, such singularities emerge when calculating the diagrams in terms of the pole quark mass, and they become stronger when one rearranges the perturbative expansion in terms of the running quark mass. In this paper we discuss the proper way to handle such singularities., Comment: 7 pages, Extended version, Proof by induction is given in Appendices A and B, Conclusions remain unchanged

International audience; Considering quantum chromodynamics in the consistent limit of simultaneous correlated increase of the number of colours, $N_c$, beyond bounds and decrease of the strong coupling to zero allows for solid statements about qualitative features of the class of “truly exotic” tetraquark mesons carrying four mutually distinct quark flavours. Consistency criteria extracted from correlation functions for two-ordinary-meson scattering suggest the existence of more than one such tetraquarks, at least, of two tetraquarks of identical quark-flavour content and large-$N_c$ behaviour of the total decay widths but differing in, and hence discriminable by, their predominant decay modes into two conventional mesons. This pairwise appearance is in conflict with the unique variant of such a four-quark bound state arising from the binding of diquark and antidiquark to a tetraquark by the strong interactions.

We consider quark-hadron duality relations and QCD sum rules for correlators involving exotic tetraquark currents, here specializing to the case of quark-exchange processes. We point out the differences they exhibit with respect to the cases involving ordinary bilinear quark currents. Based on the observation that only diagrams possessing at least four-quark singularities can contribute to the formation of tetraquark states, we show that the quark-hadron duality relations and the corresponding sum rules split into two non-overlapping relations. The ultimate tetraquark-adequate QCD sum rule is concerned only with one of these relations, in which the operator product expansion starts with diagrams of order $O(\alpha_s^2)$., Comment: 8 pages, version to appear in Phys. Rev. D

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., Comment: 7 pages, 7 figures, talk presented at the "XXIV International Workshop on High Energy Physics and Quantum Field Theory" (22 - 29 September 2019, Sochi, Russia)

With the experimental observation of several credible candidates for multiquark hadrons, the latter states re-entered the focus of interest of theoretical strong-interaction physics. Proper treatment of hadronic bound states by quantum chromodynamics, QCD, the quantum field theory governing all strong interactions, necessitates a nonperturbative approach. A well-established framework of this kind is provided by QCD sum rules relating hadron features to the parameters of QCD. Conceptual reconsideration, however, reveals that, in order to really match the peculiarities of multiquarks, the long-standing conventional QCD sum-rule techniques evidently must be subjected to considerable modification. The so far overlooked necessity for such adaptations is most easily demonstrated for the case of least complexity, that is, for tetraquarks, bound states of two quarks and two antiquarks., 6 pages, 6 figures, contributed to the "European Physical Society Conference on High Energy Physics - EPS-HEP 2019" (10 - 17 July 2019, Ghent, Belgium)

International audience; Flavour-exotic tetraquark mesons, by definition bound states of two quarks and two antiquarks of four mutually different quark flavours, are, for given Lorentz features, subject to two incompatible constraints: On the one hand, within quantum chromodynamics a formation of compact tetraquark states is most easily envisaged by merging two colour-antisymmetric two-quark clusters, a diquark and an antidiquark. This path, however, leads to merely a single tetraquark state of chosen Lorentz characteristics. On the other hand, in the limit of the number of colour degrees of freedom growing beyond bounds, internal consistency at leading order calls for the presence of (at least) two of such tetraquark states of identical quark-flavour composition. The failure of attempts to reconcile these two contradictory insights suggests the nonexistence of compact flavour-exotic tetraquark mesons.

It is shown that the multiquark gauge-invariant operators can, in general, be decomposed into combinations of products of ordinary hadronic operators, exhibiting their cluster reducibility. The latter property inhibits the formation of completely compact multiquark bound states. Multiquark operators still play a crucial role in the description of exotic states in regions of configuration space where the hadronic clusters are close to each other. Our proof gives a foundation for a unified viewpoint, where the multiquark-type and the molecular-type approaches play complementary roles, at the gauge-invariant nonlocal operator level., 16 pages, 12 figures. A sentence has been changed in the abstract. A few minor changes in the main text

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 $O(\alpha_s^2)$., Comment: 6 pages, version to be published in Physical Review D

A salient feature shared by all tetraquark candidates observed in experiment is the absence of flavor-exotic states of the type $\bar a b\bar c d$, with four different quark flavors. This phenomenon may be understood from the properties of large-$N_c$ QCD: On the one hand, consistency conditions for flavor-exotic Green functions, potentially containing these tetraquark poles, require the existence of two tetraquarks $T_A$ and $T_B$: each of them should decay dominantly via a single two-meson channel, $T_A\to M_{\bar a b}M_{\bar c d}$ and $T_B\to M_{\bar a d}M_{\bar c b}$, with suppressed rates $T_A\to M_{\bar a d}M_{\bar c b}$ and $T_B\to M_{\bar a b}M_{\bar c d}$. On the other hand, we have at hand only one diquark-antidiquark flavor structure $(\bar a \bar c)(b d)$ that might produce a compact tetraquark bound state. Taking into account that the diquark-antidiquark structure is the only viable candidate for a compact tetraquark state, one concludes that it is impossible to have two different narrow tetraquarks decaying dominantly into different two-meson channels. This contradiction suggests that large-$N_c$ QCD does not support the existence of narrow flavor-exotic tetraquarks. This argument does not rule out the possible existence of broad molecular-type flavor-exotic states, or of molecular-type bound states lying very close to the two-meson thresholds., 8 pages

We explore, by a rather peculiar limit of QCD sum rules subject to a Borel transformation (realized by allowing the related Borel mass parameter to approach infinity), how the small difference of the masses of up and down quark translates into the leptonic decay constants of pseudoscalar or vector heavy-light mesons. For the charmed and bottom mesons, we find that the decay constants of their lowest-lying charged and neutral representatives should differ by an amount of the order of 1 MeV., 8 pages, 4 figures, talk presented at "XIII Quark Confinement and the Hadron Spectrum - Confinement2018" (31 July - 6 August 2018, Maynooth University, Ireland)

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 $D,$ $D^\ast,$ $B$ and $B^\ast$ mesons differ by approximately 1 MeV., 7 pages, 5 figures, talk presented at "QCD@Work 2018 - International Workshop on Quantum Chromodynamics: Theory and Experiment" (25 - 28 June 2018, Matera, Italy)

International audience; We analyse exotic tetraquark mesons — bound states formed by two quarks and two antiquarks — for the specific case of four different quark flavours within the framework of a well-defined limit of quantum chromodynamics characterized by the correlated growth without bound of the number of colour degrees of freedom and approach to zero of the coupling constant of the strong interactions. On the one hand, the assumption that the tetraquarks of the kind defined above show up, as poles in the amplitudes for the scattering of two ordinary mesons with flavour quantum numbers that match those of these tetraquarks, already at lowest possible order in an expansion in inverse powers of the number of colours implies the existence of two types of flavour-exotic tetraquarks, distinguishable by their dominant transitions to two ordinary mesons. On the other hand, we are aware of merely a single, unique colour-singlet arrangement of two quarks and two antiquarks capable of tolerating a compact flavour-exotic tetraquark, a bound state of colour-antisymmetric diquark and antidiquark. In view of these two clearly contradictory observations, we are led to the plausible conclusion that, within the considered limiting case of quantum chromodynamics, a conceivable explanation of the riddle might consist in the non-existence of any flavour-exotic tetraquarks in formof narrowstates.

Two-ordinary-meson scattering in large-$N_c$ QCD implies consistency criteria for intermediate-tetraquark contributions. Their fulfilment at $N_c$-leading order constrains the nature of the spectrum of genuinely exotic tetraquark states., Comment: 5 pages, 4 figures, contributed to "QCD@Work 2018 - International Workshop on Quantum Chromodynamics: Theory and Experiment" (25 - 28 June 2018, Matera, Italy)

We embark on systematic explorations of the behaviour of tetraquark mesons (colour-singlet bound states of two quarks and two antiquarks) in the (idealized) limit of a large number $N_c$ of colour degrees of freedom of quantum chromodynamics. 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 $N_c$, 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 $1/N_c^2$ and that internal consistency requires all the members of the first species to exist pairwise, distinguishable by their favoured two-ordinary-meson decay channels., 8 pages, 5 figures, talk presented at "QUARKS-2018 - XXth International Seminar on High Energy Physics" (27 May - 2 June 2018, Valday, Russia)

We revisit rare radiative leptonic decays $B_{s,d}\to \gamma e^+e^-$ and $B_{s,d}\to \gamma \mu^+\mu^-$ in the Standard Model and provide the updated estimates for various differential distributions (the branching ratios, the forward-backward asymmetry, and $R_{\mu/e}$, the ratio of the differential distribution for muons over electrons in the final state). The new ingredients of this work compared to the existing theoretical analyses are the following: (i) we calculate all $B_d\to\gamma$ and $B_s\to\gamma$ form factors induced by the vector, axial-vector, tensor and pseudotensor quark currents within the relativistic dispersion approach based on the constituent quark picture; (ii) we perform a detailed analysis of the charm-loop contributions to radiative leptonic decays: we obtain constraints imposed by the electromagnetic gauge invariance and discuss the existing ambiguities in the charmonia contributions.

Scrutinizing the scattering of ordinary mesons in the limiting case of the number of colour degrees of freedom $N_{\rm c}$ of quantum chromodynamics approaching infinity, we formulate Feynman-diagram selection criteria and from these deduce rigorous self-consistency conditions for the manifestation of a tetraquark, a two-quark-two-antiquark bound state, as a pole in the corresponding amplitudes. Our constraints bear rather far-reaching consequences: In particular, all flavour-exotic tetraquarks, composed of four (anti)quarks of disparate flavour, must come in, at least, two variants differing in (and thus readily identifiable by) the large-$N_{\rm c}$ behaviour of their couplings to two ordinary mesons. Quite generally, irrespective of their flavour composition, all tetraquarks prove to be narrow. Their decay rates behave, for large $N_{\rm c},$ like $1/N_{\rm c}^2$ and thus decrease faster than those of ordinary mesons., Comment: 4 pages, 2 figures, contributed to "XVII International Conference on Hadron Spectroscopy and Structure - Hadron2017" (25 - 29 September 2017, Salamanca, Spain)

QCD sum rules are analytic predictions of hadron observables from quantum chromodynamics. In the so-called local-duality limit of their Borel-transformed form, all nonperturbative contributions are encompassed by just a single quantity, an effective threshold beyond which, by assumption, all hadronic contributions are reliably described by perturbative QCD. Reconstructing its quark-mass dependence enables us to investigate the differences of the leptonic decay constants of heavy--light mesons effectuated by the tiny isospin-violating discrepancy of the masses of up and down quarks. By and large, our findings enjoy excellent agreement with the outcomes of earlier studies, the only exception being a lattice-QCD prediction for the $B$ mesons, where we find dramatic disagreement.

We revisit the calculation of nonfactorizable corrections induced by charm-quark loops in exclusive FCNC $B$-decays. For the sake of clarity, we make use of a field theory with scalar particles: this allows us to focus on the conceptual issues and to avoid technical complications related to particle spins in QCD. We perform a straightforward calculation of the appropriate correlation function and show that it requires the knowledge of the full generic three-particle distribution amplitude with non-aligned arguments, $\langle 0|\bar s(y)G_{\mu\nu}(x)b(0)|B(p)\rangle$. Moreover, the dependence of this quantity on the variable $(x-y)^2$ is essential for a proper account of the $\left(\Lambda_{\rm QCD}m_b/m_c^2\right)^n$ terms in the amplitudes of FCNC $B$-decays., Comment: 5 pages, minor clarifications added, version to appear in PLB

We present our recent results for long-distance QCD effects in the flavour-changing neutral current radiative leptonic decays $B\to\gamma\ell^+\ell^-$, $\ell=\{e,\mu\}$. One encounters here two distinct types of long-distance effects: those encoded in the $B\to\gamma$ transition form factors induced by the $b\to q$ quark currents, and those related to the charm-loop effects. We calculate the $B\to\gamma$ form factors in a broad range of the momentum transfers making use of the relativisitc dispersion approach based on the constituent quark picture which has proven to provide reliable predictions for many weak-transition form factors. Concerning the description of the charm-loop contributions, we point out two observations: First, the precise description of the charmonium resonances, in particular, the relative phases between $\psi$ and $\psi'$, has impact on the differential distributions and on the forward-backward asymmetry, $A_{\rm FB}$, in a broad range of $q^2\ge 5$ GeV$^2$. Second, the shape of $A_{\rm FB}$ in $B\to\gamma\ell^+\ell^-$ and in $B\to V\ell^+\ell^-$ ($V$ the vector meson) {\it in the $q^2$-region between $\psi$ and $\psi'$} provides an unambiguous probe of the relative phases between $\psi$ and $\psi'$. Fixing the latter will lead to a strong reduction of the theoretical uncertainties in $A_{\rm FB}$ at $q^2=5-9$ GeV$^2$ where it has the sensitivity to physics beyond the SM.

Discussing four-point Green functions of bilinear quark currents in large-$N_c$ QCD, we formulate rigorous criteria for selecting diagrams appropriate for the analysis of potential tetraquark poles. We find that both flavor-exotic and cryptoexotic (i.e., flavor-nonexotic) tetraquarks, if such poles exist, have a width of order $O(1/N_c^2)$, so they are parametrically narrower compared to the ordinary $\bar qq$ mesons, which have a width of order $O(1/N_c)$. Moreover, for flavor-exotic states, the consistency of the large-$N_c$ behavior of "direct" and "recombination" Green functions requires two narrow flavor-exotic states, each coupling dominantly to one specific meson-meson channel., 5 pages, version to appear in PRD, minor text modifications, conclusions remain unchanged

We determine the strong couplings of three mesons that involve, at least, one $\eta_c$ or $J/\psi$ meson, within the framework of a constituent-quark model by means of relativistic dispersion formulations. For strong couplings of $J/\psi$ mesons to two charmed mesons, our approach leads to predictions roughly twice as large as those arising from QCD sum rules., Comment: 5 pages, 3 figures, contributed to "Quark Confinement and the Hadron Spectrum XII" (28 August - 3 September 2016, Thessaloniki, Greece)

Considering four-point correlation functions of color-singlet quark bilinears, we investigate, in the large-$N_{\mathrm{c}}$ limit of QCD, the subleading diagrams that involve, in the $s$-channel of meson-meson scattering amplitudes, two-quark--two-antiquark intermediate states. The latter contribute, together with gluon exchanges, to the formation, at the hadronic level, of two-meson and tetraquark intermediate states. It is shown that the two-meson contributions, which are predictable, in general, from leading-order $N_{\mathrm{c}}$-behaviors, consistently satisfy the constraints resulting from the $1/N_{\mathrm{c}}$ expansion procedure and thus provide a firm basis for the extraction of tetraquark properties from $N_{\mathrm{c}}$-subleading diagrams. We find that, in general, tetraquarks, if they exist in compact form, should have narrow decay widths, of the order of $N_{\mathrm{c}}^{-2}$. For the particular case of exotic tetraquarks, involving four different quark flavors, two different types of tetraquark are needed, each having a preferred decay channel, to satisfy the consistency constraints., 23 pages, 24 figures. A few clarifying paragraphs, two figures and one reference have been added

Evaluation of Borelized QCD sum rules in the so-called local-duality limit of infinitely large Borel mass parameter provides an alternate route for extraction of the dependence of the decay constants of heavy-light mesons on the mass $m_q$ of the involved light quark $q$: For appropriate choices of the two-point correlation functions of currents interpolating the hadrons under study, the local-duality limit forces all nonperturbative contributions parametrized by vacuum condensates to such kind of correlator to vanish. As a consequence, the sought $m_q$ dependence of the heavy-light meson decay constants proves to be controlled primarily by the correlator contributions from perturbative QCD. Our knowledge of the analytic behaviour of the latter as functions of $m_q$ enables us to derive the $m_q$ dependence of the decay constants of both pseudoscalar and vector heavy-light mesons, for which we estimate strong isospin breaking to be of the order of 1 MeV for both charm and beauty sectors., Comment: 6 pages, 3 figures, talk presented at the "XVII International Conference on Hadron Spectroscopy and Structure - Hadron2017" (25 - 29 September 2017, Salamanca, Spain)

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-quark (or, respectively, five-quark in the pentaquark case) intermediate states and the corresponding cuts. It is shown that some diagrams which "visually" 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-$N_c$ 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-$N_c$ 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 $N_c$. 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 $\bar qq$ mesons with a width of order $O(1/N_c)$. Moreover, for flavor-exotic states, the large-$N_c$ consistency conditions require two narrow flavor-exotic states, each of these states coupling dominantly to one specific meson-meson channel., Plenary talk given at the XXIII International Workshop "High Energy Physics and Quantum Field Theory" (QFTHEP 2017), June 26-July 3, 2017, Yaroslavl, Russia

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., Comment: 5 pages, 2 figures, contributed to "QCD@Work 2016 - International Workshop on Quantum Chromodynamics: Theory and Experiment" (27 - 30 June 2016, Martina Franca, Italy)

The relative magnitude of the decay constants of the pseudoscalar and vector beauty mesons poses (in contrast to the case of charmed mesons) a long-standing puzzle. We revisit this problem within the framework of our recent improvements of the QCD sum-ruleformalism for relating observable properties of mesons to quantum chromodynamics and are led to conclude that the decay constants of the beauty vector mesons are undoubtedly smaller than those of their pseudoscalar counterparts.

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 observables and discuss the possibility to gain control over theoretical predictions for charming loops., Comment: 15 pages, Plenary talk at the XXIV International Workshop "High Energy Physics and Quantum Field Theory" (QFTHEP2019) September 22-29, 2019, Sochi, Russia

We discuss the extraction of form factors from three-point sum rules making use of harmonic-oscillator model, where we derive the exact expression for the relevant correlator. We determine the form factor of the ground state by the standard procedures adopted in the method of sum rules, and compare the obtained results with the known exact values. We show that the uncontrollable uncertainty in the extracted value of the form factor is typically much larger than that for the decay constant. In the example considered, we find the uncontrolled systematic error in the extracted form factor to exceed the 10% level., Comment: 6 pages

We study systematic errors of the ground-state parameters obtained from Shifman—Vainshtein—Zakharov sum rules, making use of the harmonic-oscillator potential model as an example. In this case, one knows the exact solution for the polarization operator, which allows one to obtain both the OPE to any order and the parameters (masses and decay constants) of the bound states. We determine the parameters of the ground state making use of the standard procedures of the method of sum rules and compare the obtained results with the known exact values. We show that, in the situation when the continuum contribution to the polarization operator is not known and is modeled by an effective continuum, the method of sum rules does not allow one to control the systematic uncertainties of the extracted ground-state parameters.

We present the first systematic analysis of the off-light-cone effects in correlators relevant for the extraction of the heavy-to-light form factors within the method of light-cone sum rules. In a model with scalar constituents, the correlator is calculated in two different ways: (i) by performing the expansion of the Bethe-Salpeter amplitude of the light meson near the light cone x2 = 0 and (ii) by adopting the known solution for the Bethe-Salpeter amplitude which allows one to calculate the correlator without invoking any expansion. We demonstrate that the contributions to the correlator from the off-light-cone terms x2 ≠ 0 are not suppressed by any large parameter compared to the contribution of the light-cone term x2 = 0. For decays of heavy particles of mass in the range 1.5–5 GeV, the light-cone correlator is shown to systematically overestimate the full correlator, numerically the difference being 10–20%.

We obtain predictions for a number of radiative decays ${B}_{(s)}\ensuremath{\rightarrow}V\ensuremath{\gamma}$, $V$ the vector meson, which proceed through the weak-annihilation mechanism. Within the factorization approximation, we take into account the photon emission from the $B$-meson loop and from the vector-meson loop; the latter subprocesses were not considered in the previous analyses but are found to have a sizeable impact on the ${B}_{(s)}\ensuremath{\rightarrow}V\ensuremath{\gamma}$ decay rate. The highest branching ratios for the weak-annihilation reactions reported here are $\mathcal{B}({\overline{B}}_{s}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}\ensuremath{\gamma})=1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ and $\mathcal{B}({B}^{\ensuremath{-}}\ensuremath{\rightarrow}{\overline{D}}_{s}^{*\ensuremath{-}}\ensuremath{\gamma})=1.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$, the estimated accuracy of these predictions being at the level of 20%.

We discuss the strong couplings ${g}_{PPV}$ and ${g}_{VVP}$ for vector ($V$) and pseudoscalar ($P$) mesons, at least one of which is a charmonium state $J/\ensuremath{\psi}$ or ${\ensuremath{\eta}}_{c}$. The strong couplings are obtained as residues at the poles of suitable form factors, calculated in a broad range of momentum transfers using a dispersion formulation of the relativistic constituent quark model. The form factors obtained in this approach satisfy all constraints known for these quantities in the heavy-quark limit. Our results suggest sizably higher values for the strong meson couplings than those reported in the literature from QCD sum rules.