Search

We discuss a nonfactorizable (NF) contribution of a charm loop to the FCNC $B$-decay amplitude given through the three-particle Bethe-Salpeter amplitude (3BS) of the $B$-meson. This 3BS contains one heavy-quark field and two light fields (a light quark and a gluon). Our discussion is aimed at clarifying properties of the $B$-meson 3BS necessary to describe properly charm-loop contributions to the amplitudes of FCNC $B$-decays. We demonstrate that the dominant contribution of nonfactorizable charm to FCNC $B$-decay amplitude is given in the heavy-quark limit by a convolution of some hard kernel and the $B$-meson 3BS in a ``double-collinear'' light cone (LC) configuration: one of the light degrees of freedom $\phi(x)$, $x^2=0$, lies on the $(+)$-direction of the LC, whereas another light degree of freedom $\phi'(x')$, $x'^2=0$ lies on the $(-)$-direction. We show the emergence of new constraints on the distribution amplitudes which parametrize the 3BS in this double-collinear configuration., Comment: 12 pages, a discussion of the differences between the 3BS in the collinear and the double-collinear configurations is added [Subsection 3.A.6, Conclusions item (iii) and item (iv)]

We compare a nonfactorizable charming-loop correction to an exclusive FCNC B decay given in terms of the three-particle Bethe-Salpeter amplitude (3BS) of the B meson, ⟨0|q¯(x)Gμν(z)b(0)|B(p)⟩, with the corresponding correction to the B-meson semileptonic form factor. In spite of certain similarities, these two corrections are shown to have substantial differences: the form-factor correction is dominated by the collinear light-cone configuration of 3BS (zμ=uxμ, 0

We compare a non-factorizable charming-loop correction to an exclusive FCNC $B$-decay given in terms of the 3-particle Bethe-Salpeter amplitude (3BS) of the $B$-meson, $\langle 0|\bar q(x)G_{\mu\nu}(z)b(0)|B(p)\rangle$, with the corresponding correction to the $B$-meson semileptonic form factor. In spite of certain similarities, these two corrections are shown to have substantial differences: The form factor correction is dominated by the collinear light-cone configuration of 3BS: $z_\mu= u x_\mu$, $0 < u < 1$, $x^2=0$. In contrast, the FCNC amplitude is dominated by a different configuration with non-collinear arguments: $x^2=0$, $z^2=0$, but $(x-z)^2\ne 0$ (i.e., $z_\mu\ne u x_\mu$)., Comment: 10 pages, a few comments added, version accepted to PRD

We study the effects of identical leptons in the final state of the B+→ℓ+ℓ−ℓ+ν¯ℓ decay. The amplitude of the process is described by the same form factors as the amplitude of the B→ℓℓℓ′ν¯ℓ′ decay for nonidentical leptons in the final state. However, the differential distributions are strongly different, as the B+→ℓ+ℓ−ℓ+ν¯ℓ amplitude contains both the direct (Ma) and exchange (Mb) diagrams. We calculate a number of the differential distributions. In particular, we propose an interesting observable that can be readily measured experimentally: the differential distribution over the invariant mass of the pair of leptons of the same charge, ℓ+ℓ+. The good news is that the interference between Ma and Mb, dBab is found to be at the level of less than 1% in all considered differential distributions and therefore can be neglected in the full kinematical region of this decay.

We study the effects of the identical leptons in the final state of the $B^+\to \ell^+ \ell^- \ell^+\bar\nu_{\ell}$ decay. The amplitude of the process is described by the same form factors as the amplitude of the ${B\to \ell \ell \ell'\bar\nu'_{\ell}}$ decay for non-identical leptons in the final state. However, the differential distributions are strongly different, as the ${B^+\to \ell^+ \ell^- \ell^+\bar\nu_{\ell}}$ amplitude contains both the direct ($M_a$) and the exchange ($M_b$) diagrams. We calculate a number of the differential distirbutions. In particular, we propose an interesting observable that can be readily measured experimentally - the differential distribution over the invariant mass of the pair of leptons of the same charge, $\ell^+ \ell^+$. The good news is that the interference between $M_a$ and $M_b$, $d{\cal B}_{ab}$, is found to be at the level of less than 1\% in all considered differental distributions and therefore can be neglected in the full kinematical region of this decay., Comment: 9 pages. arXiv admin note: text overlap with arXiv:2107.07247

We discuss the amplitude of the $B\to l^+l^-l'\nu'$ decays and the differential decay rate $d^2\Gamma/dq^2dq'^2$, $q$ the momentum of the $l^+l^-$ pair emitted from the electromagnetic vertex and $q'$ the momentum of the $l'\nu'$ pair emitted from the weak vertex. For the relevant form factors, we construct dispersion representations in $q^2$ which consistently take into account the Ward identity constraints at $q^2=0$ and the contributions of light vector resonances. This allows a reliable description of the form factors in the range $0 < q^2 \le 1$ GeV$^2$ that saturates around 99% of the decay rate. The differential decay rate behaves at small $q^2$ as $d\Gamma(B\to l^+l^-l' \nu')/dq^2\propto 1/q^2$ in the limit $m'_l=0$, but contains also more singlular contribution of order ${m'^2_l}/q^4$, which we take into account. For the case $m_l'\le m_l$, the latter may be neglected and one obtains a mild logarithmic dependence of $\Gamma(B\to l^{+}l^{-}l'\nu')$ on $m_l$. For the case $m_l\ll m'_l$, however, the ${m'^2_l}/q^4$ terms dominate the decay rate leading to $\Gamma(B\to l^{+}l^{-}l'\nu')\sim m'^2_l/m^2_l$. We find the following features of the four-lepton $B$-decays: (i) The decay rates $\Gamma\left(B\to \mu^+\mu^-(\mu \nu_\mu,e\nu_e)\right)$ are fully dominated by the region of light vector resonances $q^2\simeq M_\rho^2, M_\omega^2$; (ii) The decay rate $\Gamma(B\to e^{+}e^{-}e \nu_e)$ receives comparable contributions from the region near $q^2\sim 4m_e^2$ and from the resonance region; (iii) One finds a strong enhancement of the decay rate $\Gamma(B\to e^+e^- \mu \nu_\mu)\sim m_\mu^2/m_e^2$ which is dominated by the region $q^2\sim 4m_e^2$ due to the terms $O(m_\mu^2/q^4)$ in the differential distribution., Comment: 14 pages. The branching fractions for the leptonic B decays into the final states containing identical leptons have been updated. Version to appear in Physical Review D

We discuss the operator product expansion (OPE) and quark-hadron duality for two-point Green functions of tetraquark currents. We emphasize that the factorizable part of the OPE series for such Green functions, including nonperturbative contributions described by QCD condensates, is saturated by the full system of ordinary hadrons and therefore cannot have any relationship to the possible tetraquark bound states. Possible tetraquark bound states may be contained in nonfactorizable parts of these Green functions. In the framework of the 1/Nc expansion in QCD(Nc), nonfactorizable parts of the two-point Green functions of tetraquark currents provide Nc-suppressed contributions compared to the Nc-leading factorizable parts. A possible exotic tetraquark state may appear only in Nc-subleading contributions to the QCD Green functions, in full accord with the well-known rigorous properties of large-Nc QCD.

The present work reviews the various aspects of the extension of the large-$N_c$ approach, as had been proposed and developed by 't Hooft, 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 priviledged 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., Comment: 132 pages, 53 figures. Review article. v2: Sections 2.7 and 5.4 have been slightly extended; a few clarifying comments have been added in other sections; figure 43 has been completed; references have been added

We discuss the general properties of the B-meson decay form factors F(q2,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 q2 and q′2, where perturbative QCD can be applied for obtaining predictions for the physical form factors.

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., 7 pages, 4 figures, talk presented at the "European Physical Society Conference on High Energy Physics - EPS-HEP 2019" (10 - 17 July 2019, Ghent, Belgium)

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 form of narrow states., 7 pages, 5 figures, talk presented at "XIII Quark Confinement and the Hadron Spectrum - Confinement2018" (31 July - 6 August 2018, Maynooth University, Ireland)

This presentation reviews the main results of our recent work [A.K., D.M., N.N., Phys. Rev. D97, 053007 (2018)] on rare radiative leptonic decays $B_{d,s}\to\gamma\mu^+\mu^-$ and $B_{d,s}\to\gamma e^+e ^-$ induced by flavour-changing neutral currents (FCNC) in the Standard Model., Comment: 5 pages, contributed to "QCD@Work 2018 - International Workshop on Quantum Chromodynamics: Theory and Experiment" (25 - 28 June 2018, Matera, Italy)

We revisit rare radiative leptonic decays Bs,d→γe+e− and Bs,d→γμ+μ− in the standard model and provide the updated estimates for various differential distributions (the branching ratios, the forward-backward asymmetry, and Rμ/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 Bd→γ and Bs→γ 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 electromagnetic gauge invariance and discuss the existing ambiguities in the charmonia contributions.

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., Comment: 27 pages. Version to appear in Phys. Rev. D

Considering four-point correlation functions of color-singlet quark bilinears, we investigate, in the large-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N_{\mathrm {c}}$$\end{document}Nc 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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N_{\mathrm {c}}$$\end{document}Nc-behaviors, consistently satisfy the constraints resulting from the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1/N_{\mathrm {c}}$$\end{document}1/Nc expansion procedure and thus provide a firm basis for the extraction of tetraquark properties from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N_{\mathrm {c}}$$\end{document}Nc-subleading diagrams. We find that, in general, tetraquarks, if they exist in compact form, should have narrow decay widths, of the order of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N_{\mathrm {c}}^{-2}$$\end{document}Nc-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.

We present our recent results for long-distance QCD effects in the FCNC 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., Comment: 6 pages, talk given at "The European Physical Society Conference on High Energy Physics - EPS-HEP 2017" (5 - 12 July 2017, Venice, Italy)

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., 4 pages, 1 figure, contributed to "The European Physical Society Conference on High Energy Physics - EPS-HEP 2017" (5 - 12 July 2017, Venice, Italy)

Considering four-point correlation functions of color-singlet quark bilinears, we investigate, in the large- Nc 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 Nc -behaviors, consistently satisfy the constraints resulting from the 1/Nc expansion procedure and thus provide a firm basis for the extraction of tetraquark properties from Nc -subleading diagrams. We find that, in general, tetraquarks, if they exist in compact form, should have narrow decay widths, of the order of Nc-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.

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., Comment: 5 pages, 3 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-rule formalism 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., 7 pages, 2 figures, contributed to "The European Physical Society Conference on High Energy Physics - EPS-HEP 2015" (22 - 29 July 2015, Vienna, Austria)

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 $J/\psi$ or $\eta_c$. 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., Comment: 8 pages, typo in Eq (2.1) corrected, minor stylistic changes, version to appear in Physical Review D