A narrow "peanut" pentaquark

We analyse the decay $\Theta_s(1/2^+)\to NK$ in a non-relativistic Fock space description using three and five constituent quarks for the nucleon and the pentaquark, respectively. Following Jaffe and Wilczek \cite{jw}, we assume that quark-quark correlations in spin-zero state play an important role for the pentaquark internal structure. Within this scenario, a strong dynamical suppression of the decay width is shown to be possible only if the pentaquark has an asymmetric "peanut" structure with the strange antiquark in the center and the two extended composite diquarks rotating around. In this case a decay width of $\simeq$ 1 MeV may be a natural possibility.Comment: Talk given at the Conference "Quark Confinement and Hadron Spectrum VI", Villasimius (Cagliari) Sardinia, Italy, 21 - 25 September 200

Dispersion approach to quark-binding effects in weak decays of heavy mesons

Dispersion approach based on the constituent quark picture and its applications to weak decays of heavy mesons are reviewed. Meson interaction amplitudes are represented within this approach as relativistic spectral integrals over the mass variables in terms of the meson wave functions and spectral densities of the corresponding Feynman diagrams. Various applications of this approach are discussed: Relativistic spectral representations for meson elastic and transition form factors at spacelike momentum transfers are constructed. Form factors at $q^2>0$ are obtained by the analytical continuation. As a result of this procedure, form factors are given in the full $q^2$ range of the weak decay in terms of the wave functions of the participating mesons. The 1/m_Q expansion of the obtained spectral representations for the form factors for the particular limits of the heavy-to-heavy and heavy-to-light transitions are analysed. Their full consistency with the constraints provided by long-distance QCD for these limits is demonstrated. Predictions for form factors for B, B(s), D, and D(s) decays to light mesons are given. The B\to\gamma l\nu decay and the weak annihilation in rare radiative decays are considered. Nonfactorizable corrections to the B^0-\bar B^0 mixing are calculated. Inclusive weak B-decays are analysed and the differential distributions are obtained in terms of the B-meson wave function.Comment: revtex, 119 pages. Summary of changes made: In Sect. V comparison with the recent experimental data is added, in Sect. VI discussion of contact terms in B->V\gamma is extended and comments on the recent publications are given, in Sect. VII signs of the decay constants are brought in agreement with other Sections, typoes correcte

Exotic polyquark states and their properties in QCD

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.Comment: Plenary talk given at the XXIII International Workshop "High Energy Physics and Quantum Field Theory" (QFTHEP 2017), June 26-July 3, 2017, Yaroslavl, Russi

Advances in QCD sum rule calculations

We review the recent progress in the applications of QCD sum rules to hadron properties with the emphasis on the following selected problems: (i) development of new algorithms for the extraction of ground-state parameters from two-point correlators; (ii) form factors at large momentum transfers from three-point vacuum correlation functions; (iii) properties of exotic tetraquark hadrons from correlation functions of four-quark currents.Comment: 12 pages, plenary talk given at the XIth International Conference on Quark Confinement and the Hadron Spectrum, Saint Petersburg, Russia, September 8-12, 201

Form factors of exclusive b→ub\to u transitions

We present the form factors of the $B\to\pi,\rho$ transitions induced by the $b\to u$ quark currents at all kinematically accessible $q^2$. Our analysis is based on the spectral representations of the form factors within the constituent quark picture: we fix the soft meson wave functions and the constituent quark masses by fitting $A_1(q^2)$ and $T_2(q^2)$ to the lattice results at small recoils ($17\lesssim q^2\lesssim 20 GeV^2$). We then calculate the $B\to\pi,\rho$ transition form factors down to $q^2=0$. For the $B\to\pi$ case the region $q^2\lesssim 20 GeV^2$ however does not cover the whole kinematically accessible range. Due to the smallness of the pion mass the region of small recoils is close to the nearby $B^*(5234)$ resonance. We develop a parametrization which includes the $B^*$ dominance of the form factors $f_+$ and $f_-$ at small recoils and numerically reproduces the results of calculations at $q^2\lesssim 20 GeV^2$. We find $\Gamma(B\to\pi\ell\nu)=8.0^{+0.8}_{-0.2} |V_{ub}|^2$ps$^{-1}$ and $\Gamma(B\to\rho\ell\nu)=15.8\pm 2.3 |V_{ub}|^2$ps$^{-1}$.Comment: revtex, 6 pages, 1 figur

On properties of the exotic hadrons from QCD sum rules

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.Comment: 6 pages, 3 figures, talk presented at "QCD@Work 2016 - International Workshop on Quantum Chromodynamics: Theory and Experiment" (27 - 30 June 2016, Martina Franca, Italy