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Masses of the ground and excited (1P, 2S, 1D, 2P, 3S) states of the fully-heavy tetraquarks, composed of charm ($c$) and bottom ($b$) quarks and antiquarks, are calculated in the diquark-antidiquark picture within the relativistic quark model based on the quasipotential approach and quantum chromodynamics. The quasipotentials of the quark-quark and diquark-antidiquark interactions are constructed similarly to the previous consideration of mesons and baryons. Relativistic effects are consistently taken into account. A tetraquark is considered as a bound state of a diquark and an antidiquark. The finite size of the diquark is taken into account, using the form factors of the diquark-gluon interaction. It is shown that most of the investigated states of tetraquarks lie above the decay thresholds into a meson pair, as a result they can be observed only as broad resonances. The narrow state X(6900) recently discovered in the di-$J/\psi$ production spectrum by the LHCb, CMS and ATLAS Collaborations corresponds to an excited state of the fully-charmed tetraquark. Other recently discovered exotic heavy resonances X(6200), X(6400), X(6600), X(7200), X(7300) can also be interpreted as the different excitations of the fully-charmed tetraquark., Comment: 36 pages, 2 figures

Rare decay process of the Higgs boson into a pair of $J/\Psi$ and $\Upsilon$ particles is studied within perturbative Standard Model and relativistic quark model. The relativistic corrections connected with the relative motion of quarks are calculated in the production amplitude and the wave functions of the bound states. Numerical values of the decay widths of the Higgs boson are obtained, which can be used for comparison with experimental data., Comment: 20 pages, 5 figures

Recently the LHCb collaboration put the upper limit on the $\Xi^{-}_{b} \rightarrow \Xi^{-}\gamma$ decay branching ratio $Br(\Xi^{-}_{b} \rightarrow \Xi^{-}\gamma)< 1.3\times 10^{-4}$. The measured value is below the light-cone sum rule prediction. In this paper the rare radiative decay of the $\Xi^{-}_{b}$ baryon is studied in the framework of the relativistic quark model based on the quasipotential approach and QCD. The decay form factors are calculated with the comprehensive account of the relativistic effects. The obtained result for the branching ratio is found to be below the upper limit set by LHCb and is consistent with theoretical predictions based on the SU(3) flavor-symmetry, light-front quark model and light-cone QCD sum rules in full theory within theoretical uncertainties., Comment: 8 pages

The form factors of the semileptonic $B$, $B_s$ and $B_c$ meson decays are calculated in the framework of the relativistic quark model based on the quasipotential approach in QCD. They are expressed through the overlap integrals of the meson wave function. All relativistic effects are consistently taken into account. The momentum transfer $q^2$ behavior of form factors is determined in the whole accessible kinematical range. We do not use any extrapolations, heavy quark $1/m_Q$ expansion or model assumptions about the shape of form factors. Convenient analytic expressions of the form factors are given, which very accurately reproduce the numerical results of our calculation. On the basis of these form factors and helicity formalism, the differential and total branching fractions of various semileptonic decays of bottom meson are calculated. The mean values of the forward-backward asymmetry $\langle A_{FB}\rangle$, lepton-side convexity parameter $\langle C^\ell_{F}\rangle$, longitudinal $\langle P^\ell_{L}\rangle$ and transverse $\langle P^\ell_{T}\rangle$ polarization of the charged lepton, and the longitudinal polarization fraction $\langle F_{L}\rangle$ for final-state vector meson are also evaluated. We present a detailed comparison of the obtained predictions with the calculations based on the covariant light-front quark model and confront them to available lattice QCD and experimental data. It is found that although both models predict close values of the total branching fractions, the differential distributions and forward-backward asymmetry and polarization parameters differ significantly, especially for the heavy-to-light semileptonic decays. We identify observables which measurement can help to discriminate between models., Comment: 24 pages, 5 figures, minor changes, references added, version to appear in Physical Review D

The ground state hyperfine splitting of light muon-electron ions of lithium, beryllium, boron and helium is calculated on the basis of analytical perturbation theory in terms of small parameters of the fine structure constant and electron-muon mass ratio. The corrections of vacuum polarization, nuclear structure and recoil effects and electron vertex corrections are taken into account. The dependence of the corrections on the nucleus charge Z is studied. The obtained total values of hyperfine splitting intervals can be used for comparison with future experimental data., Comment: 35 pages, 9 figures

A hadronic vacuum polarization correction to the photon propagator is found by using the Dubnicka-Meshcheryakov parameterization of the pion electromagnetic form factor and new experimental data on the $e^+e^-$ hadrons annihilation cross section. Then, the contribution from the hadronic vacuum polarization to the muon anomalous magnetic moment and the Lamb shift in muonic atoms are calculated., Comment: 12 pages, unpublished JINR preprint 1978

Triply heavy baryons are investigated in the framework of the relativistic quark model based on the quark-diquark picture in the quasipotential approach in QCD. Masses of the ground and excited states of the $\Omega_{ccc}$, $\Omega_{bbb}$, $\Omega_{ccb}$ and $\Omega_{cbb}$ baryons are calculated. Orbital and radial excitations between the diquark and quark as well as between quarks inside the diquark are considered. The diquark internal structure is consistently taken into account by the form factor of the diquark-gluon interaction expressed through the overlap integral of the diquark wave functions. The detailed comparison with previous calculations is given., Comment: 13 pages

We investigate the rare production of the pair of $S-$ and $P-$ wave $B_c$-meson in the Higgs boson decay in the perturbative Standard Model and relativistic quark model. Relativistic amplitudes and decay widths are constructed with the account of the relative motion of heavy quarks forming $B_c$ mesons. When constructing the Higgs boson decay amplitudes, the method of projection operators on the $S-$ and $P-$wave states of quarks is used. Relativistic corrections are expressed in terms of special relativistic parameters and are calculated numerically in the quark model. The dependence of the decay widths of the Higgs boson on various sources of relativistic corrections is investigated., Comment: 18 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:2105.02207

We give a review of the calculations of the masses of tetraquarks with two and four heavy quarks in the framework of the relativistic quark model based on the quasipotential approach and QCD. The diquark-antidiquark picture of heavy tetraquarks is used. The quasipotentials of the quark-quark and diquark-antidiquark interactions are constructed similarly to the previous consideration of mesons and baryons. Diquarks are considered in the colour triplet state. It is assumed that the diquark and antidiquark interact in the tetraquark as a whole and the internal structure of the diquarks is taken into account by the calculated form factor of the diquark-gluon interaction. All parameters of the model are kept fixed from our previous calculations of meson and baryon properties. A detailed comparison of the obtained predictions for heavy tetraquark masses with available experimental data is given. Many candidates for tetraquarks are found. It is argued that the structures in the di-$J/\psi$ mass spectrum observed recently by the LHCb Collaboration can be interpreted as $cc\bar c\bar c$ tetraquarks., Comment: 25 pages, 1 figure, talk at the XXXII International Workshop on High Energy Physics "Hot problems of Strong Interactions" November 9-13, 2020, based on arXiv:0706.3853, arXiv:0808.3912, arXiv:0812.3477, arXiv:2009.13237; v2: published version, references added, note on new LHCb data (arXiv:2103.01803) added

The energy interval $ (3S-1S) $ in muonic hydrogen is calculated on the basis of quasipotential approach in quantum electrodynamics. We take into account different corrections of orders $\alpha^3\div \alpha^6 $, which are determined by relativistic effects, the effects of vacuum polarization, nuclear structure and recoil, as well as combined corrections including the above. Nuclear structure effects are expressed in terms of the charge radius of the proton in the case of one-photon interaction and the proton electromagnetic form factors in the case of two-photon exchange interaction. The value of the energy interval (3S-1S) can be used for a comparison with future experimental data and determining the proton charge radius with greater accuracy., Comment: 25 pages, 14 figures

Masses of the ground-state teraquarks composed from heavy $c$ and $b$ quarks and antiquarks are calculated in the diquark-antidiquark picture in the framework of the relativistic quark model based on the quasipotential approach. The quasipotentials of the quark-quark and diquark-antidiquark interactions are constructed similarly to the previous consideration of mesons and baryons. It is assumed that the diquark and antidiquark interact in the tetraquark as a whole and the internal structure of the diquarks is taken into account. All such tetraquarks are found above the thresholds of decays to two heavy quarkonia. This is a result of the consideration of the diquark not to be a point-like object. Therefore such tetraquarks can be observed as broad structures decaying dominantly to quarkonia. The broad structure next to the di-$J/\psi$ mass threshold, recently observed by the LHCb Collaboration, can correspond to the ground $2^{++}$-state tetraquark consisting of four charm quarks., Comment: 12 pages, references added, published version

We study the pair production of $B_c$ mesons in the photon-photon interaction in the framework of perturbative quantum chromodynamics and the relativistic quark model. The production amplitudes of a pair of pseudoscalar and vector $B_c$ mesons are constructed in the nonrelativistic approximation and taking into account relativistic effects. Relativistic corrections related to the relative motion of heavy quarks in the production amplitude, as well as in the wave function of the bound state of heavy quarks, are taken into account. Analytical expressions are constructed for the relativistic differential and total cross sections for the pair $B_c$ meson production. Based on them, numerical values of the production cross sections are obtained for various energies and scattering angles., Comment: 18 pages, 4 figures

The form factors parameterizing the weak $D$ and $D_s$ transitions to light pseudoscalar and vector mesons are calculated in the framework of the relativistic quark model based on the quasipotential approach. The special attention is paid to the systematic account of the relativistic effects including transformation of the meson wave function from the rest to moving reference frame and contributions of the intermediate negative-energy states. The form factors are expressed through the overlap integrals of the meson wave functions, which are taken from previous studies of meson spectroscopy. They are calculated in the whole range of the transferred momentum $q^2$. Convenient parameterization of the form factors which accurately reproduces numerical results is given. The obtained values of the form factors and their ratios at $q^2=0$ agree well with the ones extracted form the experimental data. On the basis of these form factors and helicity formalism, differential and total semileptonic decay rates of $D$ and $D_s$ mesons as well as different asymmetries and polarization parameters are calculated. The detailed comparison of the obtained results with other theoretical calculations and experimental data is given., Comment: 20 pages, 6 figures

The form factors of the weak $\Xi_c\to \Xi(\Lambda)$ transitions are calculated in the framework of the relativistic quark model based on the quasipotential approach. All relativistic effects including transformations of the baryon wave functions from the rest to moving reference frame and contributions of the intermediate negative energy states are systematically taken into account. The explicit analytic expressions which reliably approximate the momentum transfer $q^2$ dependence of the form factors in the whole accessible kinematical range are given. The calculated form factors are applied for the evaluation of the semileptonic $\Xi_c\to \Xi \ell\nu_\ell$ and $\Xi_c\to \Lambda \ell\nu_\ell$ ($\ell=e,\mu$) decay rates, different asymmetry and polarization parameters within helicity formalism. The obtained results are compared with available experimental data and previous calculations., Comment: 11 pages, 7 figures, v2: normalization of form factors corrected, extended discussion, published version

Masses of heavy baryons are calculated in the relativistic quark-diquark picture. Obtained results are in good agreement with available experimental data including recent measurements by the LHCb Collaboration. Possible quantum numbers of excited heavy baryon states are discussed., Comment: 10 pages, 1 figure, talk at XXIV International Baldin Seminar on High Energy Physics Problems, Sep 17-22, 2018, Dubna, Russia

Semileptonic decays of the $\Xi_b$ baryon are studied in the framework of the relativistic quark-diquark model based on the quasipotential approach. The weak decay form factors are calculated with the comprehensive account of all relativistic effects without employing nonrelativistic and heavy quark expansions. On this basis differential and total decay rates as well as different asymmetry parameters are calculated for the heavy-to-heavy $\Xi_b\to \Xi_c\ell\nu_\ell$ and heavy-to-light $\Xi_b\to \Lambda\ell\nu_\ell$ semileptonic decays. Predictions for the ratios of such decays involving $\tau$ lepton and muon are presented., Comment: 9 pages, 7 figures

The relativistic quark model based on the quasipotential approach with the QCD-motivate potential is employed for the calculation of the form factors of the $\Lambda_c\to p$ rare weak transitions. Their momentum dependence is explicitly determined without additional assumptions and extrapolations in the whole kinematical range of the momentum transfer squared $q^2$. The differential $\Lambda_c\to p l^+l^-$ decay branching fractions and angular distributions are calculated on the basis of these form factors. Both the perturbative and effective Wilson coefficients, which include contributions of vector meson resonances, are used. The calculated branching fraction of the $\Lambda_c\to p \mu^+\mu^-$ rare decay is well consistent with the experimental upper limit very recently set by the LHCb Collaboration., Comment: 12 pages, 4 figures, Published version. arXiv admin note: text overlap with arXiv:1610.00957

In the framework of the quasipotential method in quantum electrodynamics we calculate the contribution of light pseudoscalar (PS) and axial-vector (AV) mesons to the interaction operator of a muon and a proton in muonic hydrogen atom. The coupling of mesons with the muon is via two-photon intermediate state. The parametrization of the transition form factor of two photons into PS and AV mesons, based on the experimental data on the transition form factors and QCD asymptotics, is used. Numerical estimates of the contributions to the hyperfine structure of the spectrum of the S and P levels are presented. It is shown that such contribution to the hyperfine splitting in muonic hydrogen is rather important for a comparison with precise experimental data., Comment: 6 pages, 1 figure; Invited talk contribution to XVII Workshop on High Energy Spin Physics: DSPIN-17; Dubna, Russia, September 11 - 15, 2017

The form factors of the rare $\Lambda_b\to n l^+l^-$ decays are calculated in the framework of the relativistic quark-diquark picture of baryons with the consistent account of the relativistic effects. Their momentum transfer squared dependence is determined explicitly in the whole accessible kinematical range. The decay branching fractions, forward-backward asymmetries and the fractions of longitudinally polarized dileptons are determined. The branching fraction of the rare $\Lambda_b\to n\mu^+\mu^-$ decay are found to be ${\rm Br}(\Lambda_b\to n\mu^+\mu^-)=(3.75\pm0.38)\times10^{-8}$ and thus could be measured at the LHC. Prediction for the branching fraction of the rare radiative $\Lambda_b\to n \gamma$ decay is also given., Comment: 7 pages, 4 figures

On the basis of quasipotential method in quantum electrodynamics we calculate nuclear finite size radiative corrections of order $\alpha(Z \alpha)^5$ to the Lamb shift in muonic hydrogen and helium. To construct the interaction potential of particles, which gives the necessary contributions to the energy spectrum, we use the method of projection operators to states with a definite spin. Separate analytic expressions for the contributions of the muon self-energy, the muon vertex operator and the amplitude with spanning photon are obtained. We present also numerical results for these contributions using modern experimental data on the electromagnetic form factors of light nuclei., Comment: 8 pages, 1 Figure

Rare $\Lambda_b\to\Lambda l^+l^-$ and $\Lambda_b\to\Lambda\gamma$ decays are investigated in the relativistic quark model based on the quark-diquark picture of baryons. The decay form factors are calculated with the account of all relativistic effects including relativistic transformations of baryon wave functions from rest to moving reference frame and the contribution of the intermediate negative energy states. The momentum transfer squared dependence of the form factors is explicitly determined in the whole accessible kinematical range. The calculated decay branching fractions, various forward-backward asymmetries for the rare decay $\Lambda_b\to\Lambda \mu^+\mu^-$ are found to be consistent with recent detailed measurements by the LHCb Collaboration. Predictions for the $\Lambda_b\to\Lambda \tau^+\tau^-$ decay observables are given., Comment: 26 pages, 9 figures, published version

In the framework of the quasipotential method in quantum electrodynamics we calculate the contribution of pseudoscalar mesons to the interaction operator of a muon and a proton in muonic hydrogen atom. The parametrization of the transition form factor of two photons into $\pi$, $\eta$ mesons, based on the experimental data on the transition form factors and QCD asymptotics is used. Numerical estimates of the contributions to the hyperfine structure of the spectrum of the S and P levels are presented., Comment: 15 pages, 4 figures

Motivated by recent experimental progress in studying weak decays of the $\Lambda_c$ baryon we investigate its semileptonic decays in the framework of the relativistic quark model based on the quasipotential approach with the QCD-motivated potential. The form factors of the $\Lambda_c\to \Lambda l\nu_l$ and $\Lambda_c\to nl\nu_l$ decays are calculated in the whole accessible kinematical region without extrapolations and additional model assumptions. Relativistic effects are systematically taken into account including transformations of baryon wave functions from the rest to moving reference frame and contributions of the intermediate negative-energy states. Baryon wave functions found in the previous mass spectrum calculations are used for the numerical evaluation. Comprehensive predictions for decay rates, asymmetries and polarization parameters are given. They agree well with available experimental data., Comment: 12 pages, 6 figures, published version. arXiv admin note: text overlap with arXiv:1609.00199

Hadronic deuteron polarizability correction to the Lamb shift of muonic deuterium is calculated on the basis of unitary isobar model and modern experimental data on the structure functions of deep inelastic lepton-deuteron scattering and their parameterizations in the resonance and nonresonance regions., Comment: 12 pages, 2 figures

On the basis of quasipotential approach to the bound state problem in quantum electrodynamics we calculate hyperfine structure intervals Delta E^{hfs}(2P_{1/2}) and Delta E^{hfs}(2P_{3/2}) for P-states in muonic deuterium. The tensor method of projection operators for the calculation of the hyperfine structure of P-states with definite quantum numbers of total atomic momentum F and total muon momentum j in muonic deuterium is formulated. We take into account vacuum polarization, relativistic, quadrupole and structure corrections of orders alpha^4, alpha^5 and alpha^6. The obtained numerical values of hyperfine splittings are useful for the analysis of new experimental data of the CREMA collaboration regarding to muonic deuterium., Comment: 21 pages, 2 figures

Mass spectra of strange baryons are calculated in the framework of the relativistic quark model based on the quasipotential approach. Baryons are treated as the relativistic quark-diquark bound systems. It is assumed that two quarks with equal constituent masses form a diquark. The diquark excitations and its internal structure are consistently taken into account. Calculations are performed up to rather high orbital and radial excitations of strange baryons. On this basis the Regge trajectories are constructed. The obtained results are compared with available experimental data and previous predictions. It is found that all masses of the 4- and 3-star, as well as most of the 2- and 1-star states of strange baryons with established quantum numbers are well reproduced. The developed relativistic quark-diquark model predicts less excited states than three-quark models of strange baryons., Comment: 21 pages, 3 figures

Strong decays of vector ($^3S_1$) mesons to the pair of pseudoscalar ($^1S_0$) mesons are considered in the framework of the microscopic decay mechanism and the relativistic quark model based on the quasipotential approach. The quark-antiquark potential, which was previously used for the successful description of meson spectroscopy and electroweak decays, is employed as the source of the $q\bar q$ pair creation. The relativistic structure of the decay matrix element, relativistic contributions and boosts of the meson wave functions are comprehensively taken into account. The calculated rates of strong decays of light, heavy-light mesons and heavy quarkonia agree well with available experimental data., Comment: 11 pages, 1 figure, version to be published in Physics Letters B

The branching fractions of the semileptonic and rare $B_s$ decays are calculated in the framework of the QCD-motivated relativistic quark model. The form factors of the weak $B_s$ transitions are expressed through the overlap integrals of the initial and final meson wave functions in the whole accessible kinematical range. The momentum transfer dependence of the form factors is explicitly determined without additional model assumptions and extrapolations. The obtained results agree well with available experimental data., Comment: 12 pages, 2 figures, talk at the XIth International Conference on Quark Confinement and the Hadron Spectrum, 8-12 September 2014, Saint-Petersburg, Russia

On the basis of quasipotential method in quantum electrodynamics we calculate corrections of order $\alpha^5$ and $\alpha^6$ to hyperfine structure of S-wave energy levels of muonic deuterium. Relativistic corrections, effects of vacuum polarization in first, second and third orders of perturbation theory, nuclear structure and recoil corrections are taken into account. The obtained numerical values of hyperfine splitting $\Delta E^{hfs}(1S)=50.2814$ meV (1S state) and $\Delta E^{hfs}(2S)=6.2804$ meV (2S state) represent reliable estimate for a comparison with forthcoming experimental data of CREMA collaboration. The hyperfine structure interval $\Delta_{12}=8\Delta E^{hfs}(2S)-\Delta E^{hfs}(1S)=-0.0379$ meV can be used for precision check of quantum electrodynamics predictions for muonic deterium., Comment: 18 pages, 7 figures

The branching fractions of the rare weak $B\to \pi l^+l^-(\nu\bar\nu)$ and $B\to\rho l^+l^-(\nu\bar\nu)$ decays are calculated in the framework of the relativistic quark model based on the quasipotential approach. The form factors parametrizing weak decay matrix elements are explicitly determined in the whole kinematical $q^2$ range without additional assumptions and extrapolations. Relativistic effects are systematically taken into account including recoil effects in meson wave functions and contributions of the intermediate negative-energy states. New experimental data on the differential distributions in the semileptonic heavy-to-light $B\to\pi l\nu_l$ and $B\to\rho l\nu_l$ decays are analyzed in detail. Good agreement of the predictions and data is found. The obtained results for the branching fractions of the rare semileptonic decays are found to be in agreement with other theoretical estimates and recent experimental data available for the $B^+\to\pi^+ \mu^+\mu^-$ decay., Comment: 15 pages, 9 figures, minor addition, references added

On the basis of quasipotential method in quantum electrodynamics we calculate nuclear finite size radiative corrections of order $\alpha(Z\alpha)^5$ to the hyperfine structure of S-wave energy levels in muonic hydrogen and muonic deuterium. For the construction of the particle interaction operator we employ the projection operators on the particle bound states with definite spins. The calculation is performed in the infrared safe Fried-Yennie gauge. Modern experimental data on the electromagnetic form factors of the proton and deuteron are used., Comment: 8 pages, 1 figure

The branchings fractions of the rare $B_s$ decays are calculated in the framework of the QCD-motivated relativistic quark model. The form factors of the weak $B_s$ transitions to light mesons are expressed through the overlap integral of the initial and final meson wave functions in the whole accessible kinematical range. Explicit determination of the momentum transfer dependence of the form factors without additional model assumptions and extrapolations significantly improve the reliability of the obtained results. The approximate analytical form of the form factors is given in order to simplify the comparison with other predictions and experiment. The calculated form factors are applied for the investigations of the rare semileptonic, radiative and nonleptonic $B_s$ decays. The factorization approximation is used for the description of the nonleptonic decays. All results agree well with available experimental data., Comment: 23 pages, 10 figures

The form factors of the weak $B_s$ transitions to the ground state and orbitally excited strange mesons are calculated in the framework of the QCD-motivated relativistic quark model based on the quasipotential approach. These form factors are expressed through the overlap integrals of meson wave functions found in their mass spectrum evaluations. The momentum dependence of the form factors is determined in the whole accessible kinematical range without any additional assumptions and extrapolations. Relativistic effects, including the wave function transformation from the rest to a moving reference frame as well as contributions of the intermediate negative-energy states, are consistently taken into account. The calculated form factors are used for the evaluation of the charmless semileptonic decay rates and two-body nonleptonic $B_s$ decays in the factorization approximation. The obtained results are confronted with previous predictions and available experimental data., Comment: 18 pages, 6 figures. arXiv admin note: text overlap with arXiv:1212.3167

The form factors of weak decays of $B_s$ mesons to ground state $D_s^{(*)}$ mesons as well as to their radial $D_s^{(*)}(2S)$ and orbital $D_{sJ}^{(*)}$ excitations are calculated in the framework of the relativistic quark model based on the quasipotential approach. All relativistic effects, including contributions of intermediate negative-energy states and boosts of the meson wave functions, are consistently taken into account. As a result the form factors are determined in the whole kinematical range without additional phenomenological parametrizations and extrapolations. On this basis semileptonic decay branching fractions are calculated. Two-body nonleptonic $B_s$ decays are considered within the factorization approximation. The obtained results agree well with available experimental data., Comment: 29 pages, 10 figures, version to be published in Physical Review D

Semileptonic and leptonic B decays are analyzed in the framework of the relativistic quark model. Special attention is payed to the decays involving $\tau$ lepton. It is found that the calculated particular decay branching fractions are consistent with available experimental data within error bars. However, the predicted and recently measured ratios $R(D^{(*)})$ of the $B\to D^{(*)}\tau\nu_\tau$ and $B\to D^{(*)}l\nu_l$ branching fractions differ by 1.75$\sigma$ for $R(D)$ and by 2.4$\sigma$ for $R(D^*)$., Comment: 6 pages, 2 figures

The mass spectra of charmonia, bottomonia and B_c mesons are calculated in the framework of the QCD-motivated relativistic quark model based on the quasipotential approach. The dynamics of heavy quarks and antiquarks is treated fully relativistically without application of the nonrelativistic v^2/c^2 expansion. The known one-loop radiative corrections to the heavy quark potential are taken into account perturbatively. The heavy quarkonium masses are calculated up to rather high orbital and radial excitations (L=5, n_r=5). On this basis the Regge trajectories are constructed both in the total angular momentum J and radial quantum number n_r. It is found that the daughter trajectories are almost linear and parallel, while parent trajectories exhibit some nonlinearity in the low mass region. Such nonlinearity is most pronounced for bottomonia and is only marginal for charmonia. The obtained results are compared with the available experimental data, and a possible interpretation of the new charmonium-like states above open charm production threshold is discussed., Comment: 23 pages, 11 figures

The form factors of weak decays of the B meson to orbitally excited scalar, axial vector and tensor light mesons are calculated in the framework of the QCD-motivated relativistic quark model based on the quasipotential approach. Relativistic effects are systematically taken into account. The form factors are expressed trough the overlap integrals of the meson wave functions and their dependence on the momentum transfer is selfconsistently determined in the whole kinematical range. On this basis semileptonic and two-body nonleptonic B decay rates to orbitally excited light mesons are calculated. Good agreement of the obtained predictions with available experimental data is found., Comment: 21 pages, 5 figures, version to be published in Physical Review D

Mass spectra of heavy baryons are calculated in the heavy-quark--light-diquark picture in the framework of the QCD-motivated relativistic quark model. The dynamics of light quarks in the diquark as well as the dynamics of the heavy quark and light diquark in the baryon are treated completely relativistically without application of nonrelativistic v/c and heavy quark 1/m_Q expansions. Such approach allows us to get predictions for the heavy baryon masses for rather high orbital and radial excitations. On this basis the Regge trajectories of heavy baryons for orbital and radial excitations are constructed, and their linearity, parallelism, and equidistance are verified. The relations between the slopes and intercepts of heavy baryons are considered and a comparison of the slopes of Regge trajectories for heavy baryons and heavy-light mesons is performed. All available experimental data on heavy baryons fit nicely to the constructed Regge trajectories. The possible assignment of the quantum numbers to the observed excited charmed baryons is discussed., Comment: 25 pages, 10 figures

The masses of the heavy tetraquarks with open charm and bottom are calculated within the diquark-antidiquark picture in the framework of the relativistic quark model. The dynamics of the light quarks and diquarks is treated completely relativistically. The diquark structure is taken into account by calculating the diquark-gluon form factor. New experimental data on charmed and charmed-strange mesons are discussed. Our results indicate that the anomalous scalar D_{s0}^*(2317) and axial vector D_{s1}(2460) mesons could not be considered as diquark-antidiquark bound states. On the other hand, D_s(2632) and D_{sJ}^*(2860) could be interpreted as scalar and tensor tetraquarks, respectively. The predictions for masses of the corresponding bottom counterparts of the charmed tetraquarks are given., Comment: 11 pages

The form factors of weak decays of the B_c meson to orbitally excited charmonium, D, B_s and B mesons are calculated in the framework of the QCD-motivated relativistic quark model based on the quasipotential approach. Relativistic effects are systematically taken into account. The form factor dependence on the momentum transfer is reliably determined in the whole kinematical range. The form factors are expressed trough the overlap integrals of the meson wave functions which are known from the previous mass spectra calculations within the same model. On this basis semileptonic and nonleptonic B_c decay rates to orbitally excited heavy mesons are calculated. Predictions for the B_c decays to the orbitally and radially excited 2P and 3S charmonium states are given which could be used for clarifying the nature of the recently observed charmonium-like states above the open charm production threshold., Comment: 29 pages, 6 figures

We present some considerations in connection with the paper arXiv:1004.2980 [hep-ph] and give a response to the criticism of the quasipotential approach in our relativistic quark model., Comment: 3 pages

Rare semileptonic decays of B and B_c mesons are investigated in the framework of the QCD-motivated relativistic quark model based on the quasipotential approach. Form factors parametrizing the matrix elements of the weak transitions between corresponding meson states are calculated with the complete account of the relativistic effects including contributions of intermediate negative energy states and relativistic transformations of the meson wave functions. The momentum transfer dependence of the form factors is reliably determined in the whole accessible kinematical range. On this basis the total and differential branching fractions of the B\to K^{(*)}l^+l^-(\nu\bar\nu) and B_c\to D_s^{(*)}l^+l^-(\nu\bar\nu), B_c\to D^{(*)}l^+l^-(\nu\bar\nu) decays as well as the longitudinal polarization fractions F_L of the final vector meson and the muon forward-backward asymmetries A_{FB} are calculated. Good agreement of the obtained results with the recent detailed experimental data on the B\to K^{(*)}\mu^+\mu^- decays from Belle and CDF is found. Predictions for the rare semileptonic decays of the B_c mesons are given., Comment: 24 pages, 9 figures