We investigate the spectroscopy and decays of the charm-strange quarkonium system in a potential model consisting of a relativistic kinetic energy term, a linear confining term including its scalar and vector relativistic corrections and the complete perturbative one-loop quantum chromodynamic short distance potential. The masses and wave functions of the various states are obtained using a variational technique, which are then used in a perturbative treatment of the potential to find the mass spectrum of the $c\bar{s}$ system and radiative decay widths. Our results compare well with the available data for the spectrum of $D_s$ states. We include a discussion of the effect of mixing and an investigation of the Lorentz nature of the confining potential.
A model based on a nonrelativistic potential supplemented by spin dependent terms of the Breit-Fermi type is described. This model reproduces the known masses of the $\bar{b}b$ quarkonia within 1MeV and the known masses of the $\bar{c}c$ quarkonia within 5MeV. Many predictions are made, some of them, e.g. for the fine splittings of the high $L$ states of the $\bar{b}b$ quarkonia and of the mass spectrum of the $\bar{b}c$ quarkonia, significantly different from previous predictions made by other authors.
This report is devoted to the analytical calculation of heavy quarkonia production processes in modern experiments such as LHC, B-factories and superB-factories in computer. Theoretical description of heavy quarkonia is based on the factorization theorem. This theorem leads to special structure of the production amplitudes which can be used to develop computer algorithm which calculates these amplitudes automatically. This report is devoted to the description of this algorithm. As an example of its application we present the results of the calculation of double charmonia production in bottomon…
Using the quark-antiquark interactions obtained in the framework of the bootstrap method we construct a potential model, investigate the possibility of describing of heavy quarkonia and calculate the bottomonium spectrum. The potential of the interaction was obtained as a nonrelativistic limit of the relativistic quark-antiquark amplitudes Q{\bar Q} -> Q\bar Q.
The experiments at LHC have shown that the SUSY (exotic) bound states are likely to form bound states in an entirely similar fashion as ordinary quarks form bound states, i.e., quarkonium. Also, the interaction between two squarks is due to gluon exchange which is found to be very similar to that interaction between two ordinary quarks. This motivates us to solve the Schrödinger equation with a strictly phenomenological static quark-antiquark potential: $V(r)=-Ar^{-1}+κ\sqrt{r}+V_{0}$ using the shifted large $N$-expansion method to calculate the low-lying spectrum of a heavy quark with anti-sb…
Based on the two Higgs doublet model, we study the effect of Higgs-boson exchange on the (super)heavy quarkonium \bar QQ, which induces a strong attractive force between a (super)heavy quark Q and an antiquark \bar Q. An interesting application is the decay of (super)heavy quarkonia \bar QQ into a Higgs boson associated with gauge bosons. The criterion for making the \bar QQ bound state is studied. We also show that non-perturbative effects due to gluonic field fluctuations are rather small in such a heavy quark sector. Possible enhancement for productions and decays of \bar QQ bound states ma…
We discriminate gluonic hadrons from conventional $q\bar q$ states by surveying radial and orbital excitations of all I=0 and I=1 $n\bar n$ systems anticipated up to 2.1 GeV. We give detailed predictions of their quasi-two-body branching fractions and identify characteristic decay modes that can isolate quarkonia. Several of the ``missing mesons'' with L$_{q\bar q}=2$ and L$_{q\bar q}=3$ are predicted to decay dominantly into certain S+P and S+D modes, and should appear in experimental searches for hybrids in the same mass region. We also consider the topical issues of whether some of the rece…
I discuss recent theoretical results for inclusive decays of quarkonia into a photon plus hadrons, and summarize the status of perturbative calculations.
We investigate the correlations between the scalar meson configurations and Okuba-Zweig-Iizuka (OZI) rule violations in the hadronic decays of heavy quarkonia, e.g. $J/ψ$ and $Υ$, into isoscalar vector meson ($ϕ$ and $ω$) and scalar mesons ($f_0(1710)$, $f_0(1500)$, and $f_0(1370)$). It shows that the dramatic change of the values of the branching ratio fraction of $ϕf_0/ωf_0$ from low (e.g. in $J/ψ$ decays) to high energies (e.g. in $Υ$ decays) will not only test the glueball-$Q\bar{Q}$ mixings, but also provide important information about the mysterious OZI-rule violations within the scalars…
Decay rates of $c\bar c$ and $b\bar b$ mesons have been studied within the NRQCD formalism. The basic parameters of the formalism have been obtained from different potential schemes studied for the quarkonia spectra. The present results are compared with other potential model results with and without correction terms proposed through hard gluon processes involved in the decay.
We extract the $Q$-$\bar Q$ potential by using the thermodynamic quantities obtained in lattice gauge calculations. The potential is tested and found to give dissociation temperatures that agree well with those from lattice gauge spectral function analysis. Using such a $Q$-$\bar Q$ potential, we examine the quarkonium states in a quark-gluon plasma and determine the `quark drip lines' which separate the region of bound color-singlet $Q\bar Q$ states from the unbound region. The characteristics of the quark drip lines severely limit the region of possible bound $Q\bar Q$ states with light quar…
To include the explicit valence gluon degrees of freedom into spectroscopy of the lowest states of heavy quarkonia, we consider, within an adiabatic model, the properties of the lowest hybrid $\bar{Q}Qg$-mesons and estimate the effects of their mixing with low-lying vector $\bar{c}c$-charmonia. The perspectives of compatibility of the resulting picture with data are discussed.
We study inclusive processes involving two heavy quarkonia in nonrelativisitic QCD (NRQCD) and demonstrate that, in the presence of two P-wave Fock states, NRQCD factorization breaks down, leaving uncanceled infrared singularities. As phenomenologically important examples, we consider the decay $Υ\to χ_{cJ}+X$ via $b\bar{b}({}^3P_{J_b}^{[8]})\to c\bar{c}({}^3P_J^{[1]})+gg$ and the production process $e^+e^-\to J/ψ+χ_{cJ}+X$ via $e^{+}e^{-}\to c\bar{c}({}^3P_{J_1}^{[8]})+c\bar{c}({}^3P_J^{[1]})+g$. We infer that such singularities will appear for double quarkonium hadroproduction at next-to-lea…
We update our recent calculation of quarkonium Euclidean correlators at finite temperatures in a potential model by including the effect of zero modes in the lattice spectral functions. These contributions cure most of the previously observed discrepancies with lattice calculations, supporting the use of potential models at finite temperature as an important tool to complement lattice studies.
We calculate the dynamical relativistic corrections, originating from radiative one-gluon-exchange, to the leptonic decay width of heavy quarkonia in the framework of a covariant formulation of Light-Front Dynamics. Comparison with the non-relativistic calculations of the leptonic decay width of J=1 charmonium and bottomonium S-ground states shows that relativistic corrections are large. Most importantly, the calculation of these dynamical relativistic corrections legitimate a perturbative expansion in $α_s$, even in the charmonium sector. This is in contrast with the ongoing belief based on c…
Experimental data for $b\bar{b}$ quarkonia have been compared with the predictions of a variety of nonrelativistic quark models. It is found that a potential $a\sqrt{r} - b/r +$ const gives good agreement, while many others do not. Some implications of this observation are discussed.
We examine the spectra and radiative decays of the cc-bar and bb-bar systems using a model which incorporates the complete one-loop spin-dependent perturbative QCD short distance potential, a linear confining term including (spin-dependent) relativistic corrections to order v^2/c^2, and a fully relativistic treatment of the kinetic energy. We compare the predictions of this model to experiments, including states and decays recently measured at Belle, BaBar, CLEO and CDF.
The decay rates of $c\bar{c}$ and $b\bar{b}$ through two-photon or two-gluon annihilations are obtained by using totally relativistic decay amplitudes and a sophisticated quantum-chromodynamic potential model for heavy quarkonia. Our results for the photonic and gluonic widths of the 1S0, 3P0, and the 3P2 states are in excellent agreement with the available experimental data. The procedures and mathematical techniques used by us for the treatment of the fermion-antifermion bound states are also applicable to other decay processes.
In the framework of a newly developed factorization formalism which is based on NRQCD, explicit cancellations are shown for the infrared divergences that appeared in the previously calculated hadronic annihilation decay rates of P-wave and D-wave heavy quarkonia. We extend them to a more general case that to leading order in $v^2$ and next-to-leading order in $α_s$, the infrared divergences in the annihilation amplitudes of color-singlet $Q\bar{Q}(^{2S+1}L_J)$ pair can be removed by including the contributions of color-octet operators $Q\bar{Q}(^{2S+1}(L-1)_{J'})$, $Q\bar{Q}(^{2S+1}(L-3)_{J''}…
The electromagnetic E1 and M1 transitions in heavy quarkonia ($c\bar c$, $b\bar b$, $c\bar b$) and the magnetic moment of the $B_c^\pm$ are calculated within the framework of the covariant Blankenbecler-Sugar (BSLT) equation. The aim of this paper is to study the effects of two-quark exchange current operators which involve the $Q\bar Q$ interaction, that arise in the BSLT (or Schrödinger) reduction of the Bethe-Salpeter equation. These are found to be small for E1 dominated decays such as $ψ(nS)\to χ_{cJ} γ$ and $Υ(nS)\to χ_{bJ} γ$, but significant for the M1 dominated transitions. It is show…
The decay widths of top quark to S-wave $b\bar{c}$ and $b\bar{b}$ bound states are evaluated at the next-to-leading(NLO) accuracy in strong interaction. Numerical calculation shows that the NLO corrections to these processes are remarkable. The quantum chromodynamics(QCD) renormalization scale dependence of the results are obviously depressed, and hence the uncertainties lying in the leading order calculation are reduced.
We compute the Noncommutative QCD (NCQCD) contributions to the three gluon decay modes of heavy quarkonia. For triplet quarkonia (ortho-quarkonia), the NCQCD correction to the QCD three gluon decay mode, like the standard model contribution, is infrared finite. In the case of singlet quarkonia (para-quarkonia), whose QCD three gluon decay mode has infrared singularities which are removed using one-loop corrections to the two gluon mode, we find that NCQCD contribution is also infrared finite. The calculations are performed in the weak binding limit and do not require the introduction of additi…
Recently, several surprising experimental observations in the production of heavy quarkonium have been reported. In $e^+e^-$ annihilation at $\sqrt{s}=10.6$ GeV, Belle Collaboration finds that $J/ψ$ mesons are predominantly produced in association with an extra $\bar{c}c$ pair, with $σ(e^+e^- \to J/ψ\bar{c}c) / σ(e^+e^- \to J/ψX) = 0.59^{+0.15}_{-0.13}\pm 0.12$, and the BaBar collaboration reports that the produced $J/ψ$'s have mostly longitudinal polarization. In $\bar{p}p$ collisions at the Tevatron, the CDF Collaboration reported an excess of $J/ψ$ and $ψ^{\prime}$ mesons at high $p_{\perp}…
We extend our treatment of the the spectroscopy and decays of the charm-strange quarkonium system to include the effect of using the full three-loop QCD correction to the static short distance potential. As before, our potential model consists of the relativistic kinetic energy term, a scalar linear confining term including its relativistic corrections and the perturbative QCD spin-dependent terms. A set of unperturbed wave functions for the various states is obtained using a variational technique that is further constrained by requiring that the wave functions also satisfy the relativistic vi…
We model the spectral effect of open flavor meson-meson thresholds in heavy quarkonia. The proposed energy dependent quark-antiquark static potential tries to incorporate in a quark model scheme the results from unquenched lattice calculations. A good qualitative and a reasonable quantitative description of charmonium and bottomonium, including the "new charmonium-like" states, is obtained.
We consider a general scheme for calculating the leptonic constant of heavy quarkonium QQ-bar in the framework of nonrelativistic quantum chromodynamics, NRQCD, operating as the effective theory of nonrelativistic heavy quarks. We explore the approach of static potential in QCD, which takes into account both the evolution of effective charge in the three-loop approximation and the linearly raising potential term, which provides the quark confinement. The leptonic constants of bb-bar and cc-bar systems are evaluated by making use of two-loop anomalous dimension for the current of nonrelativisti…
We calculate the NLO corrections for the gluon fragmentation functions to a heavy quark-antiquark pair in ${^{1}\hspace{-0.6mm}S_{0}^{[1]}}$ or ${^{1}\hspace{-0.6mm}S_{0}^{[8]}}$ state within NRQCD factorization. We use integration-by-parts reduction to reduce the original expression to simpler master integrals (MIs), and then set up differential equations for these MIs. After calculating the boundary conditions, MIs can be obtained by solving the differential equations numerically. Our results are expressed in terms of asymptotic expansions at singular points of $z$ (light-cone momentum fract…
We investigate the effects of including the full three-loop QCD correction to the static short distance $1/r$ potential on the spectroscopy and decays in the charmonium and upsilon systems. We use a variational technique with the full three-loop corrected potential to determine a set of unperturbed trial wave functions and treat the relativistic and one-loop corrections as perturbations. The perturbed results are compared to the subset of the charmonium and upsilon spectra using a $χ^2$ test. This approach results in more accurate descriptions of the hyperfine splittings in both the $b\bar{b}$…
Heavy $c\bar c$ and $b\bar b $ quarkonia are considered as systems confined within a hard-wall potential shaped after a linear combination of a cotangent-- with a square co-secant function. Wave functions and energy spectra are then obtained in closed forms in solving by the Nikiforov-Uvarov method the associated radial Schrödinger equation in the presence of a centrifugal term. The interest in this potential is that in one parametrization it can account for a conformal symmetry of the strong interaction, and in another for its perturbation, a reason for which we here employ it to study status…
Uncertainties in the next-to-leading-order calculations of heavy-quark ($Q$) production are investigated. Predictions for total cross sections, single-inclusive distributions of heavy quarks and heavy flavoured hadrons, as well as for $Q\bar{Q}$ correlations, are compared with charm and bottom data. The description of heavy-quarkonium production requires a separation of the short-distance scale of $Q\bar{Q}$ production, which is set by the heavy-quark mass from the longer-distance scales associated with the bound-state formation. Various factorization approaches are compared, in particular wit…
We use various methods of Borel integration to calculate the binding ground energies and masses of b-bbar and t-tbar quarkonia. The methods take into account the leading infrared renormalon structure of the hard+soft part of the binding energies E(s), and of the corresponding quark pole masses m_q, where the contributions of these singularities in M(s) = 2 m_q + E(s) cancel. Beforehand, we carry out the separation of the binding energy into its hard+soft and ultrasoft parts. The resummation formalisms are applied to expansions of m_q and E(s) in terms of quantities which do not involve renorma…
This work is an extension of the work in \cite{bhatnagar18} to ground and excited states of $0^{++}, 0^{-+}$, and $1^{--}$ of heavy-light ($c\overline{u}, c\overline{s}, b\overline{u}, b\overline{s}$, and $b\overline{c}$) quarkonia in the framework of a QCD motivated Bethe-Salpeter equation (BSE) by making use of the exact treatment of the spin structure $(γ_μ\bigotimesγ_μ)$ in the interaction kernel, in contrast to the approximate treatment of the same in our previous works \cite{hluf16, bhatnagar18}), which is a substantial improvement over our previous works \cite{hluf16,bhatnagar18}. In th…
Although individual levels of toponium will be unobservable, the top--anti--top system near threshold fulfills all requirements of a rigorous perturbation theory in QCD for weakly bound systems. Corresponding techniques from positronium may thus be transferred successfully to this case. After clarifying the effect of a non-zero width we calculate the $t\bar{t}$ potential to be used for the calculation of e.g. the cross-sections near threshold.
We calculated the polarization of ψ' due to gg \to Q\bar{Q}[^3P_J^(8)]g \to ψ^λcolor-octet quarkonia production. We find that at low transverse momenta the ψ' is unpolarized due to the contributions proportional to the L=S=0 and L=S=1 color-octet matrix elements. As p_\perp increases, the ψ' mesons become 100% polarized, as predicted by fragmentation calculations. Polarization due to lowest order color-singlet production is also considered, which qualitatively has a similar shape to the color-octet production.
The two photon transition of $\bar{c}c$ quarkonia are studied within a covariant approach based on the consistent truncation scheme of the quantum chromodynamics Dyson-Schwinger equation for the quark propagator and the Bethe--Salpeter equation for the mesons. We find the decay widths of $η_{c}^{} \to γγ$ and $χ_{c0,2}^{} \to γγ$ in good agreement with experimental data. The obtained transition form factor of $η_{c}^{} \to γγ^{\ast}$ for a wide range of space-like photon momentum transfer squared is also in agreement with the experimental findings of the BABAR experiment. As a by-product, the …
I discuss exclusive production of the $η'$, $J/ψ$, and $χ_c(0^+)$ mesons in $pp$ and $p \bar p$ collisions at high energies. QCD diffractive mechanisms as well as nondiffractive mechanisms are discussed. Different unintegrated gluon distribution functions (UGDF) are used. Some differential distributions are shown and discussed.
A nonrelativistic Hamiltonian with plausible spin dependent corrections is proposed for the quarkonia below their respective strong decay thresholds. With only six free parameters this model reproduces the nine known masses of the bottomonia within about 1 MeV, the six known masses of the charmonia within a few MeV and the five known leptonic decay widths of the ${}^3S_1$ states within about {20 %}. The model is then used to predict the masses of the remaining 43 quarkonia (some of them for the first time) and of the leptonic decay widths of the two ${}^1S_0(\bar{b}c)$ states. Comparison with …
The perturbative renormalization group for light-front QCD Hamiltonian produces a logarithmically rising interquark potential already in second order, when all gluons are neglected. There is a question if this approach produces also color van der Waals forces between heavy quarkonia and of what kind. This article shows that such forces do exist and estimates their strength, with the result that they are on the border of exclusion in naive approach, while more advanced calculation is possible in QCD.
We present a new factorization theorem for the decay rates of P-wave states of heavy quarkonia. Infrared logarithms that had appeared in previous perturbative calculations of P-wave decays are absorbed into a quantity that is related to the amplitude for the heavy quark and antiquark to be in a relative color-octet S-wave state. We predict all of the light-hadronic and electromagnetic decays rates of the $χ_c$ and $h_c$ states in terms of two phenomenological parameters.
We examine to what extent several recently discovered narrow resonances can be interpreted as conventional $c\bar{c}$ bound states describable using a potential model. In doing so, we use a semirelativistic approach, which includes both the $v^2/c^2$ and QCD one-loop corrections to the short distance potential and a long range linear potential together with its scalar and vector $v^2/c^2$ spin-dependent terms.
We investigate the properties of mesons with the exotic J^PC = 1^-+ quantum numbers. Starting out from the light-quark domain, where the π_1 states are used as references, we predict the masses of analogous quarkonia for c\bar{c} and b\bar{b} configurations. We employ a covariant Dyson-Schwinger-Bethe-Salpeter-equation approach with a rainbow-ladder truncated model of quantum chromodynamics.
Some of the non-relativistic QQ/bar interaction potentials and its isospectral partner-potentials have been employed to evaluate the masses and leptonic decay widths of Charmonium and Upsilon states. An attempt has been made to develop a prescription to provide a simultaneous fit to Masses and leptonic decay widths of Quarkonia. Preliminary calculation shows that the class of isospectral-potentials corresponding to: V(r)= -(alphas/r)+ar^n appears to yield the desired results. The various associated theoretical and phenomenological issues are discussed in light of recent data. The possible rela…
We present an implementation of heavy quarkonium production within a perturbative QCD cascade based on the Colour Dipole Cascade model. We consider the processes most relevant in the context of the psi' surplus at the Tevatron; g -> psi' and c -> psi' in the colour-singlet model and g -> psi' through the colour-octet mechanism. Our implementation is, however, easily extendible to other quarkonia and other production mechanisms. Where comparison is possible we find good agreement with analytical calculations. We present some suggestions for measurements at the Tevatron that would be sensitive t…
recently proposed strictly phenomenological static quark-antiquark potential belonging to the generality $V(r)=-Ar^{-α}+κr^β+V_{0}$ is tested with heavy quarkonia in the context of the shifted large N-expansion method. This nonrelativistic potential model fits the spin-averaged mass spectra of the $c\bar{c},$ $b\bar{b}$ and $c% \bar{b}$ quarkonia within a few ${\rm MeV}$ and also the five experimentally known leptonic decay widths of the $c\bar{c}$ and $b% \bar{b}$ vector states. Further, we compute the hyperfine splittings of the bottomonium spectrum as well as the fine and hyperfine splittin…
In this talk I review the recent progress made in the calculations of quarkonia production in fixed target experiments. NRQCD organizes the calculations in a systematic expansion in $α_s$ and $v$, the relative velocity between the heavy quarks. Within this formalism there are octet contributions which are not included in the color singlet model. These contributions depend upon unknown matrix elementsof local operators which are fit to the data. Using these fits, there are several predictions which do indeed improve agreement with the data. However, the prediction for the polarization of the pr…
We investigate the reaction gamma+p -> V+p, with V denoting a Phi or a J/Psi meson, within the scope of perturbative QCD, treating the proton as a quark-diquark system. Our predictions extrapolate the existing forward differential cross-section data into the few-GeV momentum-transfer region. In case of the J/Psi reasonable results are only obtained by properly taking into account its mass in the perturbative calculation of the hard-scattering amplitude.
We calculate the annihilation decay widths of spin-singlet heavy quarkonia $h_c, h_b$ and $η_b$} into light hadrons with both QCD and relativistic corrections at order $O(α_{s}v^{2})$ in nonrelativistic QCD. With appropriate estimates for the long-distance matrix elements by using the potential model and operator evolution method, we find that our predictions of these decay widths are consistent with recent experimental measurements. We also find that the $O(α_{s}v^{2})$ corrections are small for $b\bar{b}$ states but substantial for $c\bar{c}$ states. In particular, the negative contribution …
We review non-perturbative static potentials commonly used in potential models for quarkonia at finite T. Potentials derived from Polyakov loop correlators are shown to be inappropriate for this purpose. The q\bar{q} free energy is physical but has the wrong spatial decay and perturbative limit. The so-called singlet free energy is gauge dependent and unphysical. An appropriate static real time potential can be defined through a generalisation of pNRQCD to finite T. In perturbation theory, its real part reproduces the Debye-screened potential, its imaginary part accounts for Landau damping. Po…
The $Q \bar{Q}$ semirelativistic interaction in QCD can be expressed in terms of the Wilson loop and its functional derivatives. In this framework we discuss the complete (velocity and spin dependent) $1/m^2$ potential in the stochastic vacuum model and in the dual theory.
Within the nonrelativistic quantum chromodynamics framework, we make a comprehensive study on the exclusive production of excited charmonium and bottomonium in $e^+e^-\to γ^*/Z^0 \to|(Q\bar{Q})[n]\rangle +γ$ ($Q=c$ or $b$ quarks) at future $Z$ factory, where the $[n]$ represents the color-singlet $n^1S_0,~n^3S_1,~n^1P_0$ and $n^3P_J$ ($n=1,2,3,4; J=0,1,2$) Fock states. The "improved trace technology" is adopted to derive the analytic expressions at the amplitude level, which is useful for calculating the complicated $nP$-wave channels. Total cross sections, differential distributions, and unce…
The radiative spin-flip transition rates of heavy quarkonium states depend sensitively on the matrix elements of the effective confining interaction through the associated two-quark exchange current operator. The Hamiltonian model based on a scalar linear confining interaction with a single gluon exchange hyperfine term is shown to provide an adequate description of the $J/ψ\to η_cγ$ and $ψ(2S)\to η_cγ$ decay widths once the relativistic single quark magnetic moment operator is treated without approximation and the exchange current is taken into account. Predictions are given for the radiative…
We present a calculation of the two-photon and two-gluon widths for the equal mass quarkonium states $^1S_0$, $^3P_0$ and $^3P_2$ of the charmonium and upsilon systems. The approach taken is based on using the full relativistic $q\bar{q}\to\ga\ga$ amplitude together with a wave function derived from the instantaneous Bethe-Salpeter equation. Momentum space radial wave functions obtained from an earlier fit of the charmonium and upsilon spectra are used to evaluate the necessary integrals.
Based on Martin like potential, the S-wave masses of quarkonia have been reviewed. Resultant wave functions at zero inter quark separation are employed to compute the hyperfine splitting of the nS states and the leptonic and digamma decay widths of $n{^3S_1}$ and $n{^1S_0}$ states of quarkonia respectively. Analysis on the level differences of S-wave excited states of quantum mechanical bound systems show a systematic behaviour as n-increases. In view of such systematic behaviour expected for quarkonia, we observe that Y(4263) and X(4630) $1^{--}$ states are closer to the 4S and 6S states whil…
The mass spectra and decay properties of heavy quarkonia are computed in nonrelativistic quark-antiquark Cornell potential model. We have employed the numerical solution of Schrödinger equation to obtain their mass spectra using only four parameters namely quark mass ($m_c$, $m_b$) and confinement strength ($A_{c\bar c}$, $A_{b\bar b}$). The spin hyperfine, spin-orbit and tensor components of the one gluon exchange interaction are computed perturbatively to determine the mass spectra of excited $S$, $P$, $D$ and $F$ states. Digamma, digluon and dilepton decays of these mesons are computed usin…
We revisit the calculation of the width for the radiative decay of a $1^{+-}$ heavy $Q \bar Q$ meson via the channel $1^{+-} \to 0^{-+} +γ$ in the covariant light-front quark model. We carry out the reduction of the light-front amplitude in the non-relativistic limit, explicitly computing the leading and next-to-leading order relativistic corrections. This shows the consistency of the light-front approach with the non-relativistic formula for this electric dipole transition. Furthermore, the theoretical uncertainty in the predicted width is studied as a function of the inputs for the heavy qua…
The spectra of heavy quarkonia are studied in two approaches: with the use of the Afonin-Pusenkov representation of the Regge trajectory for the squared excitation energy $E^2(nl)$ (ERT), and using the relativistic Hamiltonian with the universal interaction. The parameters of the ERTs are extracted from experimental mass differences and their values in bottomonium: the intercept $a(b\bar b)=0.131\,$GeV$^2$, the slope of the orbital ERT $b_l(b\bar b) =0.50$\,GeV$^2$, and the slope of the radial ERT, $b_n(b\bar b)=0.724$\,GeV$^2$, appear to be smaller than those in charmonium, where $a(c\bar c)=…
We calculate the annihilation decay rates of the $^3D_2(2^{--})$ and $^3D_3(3^{--})$ charmonia and bottomonia by using the instantaneous Bethe-Salpeter method. The wave functions of states with quantum numbers $J^{PC}=2^{--}$ and $3^{--}$ are constructed. By solving the corresponding instantaneous Bethe-Salpeter equations, we obtain the mass spectra and wave functions of the quarkonia. The annihilation amplitude is written within Mandelstam formalism and the relativistic corrections are taken into account properly. This is important, especially for high excited states, since their relativistic…
