Narrow Results

The recently observed by CLEO cascade decays ϒ(3S)→γχ'_bJ→γωϒ are discussed. It is shown that within the nonrelativistic description of bottomonium in the heavy b quark limit, the ratio of the rates of the transitions χ'_bJ→ωϒ with J = 1 and J = 2 should be given by the ratio of the corresponding S wave phase space factors. As a result, the rate of the observed cascade transitions through the χ'_b2 resonance should be close to that through the χ'_b1. It is suggested that the ratio of the discussed cascade rates can also be tested by measuring a simple angular correlation.

The recently obtained solutions of Dirac equation in the confining SU(3)-Yang–Mills field in Minkowski spacetime are applied to describe the energy spectra of quarkonia (charmonium and bottomonium). The nonrelativistic limit is considered for the relativistic effects to be estimated in a self-consistent way and it is shown that the given effects are extremely important for both the energy spectra and the confinement mechanism.

The properties of bottomonia are investigated in detail in the constituent quark model. The wave functions of bottomonia are obtained by solving Dirac equation and Schrödinger equation. The potentials between quark and antiquark include color confinement (linear and quadratic) and one-gluon-exchange. Based on the obtained wave functions, the electromagnetic and two-photon decay, electric dipole transition, and hadronic width of bottomonia are calculated. The calculated results are in a good agreement with the experimental data. The results also show that the nonrelativistic and relativistic version of quark model can all describe the properties of bottomonia.

The Belle-II experiment is expected to collect large data samples at the $\mathrm{{\rm Y}}(4S)$ and $\mathrm{{\rm Y}}(5S)$ resonances to study primarily $B$ and $B_s$ mesons. We discuss what other data above the $B\bar{B}$ threshold are of interest. We propose to perform a high-statistics energy scan from the $B\bar{B}$ threshold up to the highest possible energy, and to collect data at the $\mathrm{{\rm Y}}(6S)$ and at higher mass states if they are found in the scan. We emphasize the interest in increasing the maximal energy from 11.24 GeV to 11.5–12 GeV in the future. These data are needed for the investigation of bottomonium and bottomonium-like states.

The mass spectrum of $b\bar{b}$ states has been obtained using the phenomenological relativistic quark model (RQM). The Hamiltonian used in the investigation has confinement potential and confined one gluon exchange potential (COGEP). In the framework of RQM a study of $M1$ and $E1$ radiative decays of $b\bar{b}$ states has been made. An overall agreement is obtained with the experimental masses and decay widths. The possibility that some of the excited $s$ wave $b\bar{b}$ states being exotic states is explored.

The variational method and the Hamiltonian formalism of QCD are used to derive relativistic, momentum space integral equations for a quark–antiquark system with an arbitrary number of gluons present. As a first step, the resulting infinite chain of coupled equations is solved in the nonrelativistic limit by an approximate decoupling method. Comparison with experiment allows us to fix the quark mass and coupling constant, allowing for the calculation of the spectra of massive systems such as charmonium and bottomonium. Studying the results with and without the non-Abelian terms, we find that the presence of the non-Abelian factors yields better agreement with the experimental spectra.

We present the current status of the study at the Tevatron, of the exclusive processes: and , produced via two photon interactions; , and from Double Pomeron Exchange (DPE); and, , and ; from photon-pomeron fusion (photoproduction). In closing we briefly discuss the plans for, and benefits of, studying exclusive physics at the LHC.

We review results of recent studies of transitions between bottomonium states obtained from analysis of the large $e^{+}{e}^{-}$ data sample recorded by the Belle detector at various $\mathrm{{\rm Y}}$-resonances and energy scan data in the center-of-mass energy range from $\sqrt{s}=10.63$ GeV to 11.02 GeV.

We discuss three possible scenarios for the interpretation of mesons containing a heavy quark and its antiquark near and above the first threshold for a decay into a pair of heavy mesons in a relative $S$-wave. View I assumes that these thresholds force the quark potential to flatten which implies that while in these energy ranges molecular states may be formed, there should not be any quark–antiquark states above these thresholds. View II assumes that the main part of the interaction between two mesons is due to the poles which originate from the $Q\bar{Q}$ interaction. The properties of the $Q\bar{Q}$ mesons are strongly influenced by opening thresholds but the number of states is given by the quark model. In View III, both types of mesons are admitted also near and above the open flavor thresholds: $Q\bar{Q}$ mesons and dynamically generated mesons. Experimental consequences of these different views are discussed.

In the medium of relativistic heavy-ion collisions, dissociation of the quarkonium and its survival have been studied to understand the properties of Quark Gluon Plasma (QGP). The coupled rates of dissociation and recombination reactions in QGP are commonly solved with the Boltzmann transport equation in which the formation and dissociation reactions compete with each other. Since the dissociation of newly formed bound-states is not accounted in the Boltzmann equation, a framework of decoupled rates is developed to assess the combined effect of gluon-induced dissociation and recombination (though it is small for $\mathrm{\Upsilon }$) together with color screening on bottomonium production in heavy-ion collisions at center of mass energy $(\sqrt{s_{\mathrm{\text{NN}}}})=5.02$TeV. To calculate the recombination rates, we have employed an effective method of Bateman solution which ensures the correlated effect between the recombination and the dissociation of the newly combined bottomonium in the QGP medium. The modifications of bottomonium have been estimated in an inflating QGP with the constraints matching with the dynamics of $\mathrm{\text{Pb}}+\mathrm{\text{Pb}}$ collision events at LHC.

In this paper, we calculate the mass spectrum, weak decay constants, two photon decay widths, and two-gluon decay widths of ground ($1S$) and radially excited ($2S,3S,\dots$) states of pseudoscalar charmoniuum and bottomonium such as ${\eta }_c$ and ${\eta }_b$, as well as the mass spectrum and leptonic decay constants of ground state ($1S$), excited ($2S,1D,3S,2D,4S,\dots ,5D$) states of vector charmonium and bottomonium such as $J/\psi$, and $\mathrm{{\rm Y}}$, using the formulation of Bethe–Salpeter equation under covariant instantaneous ansatz (CIA). Our results are in good agreement with data (where ever available) and other models. In this framework, from the beginning, we employ a $4\times 4$ representation for two-body ($q\overline{q}$) BS amplitude for calculating both the mass spectra as well as the transition amplitudes. However, the price we have to pay is to solve a coupled set of equations for both pseudoscalar and vector quarkonia, which we have explicitly shown get decoupled in the heavy-quark approximation, leading to mass spectral equation with analytical solutions for both masses, as well as eigenfunctions for all the above states, in an approximate harmonic oscillator basis. The analytical forms of eigenfunctions for ground and excited states so obtained are used to evaluate the decay constants and decay widths for different processes.

In relativistic Heavy-Ion Collisions (HIC), scientists have discussed the bottomonium dissociation and survival to gain insights about the characteristics of Quark Gluon Plasma (QGP). The Boltzmann transport equation is commonly employed to explore the interaction between dissociation and recombination rates in QGP, where the processes of formation and dissociation exhibit competing dynamics. However, the Boltzmann equation does not account for the dissociation of new bound states created in QGP medium. To overcome this restriction, a system of independent rates has been developed. This approach assesses the combined effects of gluon-induced dissociation, recombination (although minor for the ϒ states), and color screening on the generation of bottomonium in HIC. The investigation includes PbPb and XeXe collisions at center-of-mass energies $\sqrt{s_{\mathrm{\text{NN}}}}=5.02$TeV and $\sqrt{s_{\mathrm{\text{NN}}}}=5.44$ TeV, respectively. Recombination rates are computed employing the efficient Bateman solution technique, ensuring a comprehensive examination of the interaction between the recombination and dissociation within the QGP, along with the limitations associated with PbPb and XeXe collision kinetics at the Large Hadron Collider (LHC). The model has demonstrated considerable success in accurately describing the suppression of ϒ$(nS)$ states across collision systems of different sizes.

With an extended quark pair creation model we systematically study the OZI-allowed three-body open flavor decays of higher vector charmonium and bottomonium states. We obtain that the BB^*π and B^*B^*π partial decay widths of ϒ(10860) are consistent with experiment, and the corresponding partial decay widths of ϒ(11020) can reach up to 2~3 MeV. Meanwhile the partial widths of DD^*π and D^*D^*π modes for most higher vector charmonium states can reach up to several MeV.

A new scheme for calculating masses and boost-invariant wave functions of heavy quarkonia is developed in a light-front Hamiltonian formulation of QCD. Only the simplest approximate version with one flavor of quarks and an ansatz for the mass gap for gluons is discussed. The resulting spectra look reasonably good in view of the crude approximations made in the simplest version.