Ground state admixture into the ψ″ (3.772)

The usual potential model is used to estimate the orbital mixing into the ψ″ (3.772), whose leptonic width appears to be too small. It is emphasized that the admixedS-wave component is not saturated by the first radial excitation and contains a sizable part of the ground state.     

Time Evolution of Colour Screening and Suppression of J/ψ、χ and ψ' by Quark-Gluon Plasma

We discuss the time evolution of the colour screening and J/ψ、χ and ψ' suppression by the quark-gluon plasma within the non-relativistic confining potential model.     

Bottomonium states versus recent experimental observations in the QCD-inspired potential model

In the QCD-inspired potential model where the quark-antiquark interaction consists of the usual one-gluon-exchange and the mixture of long-range scalar and vector linear confining potentials with the lowest order relativistic correction, we investigate the mass spectra and electromagnetic processes of a bottomonium system by using the Gaussian expansion method. It reveals that the vector component of the mixing confinement is anticonfining and takes around 18.51% of the confining potential. Combining the new experimental data released by Belle, BaBar and LHC, we systematically discuss the energy levels of the bottomonium states and make the predictions of the electromagnetic decays for further experiments.     

Charmonium States in QCD-Inspired Quark Potential Model Using Gaussian Expansion Method

We investigate the mass spectrum and electromagnetic processes of charmonium system with the nonperturbative treatment for the spin-dependent potentials, comparing the pure scalar and scalar-vector mixing linear confining potentials. It is revealed that the scalar-vector mixing confinement would be important for reproducing the mass spectrum and decay widths, and therein the vector component is predicted to be around 22?%. With the state wave functions obtained via the full-potential Hamiltonian, the long-standing discrepancy in M1 radiative transitions of J/ψ and ψ′ are alleviated. This work also provides an inspection and suggestion for the possible cc? states among the copious higher charmonium-like states. Particularly, the newly observed X(4160) and X(4350) are found in the charmonium family mass spectrum as M(2¹ D ₂)?= 4164.9 MeV and M(3³ P ₂)?= 4352.4 MeV, which strongly favor the J ^PC ?=?2^?+, 2⁺⁺ assignments respectively. The corresponding radiative transitions, leptonic and two-photon decay widths have been also predicted theoretically for the further experimental search.     

Light Flavor Vector and Pseudo Vector Mesons from a Light-Cone QCD Inspired Effective Hamiltonian Model with SU（3） Flavor Mixing Interactions

Based on the light-cone effective Hamiltonian with confining potential and SU （3） flavor mixing interactions, the flavor mixing mesons on the u, d, and s quark sectors are investigated. The mass eigen equations of the flavor mixing vector and pseudo vector mesons are solved. The calculated masses are in good agreement with the experimental data.     

Normal forms generalizing action-angle coordinates for Hamiltonian actions of Lie groups

Let (M, Ω) be a symplectic manifold on which a Lie group G acts by a Hamiltonian action. Under some restrictive assumptions, we show that there exists a symplectic diffeomorphism ψ of a G-invariant open neighbourhood U of a given G-orbit in M, onto an open subset ψ(U) of a vector bundle F ^*, with base space G. Explicit expressions are given for the symplectic 2-form, for the momentum map and for a Hamiltonian vector field whose Hamiltonian function is G-invariant, on the model symplectic manifold ψ(U).     

Spin-dependence and glueball mixing with θ(1640) in ordinary meson spectroscopy

It is shown from a fairly general point of view that meson spectroscopy implies that the spin-spin and tensor forces are due to very short-ranged interactions. The (Q₁, Q₂) ? (Q_A, Q_B) mixing of axial vector $\text{I =}\text{1}\text{2}$ mesons implies the presence of a substantial repulsive Thomas term as well as an attractive short-ranged spin-orbit force of comparable magnitude. This analysis makes no reference to detailed potentials or wave functions. Inverted multiplets are predicted as a consequence of the large repulsive Thomas term. The spin-dependent potentials can be interpreted as effective exchanges dominated by short-ranged vector exchange and a confining potential transforming as a Lorentz scalar, although small amounts of other exchanges are also possible. A model-dependent analysis of the gluon annihilation contribution to the mass matrix and two-body decays of the I = 0 2⁺⁺ mesons indicates significant gluon mixing in these states. The presence of a $\text{non-q}\text{q}$ state (glueball?) which mixes with f'(1514) and another I = 0 2⁺⁺ state is required by the mixing model. The possibility that this additional state is θ(1640) is considered. The mass of such a state satisfies f'(1514)<M(G₀)<θ(1640). The model predicts $\text{0.01 < Λ(θ → ηη)/Λ(θ →}\text{K}\text{K}\text{)<0.18}$, with the actual widths sensitive to the details of singlet-octet mixing in the η wave function.     

Fermionic composite models from confining SU(2)L

A class of fermionic composite models with SU(2)_L as confining group is discussed utilizing the notion of complementarity. The models are, in some sense, fermionic realizations of the bosonic Abbott-Farhi model, avoiding fundamental scalars. Model A has SU(2)_L as confining group; model B has an additional chiral SU(M) and coincides with a model by Abbott, Fahri and Schwimmer; model C has an additional vector SU(M) and provides for a closer realization of the original basonic model.     

ON THE ELECTRIC DIPOLE TRANSITIONS OF ψ(3770)

Various E1 transition rates for cc states are calculated in a QCD-motivated potential model.Relativistic corrections are found to be substantial.While a good agreement between theory and experiment is achieved for the rates of ψ(2s)→γχ_cJ and χ_cJ→γψ(1S)(J=0,1,2),the calculated rates for ψ(3770)→γχ_cJ are smaller by a factor of～2 than their experimental values obtained by the MarkⅢ collaboration.The effect of the 2³S₁—1³D1 mixing is possibly important and needed to be considered.     

Spectral properties of quantum dots influenced by a confining potential model

We obtain the exact energy spectra and corresponding wave functions of the spherical quantum dots for any (n,l) state in the presence of a combination of pseudo-harmonic, Coulomb and linear confining potential terms within the exact analytical iteration method (EAIM). The interaction potential model under consideration is labeled as the Cornell modified-plus-harmonic (CMpH) type which is a correction form to the harmonic, Coulomb and linear confining potential terms.     

Low-Energy Scattering of Heavy-Light Mesons from Nucleons

We study the low-energy scattering of charmed (D) and strange (K) mesons by nucleons. The short-distance part of the interaction is due to quark-gluon interchanges derived from a model that realizes dynamical chiral symmetry breaking and confines color. The quark-gluon interaction incorporates a confining Coulomb-like potential extracted from lattice QCD simulations in Coulomb gauge and a transverse hyperfine interaction consistent with a finite gluon propagator in the infrared. The long-distance part of the interaction is due to single vector (??, ??) and scalar (??) meson exchanges. We show results for scattering cross-sections for isospin I?=?0 and I?=?1.     

Scalar and vector meson propagation in asymmetric nuclear matter

The propagation of the scalar (σ and δ) and vector (ω and ρ) mesons in an iso-asymmetric nuclear matter is studied in detail, using the Walecka model. We calculate the invariant masses and spectral functions of the mesons, including the effect of meson mixing. At finite density, the mixing effect is quite important in the propagation of the scalar and (longitudinal) vector mesons. In the σ channel, we find a three-peak structure in the spectral function, caused by the mixing effect.     

One-dimensional hypervirial theorems in density functional theory

For a restricted class of operators hypervirial theorems are established involving wavefunctions ψ_i for N fermions which move independently in a common external one-dimensional potential V(x). Using this class it is possible to perform the summation over states ψ_i yielding exact relations between ground state density ? and kinetic energy density ?_k and potential V(x). It is checked to what extent the Thomas-Fermi expressions for ? and ?_k satisfy these relations.     

Vector states in e+e− annihilation at 3.9–4.5 GeV

The structure observed at SPEAR in e⁺e^? annihilation in the energy range 3.9–4.5 GeV is explained in an SU(8) × SL(3, R) color quark model. The model can account for the mass differences, total hadronic and leptonic widths, as well as for the rise in, and the magnitude of, R. Main predictions are the SU(3) properties of these states, strong suppression of their decays into the ψ(3.1) and the existence of another vector meson around 6 GeV.     

Region operators of wigner function: Transformations, realizations and bounds

An integral of the Wigner function of a wave function ψ>, over some region S in classical phase space is identified as a (quasi)-probability measure (QPM) of S, and it can be expressed by the ψ> average of an operator referred to as the region operator (RO). Transformation theory is developed which provides the RO for various phase-space regions such as point, line, segment, disk and rectangle, and where all those ROs are shown to be interconnected by completely positive trace increasing maps. The latter are realized by means of unitary operators in Fock space extended by 2D vector spaces, physically identified with finite-dimensional systems. Bounds on QPMs for regions obtained by tiling with discs and rectangles are obtained by means of majorization theory.     

Phenomenology of the ψ (3105) and the hypothesis of charm

We estimate the effective coupling strengths of the ψ(3105) to ordinary hadrons and examine possibility that this resonance is the uncharmed vector meson φ_c composed predominantly of charmed quarks. Distinctive decay modes of φ_c are pointed out.     

Are spin-dependent forces in charmonium generated through scalar-vector admixture?

I show that if the spin-dependent confining forces are generated through scalar-vector admixture then the ³p_J splittings restrict the vector to scalar ratio to be less than half. Further it is shown that an accurate measurement of the ¹p₁ mass can clearly distinguish this model from vector and scalar exchange models.     

3 S 1−3 D 1 mixing and E1 radiative transitions in charmonium

The radiative transitions ψ′→γ+χ _J and χ _J →γ+ψ are studied in the quark model with the ψ and ψ′ interpreted conventionally as³ S ₁ \(c\bar c\) states and the χ _J as³ P _J \(c\bar c\) states. In particular, the effect of³ S ₁?³ D ₁ mixing on the decay widths is calculated. The photon angular distributions in these decays are also studied and are found to be a more sensitive test of³ D ₁ admixtures in the Ψ states. The³ D ₁ content of the Ψ is found to be large but the estimate is very sensitive to the photon angular distributions. More precise measurements could help to explain the large ψ″ leptonic width.     

Calculation of the wave functions of the ground and weakly excited states of helium II

The wave functions of the ground (Ψ₀) and the first excited (Ψ_k) states of He II in the second-order approximation, i.e., up to the first two corrections to the corresponding solutions for a weakly nonideal Bose gas, are determined by the collective variable method, which was proposed by Bogolyubov and Zubarev and developed in the studies by Yukhnovskii and Vakarchuk. The functions Ψ₀ and Ψ_k = ψ_kΨ₀ are determined as the eigenfunctions of the N-particle Schrödinger equation from a system of coupled equations for Ψ₀, Ψ_k, and the quasiparticle spectrum E(k) of helium II. The results consist in the following: (1) these equations are solved numerically for a higher order approximation compared with those investigated earlier (the first-order approximation), and (2) Ψ₀ and ψ_k are derived from a model potential of interaction between He⁴ atoms (rather than from the structure factor as earlier) in which the potential barrier is joined with the attractive potential found from experiment. The height V ₀ of the potential barrier is a free parameter. Except for V ₀, the model does not have any free parameters or functions. The calculated values of the structure factor, the ground-state energy E ₀, and the quasiparticle spectrum E(k) of He II are in agreement with the experimental values for V ₀ ≈ 100 K. The second-order correction to the logarithm of Ψ₀ significantly affects the value of E ₀ and provides the asymptotics E(k → 0) = ck, while the second-order correction to ψ_k slightly affects the E(k). The second-order corrections to Ψ₀ and ψ_k have a smaller effect on the results compared with the first-order corrections, whereby the theory is in agreement with experiment; therefore, one may assume that the truncated Ψ₀ and ψ_k well describe the microstructure of He II. Thus, the series for Ψ₀ and Ψ_k can be truncated in spite of the fact that the expansion parameter is not very small (～1/2).