A Light-Cone QCD Inspired Meson Model with a Relativistic Confining Potential in Momentum Space

For describing the radial excited states a relativistic confining potential in momentum space is included in the meson effective light-cone Hamiltonian. The meson eigen equations are transformed from the front form to the instant form and formulated in total angular representation. Details about numerically solving these equations are discussed, mainly focusing on treating singularities arising from one-gluon exchange interactions and confinement. The results of pseudo-scalar mesons indicate that the improved meson effective light-cone Hamiltonian can describe the ground states and radial excited states well. Some radial excited states are also predicted and waiting for experimental test.     

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.     

Spinor strong interaction model for meson spectra

A model for a bound quark-antiquark system is constructed from quark spinor equations and the associated pseudoscalar massless interaction potential equations in a way departing from conventional relativistic quantum mechanics. From the so-constructed covariant meson equations, linear confinement arises naturally. Nonlinear radial equations for the pseudoscalar and vector mesons in the rest frame are derived without approximation. An internal complex space is introduced for representation of the quark flavors. Quark masses are generalized to operators operating on functions in this space. A simple model is proposed for the meson internal functions and mass operators producing the squares of the average quark masses as eigenvalues. The present space-time model calls for a particle classification scheme different from the usual nonrelativistic one. When combined with the internal model, it may account for the gross structure of the meson spectra together with the form of an empirical relation. Upper limits of bare quark masses are estimated from simplified analytical solutions of the radial equations and agree approximately with the bare quark masses obtained from baryon data in a companion paper. The radial equations are solved numerically yielding estimates of the strong interaction radii of the ground state mesons.     

坐标算符本征矢的表示与不对称投影算符的积分

借助于粒子数算符的本征态和坐标算符函数的本征方程,把坐标算符的本征矢〈f(x)|表示为一个算符对坐标本征矢〈x|的作用.由此,把不对称的坐标投影算符转换为对称的坐标投影算符,再利用坐标本征矢的完备性,给出不对称坐标投影算符的积分. 关键词： 本征矢 算符的积分 本征方程 完备性     

Hartmann势加新环型势的相对论束缚态解(英文)

在矢势与标势相等的情况下,对Hartmann势加新环型势的Klein-Gordon方程精确求解.给出了归一化的角向和径向波函数,同时获得了能谱方程.     

Towards hadron spectroscopy based on relativistic schrödinger-type potential wave equations

The relativistic potential Schrödinger-type equations are proposed as a basis for calculation of spectroscopic characteristics of different quarkonia. Within this approach the Regge-trajectory characteristics for light hadrons, some properties of higher radial excitations in light quark sector, and lowest hybrid vector mesons in the charm- and bottom-sectors are discussed, as well as evaluation of mixing of low-lying vector charmonia with the lowest hybrid (gcc)-state is presented.     

Spin Effects in Two Quark System and Mixed States

Based on the numeric solution of a system of coupled channels for vector mesons (S-and D-waves mixing)and for tensor mesons (P- and F- waves mixing) mass spectrum and wave functions of a family of vector mesons q in triplet states a e obtained. The calculations are performed using a well-known Cornell potential with a mixed Lorentz- structure of the confinement term. The spin-dependent part of the potential is taken from the Breit-Fermi approach.The effect of irregular terms of the potential is considered within the framework of the perturbation theory and/or of the configuration interaction approach, modified for a system of coupled equations. It is shown that even a small integral contribution of the D-wave to the total wave function of q system is very impotant for the calculation of certain characteristics of the meson states.     

A Study of One S- and One P-Wave Heavy Meson Interaction in a Chiral Quark Model

The analytical forms of the interaction potentials between one pseudo-scalar/vector and one scalar/tensor/axial-vector heavy mesons are deduced based on a chiral quark model. Our results explicitly show the attractive property between the two heavy mesons. Consequently, a series of possible molecular states are obtained. It is expected that our study might shed some light on the popular discussions of the newly observed XYZ states.     

Study of the nature of \iota/\eta(1440) in the chiral perturbation theory approach

The nature of is analysed in the framework of the hypothesis that it represents a single pseudoscalar resonance. Assuming that it arises due to the mixing between the glueball and the nearby states (, , and their radial excitations) two upper estimates are obtained for the partial width – one for the case when is mainly a glueball and another one when it is mainly a radial excitation of the state. Both estimates are obtained in the chiral perturbation theory approach taking into account the available data on the vector mesons and the pseudoscalar state , which is interpreted as a radial excitation of the meson. The same partial width is independently estimated on the basis of the combined OBELIX and Crystal Barrel data on the production of in annihilation. Comparing the results we show that the glueball content of is suppressed while its radial-excitation interpretation is favoured by the data. Received: 25 November 1997 / Revised version: 6 January 1998 / Published online: 24 April 1998     

瞬时相互作用近似下介子结构波函数的一些探讨(Ⅰ)——瞬时相互作用下介子波函数的一般性质

本文从一对正反费米子结合成束缚态的Bethe-Salpeter方程(以下简称B-S方程)出发,假定正反层子间相互作用可以近似地用质心系瞬时相互作用描写,得到的主要结论如下:(1)B-S方程的求解可归结为在质心系三维空间内进行。描写赝标介子和矢量介子的波函数独立旋量分量的个数分别由4个和8个减少为2个和4个;(2)如果相互作用是空间球对称的,其旋量结构是对角耦合,从赝标介子方程中可以直接看到,束缚态质量作为本征值在方程中是以平方形式出现,同时又可避免四维方程中负激发的困难;(3)在瞬时相互作用近似下给出的结构波函数,可以用来研究束缚态的质量谱和只涉及质心系的过程。     

Coupling constants and the nonrelativistic quark model with charmonium potential

Hadronic coupling constants of the vertices including charm mesons are calculated in a nonrelativistic quark model. The wave functions of the mesons which enter the corresponding overlap integrals are obtained from the charmonium picture as quark-anti-quark bound state solutions of the Schrödinger equation. The model for the vertices takes into account in a dynamical way the SU₄ breakings through different masses of quarks and different wave functions in the overlap integrals. All hadronic vertices involving scalar, pseudoscalar, vector, pseudovector and tensor mesons are calculated up to an overall normalization constant. Regularities among the couplings of mesons and their radial excitations are observed: (i) Couplings decrease with increasing order of radial excitations; (ii) in general they change sign if a particle is replaced by its next radial excitation. The k-dependence of the vertices is studied. This has potential importance in explaining the unorthodox ratios in different decay channels (e.g. $\text{D}\text{D}\text{, D}\text{D}{}^1\text{, D}{}^1\text{D}{}^1$). Having got the hadronic couplings radiative transitions are obtained with the current coupled to mesons and their recurrences. The resulting width values are smaller than those conventionally obtained in the native quark model. The whole picture is only adequate for nonrelativistic configurations, as for the members of the charmonium- or of the γ-family and most calculations have been done for transitions among charmed states. To see how far nonrelativistic concepts can be applied, couplings of light mesons are also considered.     

Radial excitations of scalar, η, and η′ mesons in a chiral quark model

First radial excitations of the scalar-meson nonet and of the pseudoscalar mesons η and η′ are described within a nonlocal chiral quark model of the Nambu-Jona-Lasinio type with ′t Hooft interaction. In this model, simple form factors are used, which allows us to describe first radial excitations of the mesons and to retain the gap equations describing spontaneous breakdown of chiral symmetry in the standard form. The external parameters of form factors are fixed by the masses of excited pseudoscalar mesons, and the same form factors are used to predict the masses of excited scalar mesons. The strong decays of excited scalar mesons and of η and η′ mesons are described in satisfactory agreement with experimental data.     

THE WAVE EQUATIONS AND MASS SPECTRA OF BARYON STATES IN THE QUARK MODEL

The independent particle approximation is used to treat the bound state problems in the quark model. The solution for meson states obtained in this approximation is the same as that obtained from the Bethe-Salpeter equation. The solution for the baryon states is also obtained. The mass spectra of mesons and baryons determined from these equations are in agreement with the experiment.     

Effective restoration of chiral symmetry in excited mesons

A fast restoration of chiral symmetry in excited mesons is demonstrated. A minimal “realistic” chirally symmetric confining model is used, where the only interaction between quarks is the linear instantaneous Lorentz-vector confining potential. Chiral symmetry breaking is generated via the nonperturbative resummation of valence quarks self-energy loops and the meson bound states are obtained from the Bethe–Salpeter equation. The excited mesons fall into approximate chiral multiplets and lie on the approximately linear radial and angular Regge trajectories, though a significant deviation from the linearity of the angular trajectory is observed.     

Effective chiral symmetry restoration in excited mesons

Results on the spectrum of ${\bar q} q$ mesons in a model with a linear Coulomb-like instantaneous confining potential are presented. The single-quark Green function as well as the dynamical chiral symmetry breaking are obtained from the Dyson-Schwinger (gap) equation. Given the dressed quark propagator, the spectrum of “usual” mesons, i.e., ${\bar q} q$ states with nonexotic quantum numbers J ^PC , is obtained from the Bethe-Salpeter equation. Effective restoration of chiral symmetry at large spins and/or radial excitations is observed and the states fall into approximate linear radial and angular Regge trajectories.     

Processes e<Superscript>+</Superscript>e<Superscript>−</Superscript> → π<Superscript>0</Superscript>(π<Superscript>0</Superscript>′) γ in extended NJL model

The processes of electron-positron annihilation into π⁰γ and into π′(1300)γ are considered within an extended NJL model. The intermediate vector mesons ρ ⁰, ω ρ′(1450), and ω(1420) are taken into account. The latter two mesons are treated as the first radial excited states. They are incorporated into the NJL model by means of a polynomial form factor. Numerical predictions for the cross-sections of these processes are received for the center-of-mass energies below 2 GeV. Our results for the π⁰γ production are in agreement with experimental data obtained in the energy region 600–1020 MeV.