Electromagnetic Form Factor of Charged Scalar Meson

Wavefunctions and the electromagnetic form factor of charged scalar mesons are studied with the vector-vectortype fiat-bottom potential model under the framework of the spinor-spinor Bethe-Salpeter equation. The obtained results are in agreement with other theories.     

Decay Constants of Vector Mesons

The light vector mesons are studied within the framework of the Beth-Salpeter equation with the vector vectortype flat-bottom potential. The Bethe-Salpeter wavefunetions and the decay constants of the vector mesons are obtained. All the obtained results, fp, f φ, and fK＊, are in agreement with the experimental values, respectively.     

Assignment of Isodoublet of 2^3S1 Meson Nonet

Inserting the masses of some states, which have been established in theexperiments or the theory of lattice QCD, we investigate the mass of theisodoublet of the 2³S₁ meson nonet. The agreement results, 1567±22.6MeV and 1576.8MeV, are given by two different approaches. We suggest that the assignment of 2³S₁ meson nonet should be re-examined in future experiments.     

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.     

A Light-Cone QCD Inspired Effective Hamiltonian Model for Pseudoscalar and Scalar Mesons

Considering the one-gluon exchange interaction and phenomenological quark confinement potential, an improved light-cone effective Hamiltonian for mesons and the corresponding radial mass eigen equations in angular momentum representation is obtained. Solving the J = 0 eigen equations numerically and using a set of adjustable parameters, the obtained solutions for ground states and radial excited states can simultaneously describe both pseudoscalar and scalar flavour-off-diagonal mesons. Some radial excited states are also predicted and wait for experimental test. More results for the vector and axial vector mesons are expected.     

The inverse problem in the case of bound states

We investigate the inverse problem for bound states in the D = 3 dimensional space. The potential is assumed to be local and spherically symmetric. The present method is based on relationships connecting the moments of the ground state density to the lowest energy of each state of angular momentum ?. The reconstruction of the density ρ(r) from its moments is achieved by means of the series expansion of its Fourier transform F(q). The large q-behavior is described by Padé approximants. The accuracy of the solution depends on the number of known moments. The uniqueness is achieved if this number is infinite. In practice, however, an accuracy better than 1% is obtained with a set of about 15 levels.The method is tested on a simple example, and applied to three different spectra.     

Quark mass dependence of the pion vector form factor

We examine the quark mass dependence of the pion vector form factor, particularly the curvature (mean quartic radius). We focus our study on the consequences of assuming that the coupling constant of the ρ   to pions, g_ρππ$g_{\rho \pi \pi }$, is largely independent of the quark mass while the quark mass dependence of the ρ mass is given by recent lattice data. By employing the Omnès representation we can provide a very clean estimate for a certain combination of the curvature and the square radius, whose quark mass dependence could be determined from lattice computations. This study provides an independent access to the quark mass dependence of the ρππ   coupling and in this way a non-trivial check of the systematics of chiral extrapolations. We also provide an improved value for the curvature for physical values for the quark masses, namely 〈r⁴〉=0.73±0.09 fm⁴$〈r^4〉=0.73\pm 0.09{\text{fm}}^4$ or equivalently cV=4.00±0.50 GeV−4$c_V=4.00\pm 0.50{\text{GeV}}^{-4}$.     

Electromagnetic form factor via Bethe-Salpeter amplitude in Minkowski space

For a relativistic system of two scalar particles, we find the Bethe-Salpeter amplitude in Minkowski space and use it to compute the electromagnetic form factor. The comparison with Euclidean space calculation shows that the Wick rotation in the form factor integral induces errors which increase with the momentum transfer Q². At JLab domain (Q ² = 10 GeV^2/c²), they are about 30%. Static approximation results in an additional and more significant error. On the contrary, the form factor calculated in light-front dynamics is almost indistinguishable from the Minkowski space one.     

Calculation of Kaon Electromagnetic Form Factor in the Framework of Coupled Schwinger—Dyson and Bethe—Salpeter Formulation

The kaon electromagnetic form factor is calculated in the framework of coupled Schwinger-Dyson equation in rainbow approximation and Bethe-Salpeter equation in ladder approximation with the modified flat-bottom potential,which is the combination of the flat-bottom potential with considerations for the infrared and ultraviolet asymptotic behaviours of the effective quark-gluon coupling.All our numerical results give good fit to experimental values and other theoretical results.     

Electromagnetic properties of strange baryons in a relativistic quark model

We present some of our results for the electromagnetic properties of excited Σ hyperons, computed within the framework of the Bonn constituent-quark model, which is based on the Bethe-Salpeter approach. The seven parameters entering the model are fitted against the best-known baryon masses. Accordingly, the results for the form factors and helicity amplitudes are genuine predictions. We compare with the scarce experimental data available and discuss the processes in which Σ ^*'s may play an important role.     

The Physics of Exclusive Reactions in QCD: Theory and Phenomenology

The modern formulation of exclusive reactions within Quantum Chromodynamics is reviewed, the emphasis being placed on the pivotal ideas and methods pertaining to perturbative and non-perturbative topics. Specific problems, related to scale locality, infrared safety, gluonic radiative corrections (Sudakov effects), and the role of hadronic size effects (intrinsic transverse momentum), are studied. These issues are more precisely analyzed in terms of the essential mechanisms of momentum transfer to a hadron while remaining intact. Different factorization schemes are considered and the conceptual lacunas are pointed out. The quite technical subject of renormalization-group evolution is given a detailed account. By combining analytical and numerical algorithms, the one-gluon exchange nucleon evolution equation is diagonalized and next-to-leading eigenfunctions are calculated in terms of Appell polynomials. The corresponding anomalous dimensions of trilinear quark operators are found to form a degenerate system whose envelope shows logarithmic large-order behavior. Selected applications of this framework are presented, focusing on the helicity-conserving elastic form factors of the pion and the nucleon. The theoretical constraints imposed by QCD sum rules on the moments of nucleon distribution amplitudes are used to determine a whole spectrum of optional solutions. They organize themselves along an “orbit” characterized by a striking scaling relation between the form-factor ratio and the projection coefficient B₄ on to the corresponding eigensolution. The main reasons for the failure of the present theoretical predictions to match the experimental data are discussed and workable explanations are sketched.     

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.     

Flavor content of nucleon form factors in a VMD approach

The strange form factors of the nucleon are studied in a two-component model consisting of a three-quark intrinsic structure surrounded by a meson cloud. A comparison with the available experimental world data from the SAMPLE, PVA4, HAPPEX and G0 Collaborations shows a good overall agreement. It is shown that the strangeness contribution to the electric and magnetic form factors is of the order of a few percent. In particular, the strange quark contribution to the charge radius is small 〈r ² _s〉_E = 0.005 fm^2 and to the magnetic moment it is positive μ_s = 0.315 μ_N .     

Helicity amplitudes and electromagnetic decays of hyperon resonances

We present results for the helicity amplitudes of the lowest-lying hyperon resonances Y^*, computed within the framework of the Bonn Constituent-Quark model, which is based on the Bethe-Salpeter approach. The seven parameters entering the model were fitted to the best-known baryon masses. Accordingly, the results for the helicity amplitudes are genuine predictions. Some hyperon resonances are seen to couple more strongly to a virtual photon with finite Q² than to a real photon. Other Y^*'s, such as the S₀₁(1670) Λ-resonance or the S₁₁(1620) Σ-resonance, couple very strongly to real photons. We present a qualitative argument for predicting the behaviour of the helicity asymmetries of baryon resonances at high Q².-1     

Form factors in RQM approaches: Constraints from space-time translations

Different relativistic quantum-mechanic approaches have recently been used to calculate properties of various systems, form factors in particular. It is known that predictions, which most often rely on a single-particle current approximation, can lead to predictions with a very large range. It was shown that accounting for constraints related to space-time translations could considerably reduce this range. It is shown here that predictions can be made identical for a large range of cases. These ones include the following approaches: instant form, front form, and “point form” in arbitrary momentum configurations and a dispersion-relation approach which can be considered as the approach which the other ones should converge to. This important result supposes both an implementation of the above constraints and an appropriate single-particle-like current. The change of variables that allows one to establish the equivalence of the approaches is given. Some points are illustrated with numerical results for the ground state of a system consisting of scalar particles.     

Electromagnetic structure and weak decay of pseudoscalar mesons in a light-front QCD-inspired model

We study the scaling of the ³S₁-¹S₀ meson mass splitting and the pseudoscalar weak-decay constants with the mass of the meson, as seen in the available experimental data. We use an effective light-front QCD-inspired dynamical model regulated at short distances to describe the valence component of the pseudoscalar mesons. The experimentally known values of the mass splitting, decay constants (from global lattice-QCD averages) and the pion charge form factor up to 4 [GeV/c]² are reasonably described by the model.     

Scalar mesons in a chiral quark model with glueball

Ground-state scalar isoscalar mesons and a scalar glueball are described in a U(3)×U(3) chiral quark model of the Nambu-Jona-Lasinio (NJL) type with 't Hooft interaction. The latter interaction produces singlet-octet mixing in the scalar and pseudoscalar sectors. The glueball is introduced into the effective meson Lagrangian as a dilaton on the base of scale invariance. The mixing of the glueball with scalar isoscalar quarkonia and amplitudes of their decays into two pseudoscalar mesons are shown to be proportional to current quark masses, vanishing in the chiral limit. Mass spectra of the scalar mesons and the glueball and their main modes of strong decay are described. Received: 14 July 2000 / Accepted: 31 July 2000