Relativistic properties of the quark-antiquark potential

The relativistic transformation properties of the heavy quark-antiquark interaction potential are considered in the framework of the relativistic quark model. A special attention is paid to the long-range (confining) contribution to the spin-independent part of interaction. The retardation effects are consistently taken into account. Received: 22 April 1998 / Revised version: 9 September 1998 / Published online: 22 October 1998     

Relativistic scattering theory of two bound quark-antiquark systems in the low- and intermediate-energy region

Relativistic three-dimensional equations for meson-meson scattering amplitudes are constructed considering the mesons as bound quark-antiquark systems. The resulting equations have a form identical with the field-theoretical Low equations for the meson-meson scattering amplitude without quark degrees of freedom. Therefore the solution of these equations and their linearized representations satisfy the unitarity condition and the low-energy theorems. In order to build the effective potential of the proposed equations one uses meson-quark-antiquark bound-state wave functions and transition matrices. Also these quark-antiquark bound-state wave functions satisfy the relativistic three-dimensional integral equation, which contains all retardation effects.Supported by Deutsche Forschungsgemeinschaft under contract no. Fa. 67/10-5     

The use of QCD in hadronic cascades between heavy quark-antiquark bound states

We argue that a perturbative calculation of the spectra and rates of hadronic transitions between heavy quark-antiquark bound states makes sense within QCD provided suitable spin-parity projections are performed. Applications are made to various kinds of cascades. We obtain the correct ψ′ → J/ψππ mass spectrum. The cascades involving the emission of at least three gluons appear very strongly suppressed as compared to those allowing two-gluon emission. Application to the ? family is made.     

Relativistic effects in the bound states of electric charge-dyon system

Study of relativistic effects in the interaction of a spin-1/2 electric charge in the radial field of a spin less point like dyon has been undertaken using Dirac’s relativistic equation. Angular momentum and energy eigen values have been obtained. The deviations of the results from those of hydrogen atom like systems have been discussed.     

Constraints on heavy quark-antiquark states

We improve on and extend previous constraints on the radii and kinetic energies of heavy quark-antiquark systems. Meaningful bounds are placed on corrections to the Van-Royen Weisskopf formula for the leptonic decay rates of these systems. Bounds on the position and width of the peak of the ground state wave functions are also derived.     

Excited states of mesons and the quark-antiquark interaction

The Dirac equation is used in an investigation of the properties of mesons according to the quark-antiquark model. The dependence of the meson mass on angular momentum excitation is considered for several models. The properties of the Dirac equation with a potential consisting of an equal mixture of scalar and vector potential are investigated.     

Relativistic Borromean states

In this work,the existence of Borromean states is discussed for bosonic and fermionic cases in both therelativistic and non-relativistic limits from the 3-momentum shell renormalization.With the linear bosonic model,we check the existence of Efimov-like states in the bosonic system.In both limits a geometric series of singularities is found in the 3-boson interaction vertex,while the energy ratio is reduced by around 70%in the relativistic limit because of the anti-particle contribution.Motivated by the quark-diquark model in heavy baryon studies,we have carefully examined the p-wave quark-diquark interaction and found an isolated Borromean pole at finite energy scale.This may indicate a special baryonic state of light quarks in high energy quark matter.In other cases,trivialresults are obtained as expected.In the relativistic limit,for both bosonic and fermionic cases,potential Borromean states are independent of the mass,which means the results would also be valid even in the zero-mass limit.     

Relativistic description of heavy tetraquarks

The masses of the ground-state and excited heavy tetraquarks with hidden charm and bottom are calculated within the relativistic diquark-antidiquark picture. The dynamics of the light quark in a heavy-light diquark is treated completely relativistically. The diquark structure is taken into account by calculating the diquark-gluon form factor. New experimental data on charmonium-like states above the open charm threshold are discussed. The obtained results indicate that X(3872), Y(4260), Y(4360), Z(4433), and Y(4660) can be tetraquark states with hidden charm. The text was submitted by the authors in English.