Heavy quark 1/m Q expansion of meson weak decay form factors in the relativistic quark model

The method of systematical expansion in the inverse powers of the heavy quark masses of the weak current matrix elements between heavy meson states is developed in the framework of the relativistic quark model based on the quasipotential approach in quantum field theory. The comparison of the first and second order terms of this expansion with the structure predicted by the heavy quark effective theory imposes strong constraints on the form of the long-range confining potential of quark-antiquark interaction. It is found that the confinig $q\bar q$ potential is effectively vector, while scalar potential is anticonfining and helps to reproduce the correct nonrelativistic limit. At large distances quarks have nonperturbative anomalous chromomagnetic moments. The obtained values of the potential parameters are in accord with the ones found in our previous consideration of meson masses and decay rates. We calculate the Isgur-Wise function. The first and the second order form factors within 1/m _Q expansion.     

Heavy baryons in the relativistic quark model

In the framework of the relativistic quasipotential quark model the mass spectrum of baryons with two heavy quarks is calculated. The quasipotentials for interactions of two quarks and of a quark with a scalar and axial vector diquark are evaluated. The bound state masses of baryons with are computed.     

Baryon properties in the relativistic quark model

Properties of heavy and strange baryons are investigated in the framework of the relativistic quark-diquark picture. It is based on the relativistic quark model of hadrons, which was previously successfully applied for the calculation of meson properties. It is assumed that two quarks in a baryon form a diquark and baryon is considered as the bound quark-diquark system. The relativistic effects and diquark internal structure are consistently taken into account. Calculations are performed up to rather high orbital and radial excitations of heavy and strange baryons. On this basis the Regge trajectories are constructed. The rates of semileptonic decays of heavy baryons are calculated. The obtained results agree well with available experimental data.     

Nuclear transparency in a relativistic quark model

We examine the nuclear transparency for the quasi-elastic (e,e′p) process at large momentum transfers in a relativistic quantum-mechanical model for the internal structure of the proton, using a relativistic harmonic oscillator model. A proton in a nuclear target is struck by the incident electron and then propagates through the residual nucleus suffering from soft interactions with other nucleons. We call the proton “dynamical” when we take into account of internal excitations, and “inert” when we freeze it to the ground state. When the dynamical proton is struck with a hard (large-momentum transfer) interaction, it shrinks, i.e. small-sized configuration dominates the process. It the travels through nuclear medium as a time-dependent mixture of nitrinsic excited states and thus changing its size. Its absorption due to the soft interactions with nuclear medium depends on its transverse-size. Since the nuclear transparency is a measure of the absorption strength, we calculate it in our model for the dynamical case, and compare the results with those for the inert case. The effect of the internal dynamics is observed, which is in accord with the idea of the “color transparency”. We also compare our results with the experimental data in regard of q²-dependence as well as A-dependence, and find that the A-dependence may reveal the color-transparency effect more clearly. Similar effects of the internal dynamics in the other semi-exclusive hard processes are briefly discussed.     

Charmed baryons in a relativistic quark model

We calculate mass spectra of charmed baryons within a relativistically covariant quark model based on the Bethe-Salpeter equation in instantaneous approximation. Interactions are given by a linearly rising three-body confinement potential and a flavor-dependent two-body force derived from QCD instanton effects. This model has already been successfully applied to the calculation of light flavor baryon spectra and is now extended to heavy baryons. Within the same framework we compare the results to those obtained with the more conventional one-gluon exchange potential.     

Heavy baryons in the relativistic quark model

We present a summary of results for exclusive decays of single and double heavy-flavored baryons in the relativistic three-quark model.     

A relativistic quark model for baryons

The Bethe-Salpeter equation for the relativistic three quark bound state is solved for an instantaneous interaction in the ladder approximation. The particular solution obtained is valid for simple potentials in both the weak and strong binding situations. The general method for calculating matrix elements for the interaction of the bound state with an external electromagnetic field is presented. Particular attention is paid to the emergence of the nonrelativistic quark model interaction as the lowest order approximation in a perturbative expansion in the inverse quark mass. Relativistic corrections to this approximation are investigated, and their importance is seen to depend on the quark mass. For light quarks these corrections can be large, and to reproduce the proton magnetic moment, for instance, a substantial anomalous moment is necessary. The model has several encouraging features. The form factors with a harmonic potential have an asymptotic k^?2 behavior, and the relativistic corrections to the SU(6) results for the form factors are of the correct order of magnitude.     

Nucleon form factors in a relativistic quark model

Electromagnetic form factors of protons and neutrons are investigated based on a relativistic quark model with the inclusion of a pion cloud. Pseudo-scalar π-quark interaction is employed to study the coupling between the nucleon and the π. The results show the important role of the pion cloud for the neutron charge form factor. Moreover, our numerical analysis indicates a difference between the relativistic and the nonrelativistic treatments. Received: 10 March 1999 / Revised version: 14 June 1999     

The light-baryon spectrum in a relativistic quark model with instanton-induced quark forces

This is the second of a series of three papers treating light-baryon resonances up to 3 GeV within a relativistically covariant quark model based on the three-fermion Bethe-Salpeter equation with instantaneous two- and three-body forces. In this paper we apply the covariant Salpeter framework (which we developed in the first paper, U. L?ring, K. Kretzschmar, B.Ch. Metsch, H.R. Petry, Eur. Phys. J. A 10, 309 (2001)) to specific quark model calculations. Quark confinement is realized by a linearly rising three-body string potential with appropriate spinorial structures in Dirac space. To describe the hyperfine structure of the baryon spectrum we adopt 't Hooft's residual interaction based on QCD-instanton effects and demonstrate that the alternative one-gluon exchange is disfavored on phenomenological grounds. Our fully relativistic framework allows to investigate the effects of the full Dirac structures of residual and confinement forces on the structure of the mass spectrum. In the present paper we present a detailed analysis of the complete non-strange-baryon spectrum and show that several prominent features of the nucleon spectrum such as, e.g., the Roper resonance and approximate “parity doublets” can be uniformly explained due to a specific interplay of relativistic effects, the confinement potential and 't Hooft's force. The results for the spectrum of strange baryons will be discussed in a subsequent paper, see U. L?ring, B.Ch. Metsch, H.R. Petry, this issue, p. 447. Received: 27 March 2001 / Accepted: 17 April 2001     

A relativistic Hartree-Fock model for quark systems

The “relativistic H—F” scheme is applied to baryons and finite multiquark sustems. A two-body confinement potential (r, r² or r³) and the one-gluon-exchange interaction are incorporated. The electric OGE term is treated consistently in all considered systems. With the electric OGE term included, the solutions indicate the little bag. (Os)-closed multiquark states, strange or non-strange, cannot be lower in energy than an aggregate of Δ or Λ.     

Electromagnetic properties of baryons in a relativistic quark model

Results on electromagnetic form factors of the nucleon and photon transition form factors of non-strange baryon resonances calculated in a relativistically covariant quark model based on the Bethe-Salpeter equation are presented. The relevance of the instanton-induced quark interaction on these properties is discussed.Received: 30 September 2002, Published online: 22 October 2003PACS: 11.10.St Bound and unstable states; Bethe-Salpeter equations - 12.39.Ki Relativistic quark model - 12.40.Yx Hadron mass models and calculations - 13.40.Gp Electromagnetic form factors     

Low-energy properties of hadrons in the relativistic quark model

The properties of light and heavy mesons, baryons and tetraquarks are discussed within a QCD-motivated relativistic quark model. The results for the mass spectra, electroweak properties and Regge trajectories of hadrons are presented.     

Semileptonic decays of baryons in a relativistic quark model

We calculate semileptonic decays of light and heavy baryons in a relativistically covariant constituent quark model. The model is based on the Bethe-Salpeter equation in instantaneous approximation. It generates satisfactory mass spectra for mesons and baryons up to the highest observable energies. Without introducing additional free parameters we compute on this basis helicity amplitudes of electronic and muonic semileptonic decays of baryons. We thus obtain form factor ratios and decay rates in good agreement with experiment.     

Two-photon decays of mesons in a relativistic quark model

We present a relativistic calculation of two-photon decays for heavy and light mesons in the framework of the Salpeter equation for quark-antiquark states. The meson-photon-photon vertex is computed by reconstructing the Bethe-Salpeter vertex function and evaluating the four-dimensional Feynman diagram with off-shell quark amplitudes.The two-photon width for light and heavy quarkonia up to spin equal six are calculated with various parameter sets taken from the literature thus giving a complete overview on mesonic two-photon physics. We find that relativistic effects including the negative-energy components of the wave function are important for any two-photon width - even for heavy quarkonia - yielding a remarkable agreement with available data as well as predictions for future experiments.     

Nucleon spin structure in a relativistic constituent quark model

The spin structure of the nucleon is analyzed using a relativistic constituent quark model in light-front formulation. We investigate, in particular, relativistic effects on the axial vector coupling constants. Electromagnetic and axial form factors are constructed in terms of quark form factors that reflect the possible non-trivial structure of the constituent quarks. We study the influence of flavour mixing effects on axial constants and discuss the extent to which such effects can renormalize the singlet axial constant g _A ⁰ from its SU(6) quark model value.