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.     

Electric transitions of the charmed-strange mesons in a relativistic quark model

The European Physical Journal C - The original version of this article was revised.     

A relativistic quark model for mesons with an instanton-induced interaction

We present new results of a relativistic quark model based on the Bethe-Salpeter equation in its instantaneous approximation. Assuming a linearly rising confinement potential with an appropriate spinorial structure in Dirac space and adopting a residual interaction based on instanton effects, we can compute masses of the light mesons up to highest observed angular momenta with a natural solution of the U _A(1) problem. The calculated ground states masses and the radial excitations describe the experimental results well. In this paper, we will also discuss our results concerning numerous meson decay properties. For processes like π⁺/K ⁺↦e ⁺υ_eγ and 0^-↦γγ at various photon virtualities, we find a good agreement with experimental data. We will also comment on the form factors of the K _?3 decay and on the decay constants of the π, K and η mesons. For the sake of completeness, we will furthermore present the electromagnetic form factors of the charged π and K mesons as well as a comparison of the radiative meson decay widths with the most recent experimental data. Received: 28 August 2000 / Accepted: 12 September 2000     

Chiral symmetry breaking and meson decays in a relativistic quark model

Applying two different Lorentz-covariant quark models, one of them being essentially nonrelativistic, chiral symmetry breaking parameters of strong interaction will be calculated. Also attention will be paid to meson decays. The model retaining relativistic spinor structure for quark-antiquark wave functions turns out to be more appropriate than the nonrelativistic one.     

Masses and electroweak properties of light mesons in the relativistic quark model

The masses, pseudoscalar and vector weak decay constants and electromagnetic form factors of light S-wave mesons are studied in the framework of the relativistic quark model based on the quasipotential approach. We use the same model assumptions and parameters as in our previous investigations of heavy meson and baryon properties. The masses and wave functions of the ground state and radially excited π, ρ, K, K^* and φ mesons, obtained by solving numerically the relativistic Schrödinger-like equation with the complete relativistic qq? potential including both spin-independent and spin-dependent terms, are presented. Novel relativistic expressions for the weak decay constants of the pseudoscalar and vector mesons are derived. It is shown that the intermediate negative-energy quark states give significant contributions which essentially decrease the decay constants bringing them in agreement with experimental data. The electromagnetic form factors of the pion, charged and neutral kaon are calculated in a broad range of the space-like momentum transfer. The corresponding charge radii are determined. All results agree well with the available experimental data.     

Masses of light tetraquarks and scalar mesons in the relativistic quark model

Masses of the ground-state light tetraquarks are dynamically calculated in the framework of the relativistic diquark–antidiquark picture. The internal structure of the diquark is taken into account by calculating the form factor of the diquark–gluon interaction in terms of the overlap integral of the diquark wave functions. It is found that scalar mesons with masses below 1 GeV, f ₀(600) (σ), K ₀^*(800) (κ), f ₀(980) and a ₀(980), agree well with the light-tetraquark interpretation.     

Heavy-light mesons in a relativistic model

We study the heavy-light mesons in a relativistic model, which is derived from the Bethe-Salpeter equation by applying the Foldy-Wouthuysen transformation to the heavy quark. The kernel we choose is based on scalar confinement and vector Coulomb potentials. The transverse interaction of the gluon exchange is also taken into account in this model. The spectra and wave functions of D, D_s, B, B_s meson states are obtained. The spectra are calculated up to the order of 1/m Q, and wave functions are treated to leading order.     

A relativistic quark model for mesons based on numerical solutions of the Bethe-Salpeter equation

A study is made to determine if the results of the nonrelativistic quark model can be reproduced by a fully relativistic model of deeply bound $\text{spin}\text{-}\text{1}\text{2}$ quarks. It is found that the relativistic model does not reproduce the nonrelativistic results, even when the quarks have nonrelativistic momenta. However, the model is rather successful in accounting for the known properties of mesons.Numerical solutions to the Bethe-Salpeter equation are obtained for pseudoscalar and vector bound states of equal mass quark-antiquark pairs, with either a scalar, pseudoscalar, or neutral vector exchange interaction. The interaction function corresponds to single particle exchange, with the addition of either one or two regulating terms. It is found that the second regulator allows the internal quark momentum to be nonrelativistic, but that the spinor structure of the wave function remains highly relativistic.Only the scalar interaction can account for the observed spectrum of states. The pseudoscalar interaction yields a vector state of lower mass than the pseudoscalar state, and the vector interaction leads to a vector state which lies approximately one quark mass above the pseudoscalar state. The λ quark is taken as slightly heavier than the p and n, and the perturbation treatment of the mass difference leads to a quadratic mass formula.The decay amplitudes for π, K → μν are calculated, and it is found, independent of parameters, that $\text{?}{}_{\mathrm{\pi }}\text{≈ ?}{}_{\mathrm{K}}$ for either a scalar or vector interaction, in agreement with experiment and in contrast with the nonrelativistic model. The amplitudes for ?^o, ω, φ → e⁺e^?, μ⁺μ^? are also calculated, but in this case the ratios (again parameter independent) are in minor discrepancy with experiment.The question of the additivity of quark amplitudes is examined by calculating (with significant restrictions) the magnetic moments of the vector mesons and the amplitudes for magnetic transitions such as ω → π^oγ. The magnetic moments of the vector mesons have the same (trivial) ratios to each other as in the nonrelativistic model, but they are strongly enhanced over the sum of the quark magnetic moments. The amplitude for magnetic transitions, however, is related to the quark magnetic moments in approximately the same ratio as in the nonrelativistic model.The model is also used to obtain parameter dependent predictions for the masses and decay amplitudes. These predictions are not experimentally correct, but are generally well within an order of magnitude for a wide range of the parameters.The most significant defect discovered of the model is the presence of ghost states (the daughters of the vector mesons, with J^PC = 0^+?) with masses of about 2 BeV.     

Mass spectra of heavy baryons in the relativistic quark model

The mass spectra of the ground state and excited heavy baryons consisting of two light (u, d, s) and one heavy (c, b) quarks are calculated. The heavy-quark-light-diquark picture is used within the relativistic quark model. An overall good agreement of the obtained predictions with available experimental data is found. The text was submitted by the authors in English.     

Decay constants of heavy quark mesons in a non-relativistic quark model

The weak decay constants of charm, bottom and top quark pseudoscalar mesons are calculated in a non-relativistic QCD potential model. The decay constants are obtained as ƒ_D > ƒ_B > ƒ_T. An opposite result, ƒ_D < ƒ_B < ƒ_T, is obtained by Mathur et al. using the QCD sum rules. A possible cause of this discrepancy and a comparison of our results with other calculations is presented also.     

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.     

Radiative transitions in mesons in a non-relativistic quark model

In the framework of the non-relativistic quark model, an exhaustive study of radiative transitions in mesons is performed. Emphasis is placed on several points. Some traditional approximations (long-wavelength limit, non-relativistic phase space, dipole approximation for E1 transitions, Gaussian wave functions) are analyzed and their effects commented. A complete treatment using three different types of realistic quark-antiquark potential is made. The overall agreement with experimental data is quite good, but some improvements are suggested. Received: 16 October 2001 / Accepted: 18 December 2001     

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.