Covariant Bethe-Salpeter Approach Research Articles

Form factors of V\u2032 \u2192 V\u2033 transition within the light-front quark models

In this paper, we calculate the matrix element and form factors of vector-to- vector (VI→ VII) transition within the standard light-front (SLF) and covariant light- front (CLF) quark models (QMs), and investigate the self-consistency and Lorentz covari- ance of the CLF QM within two types of correspondences between the manifest covariant Bethe-Salpeter approach and the LF approach. The zero-mode and valence contributions to the form factors of VI→ VII transition in the CLF QM and their relation to the SLF results are analyzed, and the main conclusions obtained via the decay constants of vector and axial-vector mesons and the form factors of P → V transition in the previous works are confirmed again. Furthermore, we present our numerical predictions for the form factors of c → (q, s) (q = u, d) induced D*→ (K*, ρ), D∗→ (ϕ, K*), J/Ψ → left({D}_s^{ast },{D}^{ast}right) , {B}_c^{ast}to left({B}_s^{ast },{B}^{ast}right) transitions and b → (c, s, q) induced B∗ → (D∗, K∗, ρ), {B}_s^{ast}to left({D}_s^{ast },phi, {K}^{ast}right) , {B}_c^{ast}to left(J/varPsi, {D}_s^{ast },{D}^{ast}right),varUpsilon (1S)to left({B}_c^{ast },{B}_s^{ast },{B}^{ast}right) the relevant phenomenological studies of meson decays.

Delta and Omega electromagnetic form factors in a three-body covariant Bethe-Salpeter approach

The electromagnetic form factors of the $\ensuremath{\Delta}$ and $\ensuremath{\Omega}$ baryons are calculated in the framework of Poincar\'e-covariant bound-state equations. The quark-quark interaction is truncated to a single dressed-gluon exchange where for the dressings we use two different models and compare the results. The calculation predicts an oblate shape for the electric charge distribution and a prolate shape for the magnetic dipole distribution. We also identify the necessity of including pion-cloud corrections at low photon-momentum transfer.

Relativistic complex separable potential of the neutron–proton system

Within a covariant Bethe–Salpeter approach, a relativistic complex separable kernel for the description of the neutron–proton interaction, is proposed. The uncoupled partial-wave states with total angular momentum J=0,1 are considered. The multirank separable potentials elaborated earlier are real-valued and, therefore, make it possible to describe only the elastic part (phase shifts, low-energy parameters, etc.) of the neutron–proton scattering. The description of the inelasticity comes out of an imaginary part introduced into these potentials. To obtain this part the experimental data for the inelasticity parameter up to the laboratory energy 3 GeV are used. A signal of wide dibaryon resonances in the P0+3 partial-wave state is discussed.

Relativistic complex separable potential for describing the neutron-proton system in [formula omitted] partial-wave state

Within a covariant Bethe-Salpeter approach the relativistic complex separable kernel of the neutron-proton interaction for the coupled $^3S_1^+$-$^3D_1^+$ partial-wave state is constructed. The rank-six separable potential elaborated earlier is real-valued, and therefore makes it possible to describe only the elastic part (phase shifts, low-energy parameters, deuteron properties, etc.) of the elastic neutron-proton scattering. The description of the inelasticity parameter comes out of the imaginary part introduced intthe potential. The complex potential parameters are obtained using the available elastic neutron-proton scattering experimental data up to 1.1 GeV.

Covariant Relativistic Separable Kernel Approach for Electrodisintegration of the Deuteron at High Momentum Transfer

The paper considers the electrodisintegration of the deuteron for kinematic conditions of the JLab experiment E-94-019. The calculations have been performed within the covariant Bethe-Salpeter approach with a separable kernel of nucleon-nucleon interactions. The results have been obtained using the relativistic plane wave impulse approximation and compared with experimental data and other models. The influence of nucleon electromagnetic form factors has been investigated.

Pion-photon transition distribution amplitudes in the Nambu–Jona-Lasinio model

We define the pion-photon transition distribution amplitudes (TDA) in a field theoretic formalism from a covariant Bethe-Salpeter approach for the determination of the bound state. We apply our formalism to the Nambu-Jona-Lasinio model, as a realistic theory of the pion. The obtained vector and axial TDAs satisfy all features required by general considerations. In particular, sum rules and the polynomiality condition are explicitly verified. We have numerically proved that the odd coefficients in the polynomiality expansion of the vector TDA vanish in the chiral limit. The role of PCAC and the presence of a pion pole are explicitly shown.

Generalized parton distributions of the pion in a Bethe-Salpeter approach

Generalized parton distribution functions (GPDs) are calculated in a field theoretic formalism using a covariant Bethe-Salpeter approach. The procedure is described in an exact calculation in scalar Electrodynamics, and then extended to the Nambu–Jona-Lasinio model. In both cases we demonstrate that all important features required by general physical considerations, like symmetry properties, sum rules and the polynomiality condition, are explicitly verified.

Generalized parton distributions of the pion in a Bethe-Salpeter approach

We calculate generalized parton distribution functions in a field theoretic formalism using a covariant Bethe-Salpeter approach for the determination of the bound-state wave function. We describe the procedure in an exact calculation in scalar Electrodynamics proving that the relevant corrections outside our scheme vanish. We extend the formalism to the Nambu--Jona-Lasinio model, a realistic theory of the pion. We go in both cases beyond all previous calculations and discover that all important features required by general physical considerations, like symmetry properties, sum rules and the polynomiality condition, are explicitly verified. We perform a numerical study of their behavior in the weak and strong coupling limits.

Separable kernel of nucleon-nucleon interaction in the Bethe-Salpeter approach for J = 0, 1

The solution for the nucleon-nucleon (NN)T matrix in the framework of the covariant Bethe-Salpeter approach for a two spin-one-half particle system with a separable kernel of interaction is analyzed. The explicit analytical connection between parameters of the separable kernel and low energy scattering parameters, deuteron binding energy and phase shifts is established. Covariant separable kernels for positive-energy partial channels with total angular momentum J = 0 ( 1S 0 +, 3P 0 +) and J = 1 ( 3S 1 + − 3 D 1 +, 1P 1 +, 3P 1 +) are constructed by using obtained relations.

Exploring skewed parton distributions with two-body models on the light front. II. Covariant Bethe-Salpeter approach

We explore skewed parton distributions for two-body, light-front wave functions. In order to access all kinematical regimes, we adopt a covariant Bethe-Salpeter approach, which makes use of the underlying equation of motion (here the Weinberg equation) and its Green's function. Such an approach allows for the consistent treatment of the non-wave function vertex (but rules out the case of phenomenological wave functions derived from ad hoc potentials). Our investigation centers around checking internal consistency by demonstrating time-reversal invariance and continuity between valence and non-valence regimes. We derive our expressions by assuming the effective qq potential is independent of the mass squared, and verify the sum rule in a non-relativistic approximation in which the potential is energy independent. We consider bare-coupling as well as interacting skewed parton distributions and develop approximations for the Green's function which preserve the general properties of these distributions. Lastly we apply our approach to time-like form factors and find similar expressions for the related generalized distribution amplitudes.