\bar{p}p low energy parameters from annihilation cross section data

The recent experimental data obtained by the OBELIX group on total $\bar{p}p$ annihilation cross section are analysed; the low energy spin averaged parameters of the $\bar{p}p$ scattering amplitude (the imaginary parts of the S-wave scattering length and P-wave scattering volume) are extracted from the data. Their values are found to be equal to $Im a_{sc} = - 0.69 \pm 0.01 (stat) \pm 0.03 (sys) fm, Im A_{sc} = - 0.76 \pm 0.05 (stat) \pm 0.04 (sys) fm^3$. The results are in very good agreement with existing atomic data.Comment: latex.tar.gz file, 8 pages, 1 figur

Deuteron electromagnetic form factors in the Light-Front Dynamics

The deuteron form factors are calculated in the framework of the relativistic nucleon-meson dynamics, by means of the explicitly covariant light-front approach. The inflluence of the nucleon electromagnetic form factors is discussed. At $Q^2\leq 3$ (GeV/c)$^2$ the prediction for the structure function $A(Q^2)$ and for the tensor polarization observable $t_{20}$ are in agreement with the recent data of CEBAF/TJNAF.Comment: 1 latex.tar.gz file (18 pages, 8 figures in 11 .ps files) Submitted for publicatio

Solutions of the Bethe-Salpeter equation in Minkowski space and applications to electromagnetic form factors

We present a new method for solving the two-body Bethe-Salpeter equation in Minkowski space. It is based on the Nakanishi integral representation of the Bethe-Salpeter amplitude and on subsequent projection of the equation on the light-front plane. The method is valid for any kernel given by the irreducible Feynman graphs and for systems of spinless particles or fermions. The Bethe-Salpeter amplitudes in Minkowski space are obtained. The electromagnetic form factors are computed and compared to the Euclidean results.Comment: 20 pages, 14 figures, contribution to proceedings of the workshop: "Relativistic Description of Two- and Three-Body Systems in Nuclear Physics", ECT*, October 19-23, 2009. To be published in Few-Body System

Explicitly covariant light-front dynamics and some its applications

The light-front dynamics is an efficient approach to study of field theory and of relativistic composite systems (nuclei at relativistic relative nucleon momenta, hadrons in the quark models). The explicitly covariant version of this approach is briefly reviewed and illustrated by some applications.Comment: 16 pages, 8 figures. Talk at the 21-st International Workshop on Nuclear Theory, Rila Mountains, Bulgaria, June 10-15, 200

Solution of the Bethe-Salpeter equation in Minkowski space for a two fermion system

The method of solving the Bethe-Salpeter equation in Minkowski space, developed previously for spinless particles, is extended to a system of two fermions. The method is based on the Nakanishi integral representation of the amplitude and on projecting the equation on the light-front plane. The singularities in the projected two-fermion kernel are regularized without modifying the original BS amplitudes. The numerical solutions for the J=0 bound state with the scalar, pseudoscalar and massless vector exchange kernels are found. Binding energies are in close agreement with the Euclidean results. Corresponding amplitudes in Minkowski space are obtained.Comment: 8 pages, 5 figures. Contribution to the proceedings of the Workshop: Light-Cone 2010, "Relativistic Hadronic and Particle Physics", June 14-18, 2010, Valencia, Spain. To be published in the online journal "Proceedings of Science" - Po

Zero energy scattering calculation in Euclidean space

We show that the Bethe-Salpeter equation for the scattering amplitude in the limit of zero incident energy can be transformed into a purely Euclidean form, as it is the case for the bound states. The decoupling between Euclidean and Minkowski amplitudes is only possible for zero energy scattering observables and allows determining the scattering length from the Euclidean Bethe-Salpeter amplitude. Such a possibility strongly simplifies the numerical solution of the Bethe-Salpeter equation and suggests an alternative way to compute the scattering length in Lattice Euclidean calculations without using the Luscher formalism. The derivations contained in this work were performed for scalar particles and one-boson exchange kernel. They can be generalized to the fermion case and more involved interactions.Comment: 11 pages, 3 figures, to be published in Phys. Lett.

Critical stability of few-body systems

When a two-body system is bound by a zero-range interaction, the corresponding three-body system -- considered in a non-relativistic framework -- collapses, that is its binding energy is unbounded from below. In a paper by J.V. Lindesay and H.P. Noyes it was shown that the relativistic effects result in an effective repulsion in such a way that three-body binding energy remains also finite, thus preventing the three-body system from collapse. Later, this property was confirmed in other works based on different versions of relativistic approaches. However, the three-body system exists only for a limited range of two-body binding energy values. For stronger two-body interaction, the relativistic three-body system still collapses. A similar phenomenon was found in a two-body systems themselves: a two-fermion system with one-boson exchange interaction in a state with zero angular momentum J=0 exists if the coupling constant does not exceed some critical value but it also collapses for larger coupling constant. For a J=1 state, it collapses for any coupling constant value. These properties are called "critical stability". This contribution aims to be a brief review of this field pioneered by H.P. Noyes.Comment: 20 pages, 7 figures, 1 tabl

Critical stability of three-body relativistic bound states with zero-range interaction

For zero-range interaction providing a given mass M_2 of the two-body bound state, the mass M_3 of the relativistic three-body bound state is calculated. We have found that the three-body system exists only when M_2 is greater than a critical value M_c (approx. 1.43m for bosons and approx. 1.35m for fermions, m is the constituent mass). For M_2=M_c the mass M_3 turns into zero and for M_2<M_c there is no solution with real value of M_3.Comment: 6 pages, 3 figures. Contribution to the workshop "Critical Stability-III", 1-6 Sept. 2003, Trento, Italy. To be published in "Few-Body Systems