Validity of the one-body current for the calculation of form factors in the point form of relativistic quantum mechanics

Form factors are calculated in the point form of relativistic quantum mechanics for the lowest energy states of a system made of two scalar particles interacting via the exchange of a massless boson. They are compared to the exact results obtained by using solutions of the Bethe-Salpeter equation which are well known in this case (Wick-Cutkosky model). Deficiencies of the point-form approach together with the single-particle current are emphasised. They point to the contribution of two-body currents which are required in any case to fulfil current conservation.Comment: 11 pages, 1 eps figur

Crossed-boson exchange contribution and Bethe-Salpeter equation

The contribution to the binding energy of a two-body system due to the crossed two-boson exchange contribution is calculated, using the Bethe-Salpeter equation. This is done for distinguishable, scalar particles interacting via the exchange of scalar massive bosons. The sensitivity of the results to the off-shell behavior of the operator accounting for this contribution is discussed. Large corrections to the Bethe-Salpeter results in the ladder approximation are found. For neutral scalar bosons, the mass obtained for the two-body system is close to what has been calculated with various forms of the instantaneous approximation, including the standard non-relativistic approach. The specific character of this result is demonstrated by a calculation involving charged bosons, which evidences a quite different pattern. Our results explain for some part those obtained by Nieuwenhuis and Tjon on a different basis. Some discrepancy appears with increasing coupling constants, suggesting the existence of sizeable contributions involving more than two-boson exchanges.Comment: 13 pages, 5 .eps figures, submitted to 'Few Body Systems

The form factor of the pion in "point-form" of relativistic dynamics revisited

The electromagnetic form factor of the pion is calculated in the "point-form" of relativistic quantum mechanics using simple, phenomenological wave functions. It is found that the squared charge radius of the pion is predicted one order of magnitude larger than the experimental value and the asymptotic behavior expected from QCD cannot be reproduced. The origin of these discrepancies is analyzed. The present results confirm previous ones obtained from a theoretical model and call for major improvements in the implementation of the "point-form" approach.Comment: 8 pages, 3 eps figure

From the Bethe-Salpeter equation to non-relativistic approaches with effective two-body interactions

It is known that binding energies calculated from the Bethe-Salpeter equation in ladder approximation can be reasonably well accounted for by an energy-dependent interaction, at least for the lowest states. It is also known that none of these approaches gives results close to what is obtained by using the same interaction in the so-called instantaneous approximation, which is often employed in non-relativistic calculations. However, a recently proposed effective interaction was shown to account for the main features of both the Bethe-Salpeter equation and the energy-dependent approach. In the present work, a detailed comparison of these different methods for calculating binding energies of a two-particle system is made. Some improvement, previously incorporated for the zero-mass boson case in the derivation of the effective interaction, is also employed for massive bosons. The constituent particles are taken to be distinguishable and spinless. Different masses of the exchanged boson (including a zero mass) as well as states with different angular momenta are considered and the contribution of the crossed two-boson exchange diagram is discussed. With this respect, the role played by the charge of the exchanged boson is emphasized. It is shown that the main difference between the Bethe-Salpeter results and the instantaneous approximation ones are not due to relativity as often conjectured.Comment: 38 pages, 12 eps figures, uses elsart.cls (included

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.Comment: 19 pages, 21 eps figures, accepted for publication in EPJ

Borromean Binding of Three or Four Bosons

We estimate the ratio $R=g_{3}/g_{2}$ of the critical coupling constants $g_{2}$ and $g_{3}$ which are required to achieve binding of 2 or 3 bosons, respectively, with a short-range interaction, and examine how this ratio depends on the shape of the potential. Simple monotonous potentials give $R\simeq 0.8$. A wide repulsive core pushes this ratio close to R=1. On the other hand, for an attractive well protected by an external repulsive barrier, the ratio approaches the rigorous lower bound $R=2/3$. We also present results for N=4 bosons, sketch the extension to $N>4$, and discuss various consequences.Comment: 12 pages, RevTeX, 5 Figures in tex include

Relativistic effects and quasipotential equations

We compare the scattering amplitude resulting from the several quasipotential equations for scalar particles. We consider the Blankenbecler-Sugar, Spectator, Thompson, Erkelenz-Holinde and Equal-Time equations, which were solved numerically without decomposition into partial waves. We analyze both negative-energy state components of the propagators and retardation effects. We found that the scattering solutions of the Spectator and the Equal-Time equations are very close to the nonrelativistic solution even at high energies. The overall relativistic effect increases with the energy. The width of the band for the relative uncertainty in the real part of the scattering $T$ matrix, due to different dynamical equations, is largest for backward-scattering angles where it can be as large as 40%.Comment: Accepted for publication in Phys. Rev.

Structures of Rotating Traditional Neutron Stars and Hyperon Stars in the Relativistic σ−ω\sigma-\omega Model

The influence of the rotation on the total masses and radii of the neutron stars are calculated by the Hartle's slow rotation formalism, while the equation of state is considered in a relativistic $\sigma-\omega$ model. Comparing with the observation, the calculating result shows that the double neutron star binaries are more like hyperon stars and the neutron stars of X-ray binaries are more like traditional neutron stars. As the changes of the mass and radius to a real neutron star caused by the rotation are very small comparing with the total mass and radius, one can see that Hartle's approximate method is rational to deal with the rotating neutron stars. If three property values: mass, radius and period are observed to the same neutron star, then the EOS of this neutron star could be decided entirely.Comment: 10 pages, 10 figure