Form factors in the "point form" of relativistic quantum mechanics: single and two-particle currents

Electromagnetic and Lorentz-scalar form factors are calculated for a bound system of two spin-less particles exchanging a zero-mass scalar particle. Different approaches are considered including solutions of a Bethe-Salpeter equation, a point form'' approach to relativistic quantum mechanics and a non-relativistic one. The comparison of the Bethe-Salpeter results, which play the role of an experiment’’ here, with the ones obtained in point form'' in single-particle approximation, evidences sizable discrepancies, pointing to large contributions from two-body currents in the latter approach. These ones are constructed using two constraints: ensuring current conservation and reproducing the Born amplitude. The two-body currents so obtained are qualitatively very different from standard ones. Quantitatively, they turn out not to be sufficient to remedy all the shortcomings of the point form’’ form factors evidenced in impulse approximation.