Comparison of Form Factors Calculated with Different Expressions for the Boost Transformation

Abstract

The effect of different boost expressions is considered for the calculation of the ground-state form factor of a two-body system made of scalar particles interacting via the exchange of a scalar boson. The aim is to provide an uncertainty range on methods employed in implementing these effects as well as an insight on their relevance when an ``exact'' calculation is possible. Using a wave function corresponding to a mass operator that has the appropriate properties to construct the generators of the Poincar\'{e} algebra in the framework of relativistic quantum mechanics, form factors are calculated using the boost transformations pertinent to the instant, front and point forms of this approach. Moderately and strongly bound systems are considered with masses of the exchanged boson taken as zero, 0.15 times the constituent mass $m$, and infinity. In the first and last cases, a comparison with ``exact'' calculations is made (Wick-Cutkosky model and Feynman triangle diagram). Results with a Galilean boost are also given. Momentum transfers up to $Q^2=100 m^2$ are considered. Emphasis is put on the contribution of the single-particle current, as usually done. It is found that the present point-form calculations of form factors strongly deviate from all the other ones, requiring large contributions from two-body currents. Different implementations of the point-form approach, where the role of these two-body currents would be less important, are sketched.Comment: Version as accepted for publication, added 6 pages of explanatorial materia