Form factors in relativistic quantum mechanics: Is there a favored approach? Why?

Abstract : Form factors of a simple system have been calculated in various forms of relativistic quantum mechanics, using a single-particle current. Their comparison has shown large discrepancies. The comparison is extented here to instant- and front-form calculations in unusual kinematics as well as to a point-form approach inspired from the Dirac's one (based on a hyperboloid surface). It is found that these new results depend on the momentum transfer, Q, through its ratio to the total mass, Q/M, (closely related to the Breit-frame velocity of the system). They evidence features similar for a part to those shown by an earlier ``point-form'' implementation (based on hyperplanes perpendicular to the velocity of the initial and final states). It thus appears that the standard instant- and front-form calculations, which generally do well compared either to experiment or to predictions of a theoretical model, rather represent exceptional cases. An argument explaining the success of these last approaches is presented and discussed. It is based on Poincare space-time translation invariance.